Vllth Vanderbilt Conference on Elementary Particle Physics

Vllth Vanderbilt Conference onElementary Particle Physics

QUARKS, STRINGS, DARK MATTER,AND

ALL THE REST

Nashville. Tennessee15-1"7 Mav 1986

vdited b\ R. S. Panvini and T. J. Weiler

CONF-8605182 —

DE87 012199

AAASTER

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QUARKS, STRINGS, DARK MATTER, AND ALL THE REST

PREFACE

The Vllth biennial Vanderbili international conference on elementary particlephysics was held at Vanderbilt University in Nashville. Tennessee, op May 15 - 17,1986. The title of the conference. "Quarks. Strings. Dark Matter, and all the rest."reflects the growing eclecticism of the field of elementary particle physics, andaccordingly, of the speakers' topics. On the experimental side, accelerators nowcompete with passive underground detectors and astronomical instruments for thediscovery-' of new part'cles. On the theoretical side, energy scales from a fractionof the eV all the way up to the Planck mass (1028 eV) are contained in the sameunification theories. The fields of high energy physics, astrophysics and cosmicray physics have merged. DeRujula symbolized this helter-skelter union in a drawinghe presented in his summary talk; the artwork is reproduced on the jacket of theproceedings.

It is not all clear to us where our field is headed (an interesting and challengingsituation!) and so we chose topics to "'cover almost all bases." as indicated in theconference title. The speakers were evenly split between experimenters and theorists,and between realists and futurists. Besides the physics presentations, the conferencefeatured a banquet catered by Nashville's bes. caterer followed by the exceptionalcountry honky-tonk piano and vocals of Nashville's own Becky Hobbs. The rapidpace of talks, infused with interludes of food and entertainment, prompted thecomic relief of Tom Ferbel who remarked "what is this, a conference or a Jewishwedding?!" With all said and done, we think this was a highly stimulating conference.

The talks are ordered in an ascending order of energy scale. The arrangementis largely arbitrary in that some low energy processes are sensitive to very highenergy mass scales.

Thanks go to our advisory committee: Larry Abbott. Ed Berger, Estia Eichten,Tom Ferbel. Ian Hinchliffe. and Paul Langacker suggested to us many of the speakersand topics. As with the past Vanderbilt conferences, the smooth functioning of theday-to-day organizing was almost entirely due to the skills and efforts of DoriaPanvini. We are deeply in her gratitude, yet again. Finally, we acknowledge withthanks, the funcing support from the Department of Energy, the National ScienceFoundation, and the Dean of the College of Arts and Science.

Robert S. Panvini and Thomas J. Weiler

Conference Chairmen

November 1986

CONTENTS

1. PREFACE

II. LIST OF PAPERS

Phenomenology of e* e~ Events at GS1:

Axions and other Goodies

CP Violation: Status and Future

Finite-Element Approximation in Quantum

Field Theory

New Charm Results Using High Precision

Vertex Detectors

Review of Charm Quark Physics

Production of Hadrons and Leptons at High Pt

and Pairs at High Mass

b -Physics

Heavy Quark Production and Missing EnergyStudies at the CERN pp Collider

Collider Physics

Physics at the Z°

To Explore the ] TeV Scale

SSC Developments

Experimental Windows to Post-Collider Energies

Experimental Bounds on (30-Decay, Cold Dark

Matter and Solar Axions with an Ultralow

Background Ge Detector

Strings in Spring '86

Recent Progress in Particle Physics

HI. CONFERENCE PROGRAM

IV. PARTICIPANTS

L. Krauss

J. Donoghue

C. Bender

R. Morrison

J. Brown

D. Kaplan

R. Wilson

A. Kernan

V. Barger

F. Gilman

C. Quigg

D. Stork

A. Melissinos

F. Avignone

P. Ramond

A.DeRujula

1

13

25

43

63

83

109

131

149

165

195

215

231

253

273

299

329

331

Phenomenology or e*e~ events at 651: axions and other goodies

Lawrence M. Krauss1

Departments of Physics and AstronomyGibbs LaboratoryYale University

New Haven CT 065 n

Abstract/ review the experimental results of the EPOS collaboration at 651

indicating the presence of correlated e*e~ pairs with kinetic energy atabout J70 KeVper particle, arising from collisions of different heavy ionsystems at about 5.9 tie Vpernucleon on stationary targets, f then discussconstraints on nuclear production mechanisms, new results on ax/ontheory and experiment, and finally, experimental constraints on any newelementary scalar particle at f. 8 Me V which couples to electrons.

1. The EPOS experiment: The original EPOS spectrometer at 6SI wasdesigned to measure the positron spectrum resulting from the collisionsof heavy ion beams on stationary thin film targets containing heavy atoms.The hope was that in such collisions, supercritical nuclear configurationswould be formed with large enough nuclear charge so that the K shellbinding energy would be greater than twice the rest mass of an electron.In this case pairs could be spontaneously created out of the vacuum! 11,with the electron binding to the system and the positron being emitted.One of the expected signals for such a phenomenon Is the large Zdependence of the rate for this process.[2l Thus, a system was designedwhich, for different combinations of beam and target, could observe thepositron energy spectra emerging rrom the collision. Beam energies werechosen in the range of 6 MeV per nucleon, which would bring the collidingnuclei together just to their coulomb barriers. The original experimentalconfiguration is shown in fig. \ [3]:

1 Also Visiting scientist, Smithsonian Astrophysica) Observatory, andBoston University. Research supported in part by DOE contract*DE-AC02-76ER0 3075 and by a Presidential Young Investigator Award.

—H=AL 25 C .

£20

lf

?DSOD BOO

•Q

(a) Nol-dttecror » 20 30 40 SO CO ID I

Fig 1: Original EPOS positron transport system

As can be seen here, the incoming beam is targeted on 3 thin foil, andthe outgoing ions are then detected at scattering angles ranging fromabout 20°-70° off the beam axis. This allows the kinematics of thecollision to be determined in coincidence with the positron measurementsand in particular, elastic scattering events fall on well-defined curves, asshown in figure 1(c) (for Uranium on lead ). Perpendicular to the beam(z) direction, a magnetic field is set up which causes positrons initiallytravelling with components along either the positive or negative x axis tospiral along the -x direction, passing through a spiral baffle. This baffleis chiral, in the sense that electrons, which wil l spiral with the oppositechirality in this magnetic field, wil l not traverse the baffle. (Also verylow energy particles are screened out) Finally, a Lithium drifted Silicondetector is located along the x axis, to detect the kinetic energy of thepositrons. Because of its location, it is only intercepted by positronswhich originate on this axis, which crosses the beam crossing point.

The major surprise of this experiment was the observation of a narrowpeak in the positron spectra at around 350 KeV, which maintained itsshape and location throughout different runs with different nuclearsystems.[4j This phenomena was not suggestive of spontaneous "sparking"

of the vacuum, because of its Z independence, but could have been due tosome long-lived neutral particle or resonance of energy about 1.7 MeVbeing produced and subsequently decaying into electron-positron pairs.

To test this conjecture, and rule out others, the experiment wasredesigned to measure both the electron and positron spectra incoincidence. The new configuration is shown below in fig. 2 ; ,

HI detectors

(03

0 200 tOO 600 100 1000 1200

E,. DceVl

Figure 2: EPOS configuration for coincident e*e~ measurements

In this new configuration the mirror magnetic field was replaced firstby a a sheet baffle to reduce low energy electrons followed by a detectorfor electrons, located off axis to further reduce the background of narrowspiralling low energy particles. As also shown, the detection efficiencyfor electrons and positrons was comparable, and the positron energyresolution was 15 KeV, while the electron resolution was 35 KeV.

Using this apparatus, both electrons and positrons could be detected incoincidence with the outgoing heavy ions, with a timing resolution on theorder of a nanosecond. The efficiency of detecting a coincidently emittedelectron and positron pair compared detecting a positron alone varied from15%, for correlated back to back emission, to 6X for spatiallyuncorrelated pairs.

In this new configuration a remarkable series of measurements wereobtained. One such example, the kinetic energy spectrum of coincidente*e" pairs resulting from collisions of Uranium on Thorium is shown infigure 3 below.[4]

UJ

0 200 100 600 BOO WOOE.. tkeV]

Figure 3: Uncut kinetic energy spectrum Tor coincident pairs (e*energy vs. e~ energy) produced in collisions of U on Th at beamenergy of 5.83 MeV/nucleon.

While this uncut spectrum appears to show no obvious specialfeatures, if one makes a cut requiring the electron energy to be in therange 340<E<420 KeV, as shown in figure 4(a) then the positron spectrum(containing the events in the slice shown) displays a sharp peak displayedIn figure 4(b), reminiscent of the peak in the original positron experiment,(the dashed curve Is a Monte Carlo simulation of the expected backgroundof dynamic positrons and positrons from nuclear pair conversions)

1000

BOO

600 •

200

0

-

.."'.•i::::i;:t*:U::'::^:::.: :"•

.:«:t:-»:&:'-;£.::*i".~-"->

• •

1 . * • * . 1

0 200 100 600 800 WOO

E^ ikeV]

CJ

(06 -

200 100 600 800 WOO

Figure (4): (a) energy cut on electron spectrum, requiring340<Ee<420 KeV. (b) resulting positron spectrum for events inthe slice from (a)

If one now instead makes the same cut first on the positron spectrum,as shown in figure 5(a), a similar peak appears at the same place in theelectron spectrum,

UJ

1000

800

600

iOO -

200

0

M r -i T"'—r ,

oCNJ

(ACo>

UJ0 200 400 600 M0 WOO0 20a 100 600 BOO 1000

E^ tkeV]

Figure 5:(a) cut on positron spectrum analagous to that In 4(a),(b) resulting electron spectrum.

Simitar cuts on the electron or positron spectrum in other energyranges produce no similar coincident peaks.

More suggestive stil l are the results obtained by making cuts on thesum and also the difference of the electron and positron kinetic energies.A line drawn at 45° on the spectrum in fig (3) wil l cross events havingfixed value of A-Eg^-Ep^. The wedge shape shown on fig. 6(a) enclosesevents having all values of EÊ^c+Epos) with the requirement that A<kZ(to allow for greater Doppler broadening with greater total kineticenergy). The magnitude of k (the size of the wedge) is chosen so that A canvary in the region of the spectrum where the electron and positron peaksare observed by an amount on the order of the width of these peaks.Similarly the parallel lines at -45° in fig. 6(b) cross events having a fixedtotal positron and electron energy, and the slice shown encompassesevents having Z in the range 710-8<-K) KeV for all values of A. If the eventsin 6(a) are plotted vs Z, and those in 6(b) vs. A, the resultant spectra areshown in figure 7.

LU

1000

800

600

X00

200

i} 0

" • . ;;vt::j ii'.

1 t

:

s

S

• ••

0 200 100 600 600 1000

E,. tkeV]0 200 XOO 600 800 WOO

Ee. ikeVJ

Figure 6: (a) wedge containing events with A<k£ for all S (seetext).(lines along 459 have constant A, those along - 4 5 1 haveconstant Z); (b) region in which 710<Z<840 KeV.

-600 -400 -200 0 200 100 BOO

[keVl

Figure 7: (a) Spectrum projected along points of constant £within the wedge in 6(a); (b) Spectnin projected onto points ofconstant A wltlMn slice in 6(b)

Significantly, the kinetic energy sum peak In 7(a) Is much narrowerthan the individual electron and positron peaks. This is the type ofbehaviour one might expect from correlated back to back emission in thecenter of mass frame, where the first order Doppler shifts would cancel.Even more surprising is the narrow difference peak shown In 7(S). While itis possible, by judicious choice of cuts, to mimic peaks in the Individualspectra, and even in the sum spectrum, a narrow peak in the differencespectrum 1s very difficult to artificially engineer.

These sum and difference peaks do net survive If the regions In ftgure7 are moved. Also, if the beam energy ',s moved from the resonant value ofabout 5.9 MeV/nucleon, all the peaks disappear. (Note also that theoutgoing ions are monitored during these measurements to assurescattering 1s near the elastic regime.) These phenomena, displayed forUranium and Thorium here, are reproduced for a variety of differentsystems, with peaks near 350-370 KeV.

Monte Carlo calculations of backgrounds from a variety of possiblesources have been done. The only one which is consistent with all the datais production of a neutral particle with kinetic energy of < 100 KeV in the

center of mass of the system, which subsequently decays into an e V pairSuch a Monte Carlo prediction Is shown In figure 8, assuming a neutralparticle of mass 1.8 MeV produced at rest In the CM frame, which decaystsotropically into an e V , and with a production rate normalized so thatIt's decays produce 3% of the total observed e+ yield. The agreement withthe observations in fgs. 3-7 is truly striking.

0 200 tDO 600 BOO 1000 0 200 iOO 600 800 1000

mer

its

UJ

20

15

TO

5

n

I/

• J-

L

500 1000 1500

[keV] E.. - E l

Figure 8: Monte Carlo prediction for Kinetic Energy Spectraresulting from Production and Decay of a new neutral particle,(see text above)

Since these remarkable results were first obtained, the experimenthas been repeated by the EPOS collaboration, with much higher statistics.AH of the originally observed phenomena have been confirmed, including

the narrow peaks in the electron and positron distributions— now wellabove the background, the narrow sum-peak and difference peak, and theindications of multiple structure in the peaks.

2. Summary of subsequent discussions

The remainder of my lecture at Vanderbm involved theoreticaldiscussions of a variety of phenomena from nuclear and particle physicswhich might be proposed to explain the observed events, andphenomenological discussions of contraints on the elementary particleinterpretations of the events using data from experiments in low, mediumand high energy physics. The details of most of these discussions appearin several recent preprints I have written [5,6] so I will merely outline thepoints raised, and refer the reader to these works, and the otherreferences cited for further details.

(a) Nuclear and electromagnetic explanations: All standardexplanations originating in nuclear-related transitions, or standardelectromagnetic production appear inconsistent with the data. Inparticular, i discussed: (1) internal pair conversion, (2) direct productionof scalar particles, both in nuclear transitions, and via the strongelectromagnetic fields near the nucleus.[7], (3) production via fissionproducts, notably 90Zr and 96Zr.

(b) Axions.! discussed the experimental data from heavy vectormeson decays which convincingly rules out standard axions, evenshort-lived ones. I then discussed a new variant on the standardaxion[5,8], with couplings only to up quarks, which appears to avoid theseconstraints, and which, until recently appeared as a viable a candidate toexplain these events.df a suitable production mechanism could be found.)

(c) General Phenomenological Constraints:(i) Atomic Physics: g-2 constraints have been used to limit the

couplings of any new scalar particle to electrons.[9] These constraints arerather severe, and limit the lifetime for decay into e4e" pairs to be

10

greater than about 5*10~M seconds. I presented similar constraints whichcould be derived using the observed hyperfine splitting in positronium,which are somewhat less severe, but which hold in a wider range of cases.

(11) Medium Energy, Rare K Decays: I discussed in detail theexisting constraints on the decay K->Tia, where a Is a short lived neutralparticle decaying into e+e". The present limits are not very severe, andthe axion variant of [5,83 can be barely accomodated withir them.

(Hi) Beam Dumps: I finally demonstrated how existing beam dumpexperiments convincingly rule out, in a model independent way, thepossibility of a new short-lived neutral particle decaying into e+e" pairs,as long as such a particle traverses meters of matter without scattering.

(After this lecture was given, Mark Wise and I combined newexperimental results on the decay TT+-> e+e~e+v with a theoreticalprediction of the branching ratio for 7T+->ae+v, for a short lived axion.[10]This appears to decisively rule out such an axion.)

it thus appears at present that the EPOS data remains live and well,while all theoretical attempts to explain the data have not survived. Inparticular there is now massive evidence against an explanation of thisphenomena in terms of a new elementary particle at 1.8 MeV. In particular,the axion interpretation is ruled out.

I would like to thank Jack Greenberg for making all the illustrationsand data presented available for my use, and also for tutoring me on theexperiment.

References:

1. J. Schweppe et al., Phys. Rev. Lett. £L 2261 (1986)2. see Quantum Electrodynamics of Strong Fields,^, by W. Greincer(Plenum Press, New York, 1983)3. All of the illustrations and data presented here was provided to me byJack Greenberg, and is published in various locations by the EPOScollaboration.4. T. Cowen et al., Phys. Rev. Lett. ^ 444 (1986)5. L. M. Krauss, F. Wilczek, YTP 86-03, Phys. Lett.B, to appear

11

6. L.M. Krauss, M. Zeller, YTP-86-08, sub. to Phys. Rev. D7. L.C.R. Wijewardhana, A.Chodos Phys. Rev. Lett. 56,302 (1986); K. Lane,HUTP-86/A0018. R.D. Peccei, T.T. Wu, T. Yanagida, DESY-86-013, Phys. Lett. B, to appear9. A. Shafer et al., J. Phys. £UL 169 (1985)10. LM. Krauss, M.B.Wise, YTP-86-13, Phys. Lett. B., to appear

13

CP Violation: Status and Future

John F. Donoghue

Department of Physics and Astronomy

University of Massachusetts

Amherst, Massachusetts 01003

Abstract

This talk reviews the mechanisms which can produce the ob-served CP violation in kaons, and discusses some of the possiblefuture directions for the field. The focus on new directions isimportant because progress cannot be made until some new form ofCP nonconservation is observed.

The subject of CP violation is interesting partly because we know so little

about it. Years of effort on the decays iL. ->-2TT and on the charge asymuetry in

iC -»-e-V7i have yielded precise measurements of the observables in these systems.

However theoretically they are understood entirely in terms of a single nonzero

number -£. Perhaps, as some theories suggest, this one number is our first in-

dication of a rich structure outside of the standard model. It may equally well

be due to the KM-phase contained within the standard model. At present we cannot

tell. Bounds on other observables (primarily E'/E and the neutron's electric

dipole moment) are in principle restrictive but in practice theories have so

far been able to accommodate the present limits.

There are in principle two sources of CP violation in the kaon system. The

dominant one appears to be an imaginary term in the mixing of a K and K -

i.e. in the mass matrix (conventionally labeled M ). This generates the param-

eter E.

14

which defines the mass eigenstates

[(l +E)K°

[(1 + E)K° -

The amplitude A. in Eq. 1 is due to the second possible source - direct CP vio-

lation in the actual K-»-27r AS-1 weak decay. Here one defines the isospin ampli-

tudes

i 6T 0Aje = <TTTI(I)]HW|K

U> . (3)

This source of nonconservation has a different pattern in K -+2TT, i.e. it gener-

ates e' in

Theoretically

noo

e' =

<7T TT

<TT 7T

" <A°

1 iTT/

1 3

/I

Hw

* w

H

Hw

TT/^

Ks>

te AQ

Im

20 Re

Re

Re

AoAo

A 2

A 0

Im

ReA°lAo]

(5)

The last form follows in models, such as the KM or Higgs models, where In A = 0

in the natural phase convention, and builds in the effect of the Al =1/2 rule,

i.e. A_/A_ = -r-r. Experimentally

E = 2.27 x 10~3

(6)e'/e < 0.01

In the standard (KM) model, all CP nonconservation is proportional to the

quantity

s^.s-s.. < 0.3 x 10"3 (7)

1 I 5 o

15

2where the bounds on the KM angles have been given. This number uses the limit

b -*-u/b +c < 0.05 which may be weakened in the near future due to model dependence

in the experimental determination. However overall this combination of angles

is a very small number, and perhaps is too small. The dominant CP-ocId effect in

this model comes from the box diagram AS=2 contribution to the mass matrix which

yields (for m =40 GeV)

(for m = 60 GeV the factor of 4 becomes a 6, while for higher masses it grows

more rapidly.) The factor B is the parameter which describes the hadronic ma-

trix element

B= 1 — ^ <K°|dy (1 +f,)s V ( l + Y<-)sJK°> . (9)1 6 FK "K

The use"" of PCAC and SU(3) relates B to the experimental K -+TT IT decay rate,

with the result B =0.33. The weakest link in this evaluation is SI)(3). QCD

sum rules and al] quark models have SU(3) breaking of order 50% >r less. The

only calculation where large breaking (of order 100%) was found was in a lead-

irg log one loop calculation in SU(3) chiral perturbation theory. This approx-

imation has produced poor results in other cases ; however it deserves to be

taken seriously as an uncertainty. I feel that a safe estimate is

B = 0.33 + 0.33 (10)

where the uncertainty will hopefully go down in the future. Combining up the

various factors we find

E- = (4 - 6 - ? ) x Sls,s,s^ x (0.33 + 0.33)Box 1 1 i o -

, (11)

< 1.5 + 1.5 x 10

so that the box diagram does appear able to explain by itself the magnitude of e.

However it is close enough to the edge of not being able to explain the magni-

tude that one is forced to entertain the thought that it may in fact not be the

16

dominant source of CP violation and other mechanisms may enter.

The other possible contributions to £ (iong distance dispersive effects ,

the Siamese penguin and Im A.) appear to be smaller than the box diagram.

However the leading contribution to E' is the so-called penguin diagram which

produces a direct AS=1 CP violation. Here we have

s.s,s,s,e'/e = 0.003( x %)? (12)

0.3 xlOwhere

<TT ir jdy (1 +y,)s QY (1 -Y.)QJK >

P = i! ^ 3 (13)0.43 GeV

has been normalized to a bag model calculation. There is considerable uncer-

tainty in P, but most models give

0.002 < e'/e < 0.01 . (14)

This should be seen in the next generation of experiments at CERN and FNAL,

which hope to have a sensitivity of 0.001.

There are also many other mechanisms which have been suggested to explain

the observed nonconservatidn of CP. The oldest mechanism, the superweak model ,

now has gauge theory realizations. In this case, there are AS»2 tree level in-

teractions mediated by superheavy scalar or vector bosons. Because of the near

mass degeneracy of K. and K,,, this interaction can be extremely weak and still

generate the correct value for E. However outside of the mass matrix there will

be little or no CP violation, so that E'/E =0. Another mechanism which uses12scalar bosons is contained in the Weinberg-Lee models where reasonably light

charged Higgs bosons mediate the CP-odd interaction. In this model the box dia-

gram is suppressed due to a derivative which appears in the effective operator.

The dominant contribution to e then comes from dispersive effects. After some

confusion over the chiral properties in K -»-2TT, the model now has a "prediction"

(at lowest order in SU(3)) of e'/e »= 0.006 to within a factor of three. The

reason for the uncertainty is that one must evaluate a chirally suppressed matrix

17

element, and the result is strongly dependent on SU(3) breaking and nn' nixing.

-24 +1The electric dipole moment of the neutron is expected at about d M O - e-cm,

which is on the edge of the experimental bound. Thus the model is alive, but

one should expect to see some effect in E'/E or d soon if the model is correct.

A third type of mechanism arises in the left-right symmetric theories. Actually

there are so many versions of these theories that many different results can be

obtained. However one version - that with the "isoconjugate" structure - gives

an interesting variation on the patterns of CP tests. In this case the left- and

right-handed sectors of the theory have an identical structure (aside from L **R)

up to a relative phase, i.e.

GF 18

H - — cos6 sin6{0T1 + ne P 0BIJ (15)

2 2

Here ri • m, /m_ < 0.003 and 8 is the CP odd phase. In any purely parity violat-

ing decay such as K -+21T (or a purely parity conserving one such as K -*-3ir), both

operators give an equal matrix element in each isospin channel and the phasei8

(1 +ne ) factors out of the amplitude leaving no CP odd signal when the ampli-

tude is squared. Thus e'/e = 0 in this version, but e, generated through the

mass matrix, is not zero.

All of these models adjust their parameters to fit E. They therefore cannot

be distinguished by the existing data. Some non-e signal needs to be observed

to distinguish the models. In the short term the c'/e measurements axe the Most

promising direction. However it would be even more useful to see CP violation

outside of the K -»-2n channel. Theorists have been working hard at discussing

possible new signals, and I will review some of these ideas below. I have divided

then into three categories: 1) Low energy tests, 2) Tests using heavy quarks,

and 3) High energy tests.

Low Energy At low energy the tests which I will discuss all occur in strangeness

changing processes. Let me introduce a parameter, x> which gives the amount of

AS«1 direct CP violation (i.e. not mass matrix effects). In most nodels, such

18

as the KM model, x "" 20e' < .2e (the factor of twenty removes the Al =3/2 suppres-

sion factor in £').

However in models where the CP violating interaction is parity conserving, X

can be as large as 4e without causing any phenomenological problems. The bound

on X comes from dispersive effects in the mass matrix.) In neutral kaon decays,

mass matrix mixing will always be present, so that any CP odd signal will be of

the generic form E + x- As an example consider Kc •*• IT TT IT . In general one can

allow a signal as large as r) . 4e although many models expect 1 +_Q E + O(20e').

The signal KM model is even smaller. The standard analysis uses PCAC to relate

n+_fl to n and noo» with the result that n+n ^ e + e'. Recently Holstein and I

realized that higher momentum terms, known to be present in the data, modify this

analysis and lead to a larger deviation from e, i.e. X) _ 'v e + 0(5e'). The pre-

sent FNAL experiment hopes to measure X) _ to 0(e), so they will not probe fine

details such as above, but they will push down the allowed magnitude of X-

Hyperon decays also exhibit CP violation. This is discussed in detail

elsewhere , but let me mention in particular a promising approach using pp re-

actions . To observe CP violation using hyperons one must compare byperon and

antihyperon decays. For example, in A -*-pir decay (or A -*-pir ) there is the an-

gular distribution

W(6) - 1 + as"A'Pp (16)

-4and estimates put the CP odd signal a + a 0.8 x 10 . In general comparison

of a and a is difficult because of systematic differences in A and A production.

The best way to look for these signals is in pp due to the fact that the initial

state in the center of mass is CP symmetric. Consider the. overall reaction

pp •*• AA •• pTT piT . The A and A are produced polarized perpendicular to the pro-

duction plane, with CP invariance of the strong interaction requiring that their

polarization be equal. If one counts the final proton and antiproton distribu-

tion above and below the production plane, this picks out a + a, i.e.

19

N (up) - N (down) + N-(up) - N-(down)m _£ p. p. p.

events

where P. is the polarization of A and A. This may be measurable at the level of

-2 -3 -k

10 •* 10 in present experiments at LEAR. To reach the 10 level requires the

next generation of machine/detectors, but does not appear to be completely out

of reach.

Heavy Quarks In some of the decays of heavy quarks it is sometimes possible to

get relatively large CP odd signals, even in the KM model, despite the theorem

that all CP violation is proportional to s.s,s,Sr. This occurs because the or-

dinary transition amplitudes are also suppressed by small KM angles, so that the

CP odd terms are a larger fraction of the total, i.e.

CP-odd „ !l¥3!i „ 1Q-3CP-even

S2

The penalty seems to be that this only occurs in rare decay modes, which are

difficult to see. In the decays of charmed quarks, the CP violation seems to

be well buried because the dominant decay has no KM angle suppression. Likewise

D -D mixing is expected to be small. In the B meson system the mixing is ex-

pected to be large (10% -*100%) for the strange B -B and smaller in the non-5 S

o -o

strange B -B . However in both cases the CP odd signal, measured by the number

of like sign dileptons in e e -*• B B

19is expected to be small in the standard model. Sanda has pointed out that

supersymraetry co'ild raise this to 0.1 and hence it is worth looking for. More

promising are decays with interfering amplitudes. For example B •+ K~TI can pro-

ceed both through the usual four fermion vertex and also through a penguin dia-

gram. This can lead to

20

- K V ) - r(5° ->KV) % 10-2 _10-i ( 2 0 )

fr + f-3 -4

However the branching ratio for this mode is small ^ 0(10 -*-10 ). Other example*

exist and they share the feature of large CP violation and small branching ratio.,

so that overall the signal is small. All cases seem to need more than a million

bb pairs if they are to be observed.

High Energy This area is new and all three proposals which I will mention date

from this past spring. The motivation arises from the push for new high energy

colliders to search for new physics. Many theories of CP violation involve new

physics which should become easier to excite at high energies. In addition,

theories like supersymmetry or composite models would be expected to have their

own CP violating interactions. However it is clear that the standard methods

for observing CP violation cannot be used at these new machines. Therefore one

must come up with new ways to see CP nonconservation. The following ideas are

a start in that direction.

With G. Valencia, I have been exploring ways in which jet variables can be

used as a tool in the study of CP invariance. In these, no reconstruction (or

perhaps only partial reconstruction) is needed and one measures primarily the

energy and direction of the jet. These can be used in e e or pp colliders

where in the center of mass the initial state is related back into itself under

the CP operation. There are many possible signals but let me just give one

example. One can order jets by their total energy or by how "fat" they are (i.e.

their total p ). In this case in the reaction e e -*• jets, the following asy-

metry

A = P l - p 2 xp 3 (21)

is C-even and P-odd and hence a nonzero average <A> would signal CP violation.

How could one generate this, even in principle? As an example consider e e

where t decays into t •* bcs. For a heavy t many of the final state configura-

tions will be resolvable into jets, with the b-jet being fatter than the c-jet.

21

If we consider the recoiling t jet to be the fattest, followed in order by

b,c,s jets then the asymmetry turns into

A • P£*Pb x Pc

or Pt"Pb x pc

This in turn can be generated by interference in the weak decay. The optimal

model to induce CP violation is the Higgs model because the couplings grow with

mass and the CP odd coupling to the t is quite large. In this model, we have

done a quark leve calculation on the Z peak and find a reasonable signal

°> * 4% (23)events

The asymmetry arise from an s *p, x p correlation in the decay amplitude. The

reason for using a top quark is that it is most likely to retain its spin while

forming bound states. For other quarks the only meson which decays weakly is

the pseudoscalar which has no spin information. For top quarks however the vector

21 *

mesons will also decay weakly , because the T -T mass splitting is so small,

and we estimate that 50% of the time the spin will be retained. This will re-

duce the signal by a factor of two. Likewise confusion of the jet signals in

the fragmentation process will reduce the signal by a factor which is more dif-

ficult to calculate. However this does demonstrate how jet variables can be

useful. We have not come up with any large signal for the standard model, so

that most likely these variables will be used as a search for possible new

physics. I would hope that these tests would be routinely done using interest-

ing classes of events, much as other searches for new physics (quark searches,

heavy lepton searches ...) are commonly done.

22 - -

Another proposal consists of looking for the decay Z -»-sb and bs. This is

a flavor changing neutral current process and therefore can be generated by loop

effects. Because these are themselves suppressed, the CP odd signal

a . rug) - r(ib) (24)

r(sb) + nib)

22

is larger but the branoinR ratio is small. In the case of three Rpner/itions

there is no real sipnal but with four generations a ^ 0(1) can bo reached with

a branching ratio of 10 . The authors claim that this is encouraging for LEP,

but the problem of identifying this react ion, distinguishing sb and bs from other

jets and from each other is so formidable that I am skeptical.

23A third idea consists of looking at

+

pp •»- e + X

at 90° in the center of mass. Here the authors interfere some new effective in-

teraction of new physics with the standard production mechanism of the standard

model. For some reasonable parameters they find

R . °<^> - O(e) 2% (25)

a(e ) + a(e )

but,as always, the problem is that o itself is not large. With proposed pp lumin-

osities this would not yet be measurable.

It is probable that none of these ideas is yet optimal. However theorists

have just started to think about the problem of observing CP violation at high

energy, and we can hope to have more, perhaps better, proposals in the future.

Overall I feel that there are two prime questions to be answered by weak

interaction experiments: 1) Where is (are) the Higgs boson(s)? and 2) What is

the origin of CP violation? Both are difficult, but are of such importance that

extreme effort is justified. The field of CP violation is dead if there are no

new experiments. There are suggestions for new experiments in many areas. At

this stage, we can only hope that they are performed and new CP-odd effects are

found.

23

References

1. References to background material and overviews of CP violation can be

fouv:d in

L. Wolfenstein, CMU-HEP86-3 to appear in Ann. Rev. of Nuc. and Part.

Science, vol 36, 1986;

J. F. Donoghue, E. Golowich and B. R. Holstein, Phys. Rep. _131, 319 (1986);

J. W. Cronin, Rev. Mod. Phys. 53, 373 (1981);

T. D. Lee and C. S. Wu, Ann. Rev. Nucl. Sci. 16_, 511 (1966).

2. Particle Data Group, Rev. Mod. Phys. 56 , No. 2 (1984).

3. R. Wilson, this conference.

4. J. F. Donoghue, E. Golowich and B. R. Holstein, Phys. Lett. 119B, 412 (1983);

T. Applequist, J. D. Bjorken and M. Chanowitz, Phys. Rev. D7, 2225 (1973).

5. E. DeRafael and A. Pich, Phys. Lett. 158B, 477 (1985).

6. J. Bijnens, H. Sonoda and M. Wise, Phys. Rev. Lett. _53_, 2367 (1984).

7. H. Pagels, Phys. Rep. 16, 221 (1975);

J. Bijnens, H. Sonoda and M. Wise, CALT-68-1221;

J. F. Donoghue and B. R. Holstein, Phys. Lett. 160B, 173 (1985).

8. J. F. Donoghue, E. Golowich and B. R. Holstein, Phys. Lett. 135B, 481 (1984);

I. I. Bigi and A. I. Sanda, Phys. Lett. 148B, 205 (1984);

M. R. Pennington, Phys. Lett. 153B, 439 (1985).

9. J. F. Donoghue, E. Golowich and G. Valencia, Phys. Rev. D33, 1387 (1986).

10. F. J. Gilman and M. Wise, Phys. Lett. 83B, 83 (1979).

11. L. Wolfenstein, Phys. Rev. Lett. 13, 562 (1964).

12. S. Weinberg, Phys. Rev. Lett. 37, 657 (1976);

T. D. Lee, Phys. Rev. D8, 1226 (1973).

13. J. F. Donoghue and B. R. Holstein, Phys. Rev. D32_, 1152 (1985) and references

therein.

14. R. N. Mohapatra and J. C. Pati, Phys. Rev. Dll, 566 (1975);

24

G. Branco, J. M. Frere and J. M. Gerard, Nucl. Phys. B221, 317 (1983);

R. N. Mohapatra, Maryland Report 85-124.

15. L. F. Li and L. Wolfenstein, Phys. Rev. D2_l_, 178 (]980).

16. J. F. Donoghue, X. G. He and S. Pakvasa (to be published in Phys. Rev.);

J. F. Donoghue and S. Pakvasa, Pbys. Rev. Lett. _55_, 162 (1985) and refer-

ences therein.

17. J. F. Donoghue, B. R. Holstein and G. Valencia, UMHEP-

18. D.-S. Du, I. Dunietz and D.-D. Wu, Enrico Fermi Institute preprint 85-24;

R. Sachs, Enrico Fermi Institute preprint;

I. I. Bigi and A. I. Sanda, Nucl. Phys. B193, 85 (1981);

L. Wolfenstein, Nucl. Phys. B246, 45 (1984);

D. D. Wu, Phys. Lett. B90, 451 (1980);

L. L. Chau and H. Y. Cheng, Phys. Rev. Lett. 53, 1802 (1984).

19. A. I. Sanda, Phys. Rev. Lett. 55, 2653 (1985); Phys. Rev. D32, 2992 (1985).

20. J. F. Donoghue and G. Valencia, UMHEP-257.

21. I. I. Bigi et al., Z. Phys. £7, 127 (1981).

22. J. Bernabeu, M. B. Gavela and A. Santamaria, CERN preprint, CERN-TH.4381/86.

23. R. Barbieri, M. Georges and P. LeDoussal, CERN preprint.

25

FINITE-ELEMENT APPROXIMATION IN QUANTUM FIELD THEORY*

Cail M. BenderDepartment of PhysicsWashington University

St. Louis, Missouri 63130

In this talk I describe a research program that has been underway for severalyears. The objective is to find a fast and accurate scheme for solving quantumfield theory on a lattice which does not involve a Monte Carlo algorithm. Weuse an alternative strategy based on the method of finite elements. We are ableto formulate fully consistent quantum-mechanical systems directly on a latticein terms of operator difference equations. One of the many advantages ofdoing this is that the fermion doubling problem is completely eliminated. Themethod for solving operator difference equations is discussed for variouselementary quantum-mechanical and field-theoretic models including theSchwinger and Sine-Gordon models. Good numerical results are obtained.

INTRODUCTION

A quantum field theory may be formulated as an operator differential equation (afield equation) and an equal-time commutation relation (ETCR). However, there areinherent ambiguities and divergences associated with such a formulation becauseoperator-valued distributions in the continuum are so singular that products of suchoperators do not exist. It is well known that introducing a space-time lattice is a verynice way to remove these ambiguities and thus to regularize a continuum quantum fieldtheory. The content of the theory is then contained in the continuum limit of the latticetheory.

Ordinarily, the lattice is introduced as a mathematical artifice to make sense of thefunctional-integral representation of a quantum field theory. In this computationalscheme the lattice regularizes the functional integral as an infinite product of ordinaryRiemann integrals. Then, the infinite product is approximated as a finite product ofintegrals which are evaluated by Monte Carlo methods. This procedure is slow;doubling the computer time gives only minimal improvements in accuracy.

'Invited talk pretested at the Seventh Vandeibilt High Energy Physics Conference, "Quarics, Strings, Dirk Matter, i*d

all the IMC", May, 19K.

26

The program discussed here uses the lattice in a completely different and morefundamental way. We show how to formulate and construct a fully consistent (unitary)quantum theory on a space-time lattice. Such a theory is defined in terms of an operatordifference equation (rather than a differential equation) and an ETCR that holds atequal-time lattice points. The operators in such a theory have none of the problems(infinities) that operators in the continuum have. We will see that while there is no hopeof solving operator differential quations, operator difference equations can be solvedexactly. Thus, for each lattice, we obtain exact closed-form solutions for the fieldoperators rather than a slowly converging sequence of Monte Carlo approximations.

THE METHOD OF FINITE ELEMENTS

The problem of how to quantize a discrete quantum field theory on a lattice can besolved by the method of finite elements, a technique well-known to appliedmathematicians for solving partial differential equations.1 The method consists of foursteps. We are given a classical partial differential equation L<j> = 0 to be solved on aregion R subject to boundary conditions given on the boundary dR. We first decomposeR into a set of nonoverlapping patches, called finite elements, which completely coverR. For classical (not quantum) differential equations the patches may have arbitrarysizes and shapes. On each patch we approximate the solution <j> to the partial differentialequation as a polynomial (the degree of this polynomial is chosen to suit the conditionsof the problem). Second, at the boundaries of contiguous patches continuity is imposed(and, sometimes continuity of higher derivatives). Third, on patches that are adjacent todR we impose the boundary conditions. Fourth, we impose the differential equationL<j> = 0 at one point (or more than one) on each patch. Conditions two, three, and fourgive a system of algebraic equations satisfied by the coefficients of the polynomials.Solving mis system gives a good numerical approximation to the solution <|>.

ILLUSTRATION USING A CLASSICAL DIFFERENTIAL EQUATION

Let us illustrate this procedure by solving a simple classical ordinary differentialequation problem:

y'(x)=y(x),y(0)= 1; show that v(l) = e =2.71828... . (2)

We begin by using just one linear finite element: y = ax + b, where 0£x <; 1.The initial condition gives one algebraic equation

y(0)= 1 => b - 1 . (3)

We must impose the differential equation at one point xo on the interval 0 £ xo <, 1;however, the choice of x0 remains ambiguous. Later we will see that unitarity inquantum mechanics removes this ambiguity and uniquely selects xo = 1/2. For now wesimply choose xo = 1/2 and proceed:

y ' ( l /2)=y(l /2) => a =a/2 + b . (4)

27

Solving (3) and (4) for a and b gives y{x) = 2x + 1, so that ^(1) = 3, which is a goodresult that differs from the exact answer by only 10%.

For the case of two linear finite elements y x = at + b,y2 = ct + d, where t is a

local variable that ranges from 0 to 1/2, the initial condition gives

l => b = 1 , (5)

Continuity at x = 1/2 gives

y1(V2)=y2(0) => a/2 + b =d , (6)

and imposing the differential equation at the center of each finite element x = 1/4 and3/4 gives

=> a = ,

y '2(l/4) = j2(l/4) =>c = c/4 + d . (7)

Simultaneous solution of (5)-(7) gives an excellent result for y(l):

= 72(1/2) = 25/9 = 2.778... , (8)

which differs from the correct answer by 2%.In general, for N finite elements the exact result for the approximate value of

which for large N approximates e with a very small relative error of l/(12/v"2).

QUANTUM MECHANICS WITH ONE DEGREE OF FREEDOMApplying the technique of finite elements to quantum problems is much more

interesting because the polynomial coefficients are operators. Consider the simplequantum-mechanical Hamiltonian

, (10)

for which Hamilton's equations are

<l -P

P=-V(q) • (11)

The system (11) constitutes a time evolution problem for the operators p(t) and q(t).The analog of the classical initial condition is an operator constraint in the form of anequal-time commutation relation (ETCR)

28

: i • (12)

If (12) is imposed at r = 0 then, by virtue of (11), it holds for all / .

To solve (11) on the interval [0,T] we introduce a lattice of N linear finiteelements. On each finite element r ranges from 0 to A and Nh =T. Letqn (n =0,1,...iV) be the approximate value of q(nh). Let us examine the nth finiteelement, where p(t) and q{t) are approximated by the linear polynomials

(13)

and 0 = t < t < h. Substituting (13) into (11) and evaluating at the center of the finiteelement t = h/2 gives a pair of algebraic equations relating the operatorsPn-l' *?n-l> .Pn>and<7n :

<?* ~ Vn-1 Pn-l+Pn ...7 = x , (14a)

Pn -Pn-l

The ETCR (12) at the lattice points nh reads

[<7n,Pj = ' • (15)

It is not obvious that (14) and (15) are consistent. To prove consistency we argue asfollows: Equation (14a) implies that

, - 0 (16a)

and (14b) implies that

Expanding and adding together the commutators in (16) gives the result

Thus, if \qo,Po\ — ' initially, then (15) holds for all values of n.

The proof of the persistence of ETCR's in (17) holds if and only if the differentialequations (11) are imposed on finite elements at t = h/2. At any other point on thefinite element (15) ceases to be true. Thus, quantum-mechanical unitarity (persistence ofETCR's) removes a basic ambiguity that occurs in the numerical solution of classicaldifferential equations; namely, where on the finite element to impose the differentialequation.

29

SOLUTION OF OPERATOR EQUATIONS

We have proved the consistency of (14) but we must now solve these equations.To do so we use (14a) to eliminate pn from (14b) which becomes

If we let x = (qn + <?n_!)/2, y = Aqn.xlh2 + 2pn^xlh, and g(;r) = V'(x) + Axlh2, then

(18) becomes

y=g(x) • (19)

While x and .y are operators, (19) implies that they commute and thus (19) can betreated as if it were a c -number equation. Its exact solution is x = g~J(y) so

^n i n — 1 o I t , ry I '

«.-IU-.-K. + V%-+-%i • (20)

This result shows that the exact operator solution after N time steps to the latticequantum theory in (14)-(i5) is a continued (nested) function.2

The unitarity of the '-ttice theory can also be demonstrated explicitly because thetransfer (lattice time evclution) operator U can be given in closed form:

where

jj _ eipihlAg\A(q.)h gip?

with

It is interesting that while the solution in (20) and the transfer operator U involvesthe function g~l, matrix elements of these operators only involve g. For example, if wedefine Fock states | n > at the initial time by

and qo = -3=(

where

a \n> = V«" |n—1> and a t | n > = Vn+1

30

then,3

<m |<7

— ) g ' """ £_dz

where /? = 4y2n~4 + A"2"/"2. c o s 9 = 2j/(Rh2), and //„ is the nth Hermite polynomial.

QUADRATIC FINITE ELEMENTS

In the case of quadratic polynomial finite elements (y = a+bx+cx2) there are twopossible schemes: (i) a stiff approximation in which we demand continuity andcontinuity of the first derivative at the boundary between two finite elements and weimpose the differential equation once, or (ii) a floppy approximation in which we demandonly continuity at a boundary and we impose the differential equation twice on eachfinite element. Both schemes are adequate for classical differential equations becausethey yield three conditions which determine the coefficients a, b, and c on eachelement. However, only the floppy approximation is consistent with unitarity. Unitarityfurther requires that the differential equation must be imposed at the pointsx = (1/2 ± 1/Vl2)rt, which are the zeros (Gauss points) of the second Legendrepolynomial.

The floppy quadratic scheme is very accurate, having an error after N steps of orderAf4. For example, with one quadratic finite element, the solution to (2) isv(l) = 19/7 = 2.714... which has a relative error of-1/7%.

For the case of d -degree polynomial finite elements, again quantum mechanicsrequires that the floppy approximation be used and the requirements of unitarity leaduniquely to Gauss-Legendre integration. The error after N time steps is of order N'24 4

ENERGY EIGENVALUES

It is easy to compute energy levels of quantum systems once the operator equationshave been solved. Here are some numerical results: For the case of the harmonicoscillator the energy gap co = E j - Eo comes out exactly. For the anharmonic oscillator,where V(q) = Xq*/4, the exact value of co is 1.08845..A1/3. One linear finite clementpredicts 1.1447lX1/3 (5.2% relative error) and one quadratic finite element predicts1.08225 (-0.57% relative error).4

It is also possible to determine all energy differences simultaneously and toarbitrary accuracy by taking large numbers of finite elements. Figure 1 shows the resultsof a short computer calculation using 1000 finite elements for the anharmonic oscillator.5

Computations involving many finite elements also give extremely accurate results inproblems involving tunneling.6

31

IO

200 400 600m 800 1000

Figure 1: A semi-log plot of \Am \2 in (3) versus m for theanharmonic oscillator V{q)-gq* with g = - 0 . 8 8 5 . Thespikes give extremely accurate approximations to energydifferences Ej -Ek of the exact spectrum. To read off thepredicted energy differences, we note that one unit on thehorizontal scale corresponds to an energy increment ofAE =2n/[(N+l)h]. Energy differences are measured fromboth the left axis and the right boundary (see Ref. 5).

MORE GENERAL HAMILTONIANS

The method of finite elements is applicable to systems whose Hamiltonians aremore complicated than that in (10). For general Hamiltonians of the form

H=H(p,q) ,

New and interesting problems arise involving the question of operator ordering. Themethod of finite elements determines a unique and well-defined procedure for orderingthe operators in such Hamiltonians. The ordering procedure involves the use ofcontinuous Hahn polynomials, a curious and rarely seen orthonormal set ofpolynomicals. A complete discussion of operator ordering is given in Ref. 7.

32

SYSTEMS WITH MANY DEGREES OF FREEDOM

For systems having more than one degree of freedom it is not as easy to show thatthe method of finite elements is consistent with unitarity. We illustrate with a systemhaving two degrees of freedom (p 4) and (M>). For the Hamiltonian

Hamiltons equations in the continuum read

q =P

P -_3_dqd

On the lattice, linear finite elements give

(21a)

(21b)

(21c)

(21d)

(22a)

(22b)

(22c)

(22d)

Note that while there is no operator ordering problem in (21c) and (2 Id) because[<?(* ),<}>(*)] = 0 , there appears to be a serious ordering problem in (22c) and (22d)because it is not clear that (q^ + q^l2 and (<J>j +<f>o)/2 commute. To resolve thisproblem we define

n 2*0 .

h

<t>i ~<t»oh

P\ ~Poh

h

2

2

dV

*q

dV30

*

<I\ + <7o <2 '

<?i + 9o 42 '

> l + <t>02

2

t =

Now, (22c) and (22d) become

(23)

33

The simultaneous solution of (23) has the fonn

a = o(a,p), t = T(a,p) .

But, a and j3 involve only operators at the initial time, so [a,P] = 0. Thus a and x alsocommute and there is in fact no ordering problem in (22c) and (22d).

It is now necessary to verify that the ETCR's are preserved in time. From thesolutions

q} = - ? o + 2o(<x,J5) ,

Pi=-Po~ 7<?i + j

it is necessary to verify that

[<?iîl = [<Mi] = ' (24a)

and that

fai,<>i) = fo1,Wi] = [4>i*i]a s[Pi,Ki]=0 . (24b)

It is easy to verify (24a):

4

,• + i . i £ 1 i + 2— \ Ai

h da. hl da [ h2

= i

However, it is harder to verify (24b):

[q^] = -2[<?0,T«X,p)] -

_ _ 4 £ _3x_ 4t dah 3a A 9p

We now show that fai,^] = 0 by verifying that 3t/3a = doVdP which is true because thesystem defined by (21) is Hamiltonian. Explicitly, we have8

_£V_dO dX

3p 3a f £ y _4_| (Vv 4 I d2V[dC2 + A2 I 3T2 + A2 I

34

BOSONIC FIELDS IN TWO SPACE-TIME DIMENSIONSFor the case of bosonic quantum field theory, a scalar quantum field can be

represented on a square linear finite element by a polynomial of the form

) = a +bx +ct +dxt . (25)

Here a, b, c, and d are operators having no space-time dependence. In terms of thevalues of hi at the four comers of the square, (25) becomes

(26)

where h and it are the lattice spacings in the t and x directions. Equation (26) is thetwo-dimensional analog of (13).

The requirements of unitarity demand that derivatives be evaluated at the center ofthe finite element t = h!2,x =kll\

"7J" => ~2£ ®mji + $m-ljt ~ ^m.n-1 ~ ^m—lî-l) >

* * . (27)

To quantize a self-interacting scalar boson field theory we rewrite the field equation•2<|> + / (<j») = 0 in first-order form

The proof that the discrete lattice quantum version of (28) is unitary is given in Ref. 9.

FERMION FIELDSThere is an inherent problem with discretizing the Dirac equation. To illustrate die

problem we use a Kogut-Susskind (discrete space, continuous time) lattice. On such alattice, the Dirac equation in one space dimension

0 (29)

becomes

A V = 0 , 1 * m £M , (30)

where A is the lattice spacing and we have used a forward difference for the spacederivative. Using the same lattice and definition of derivative, the continuum action

36

becomes

Two serious problems are now apparent First, the action (31) is not Hermitian;under Hermitian conjugation the forward difference becomes a backward difference:

- Vm)/A]+ = J » VM V(Vm - Vm_!)/A . (32)

Second, the dispersion relation is not real [this is not surprising in view of (32)]. Toobtain the dispersion relation we take a continuous time Fourier transform

and a discrete space Fourier transform

UlM , *=1,2,...Mm=l

of (30) and square the result:

= y? + -4- sin2(nk/M)exp(-2iiik/M) . (33)

On the lattice the moment p is given by

Thus, in the limit as M -> °» and A -> 0, (33) becomes the usual result

(34)

but on the lattice co2 is complex.We can solve the problem of complex co2 by using a symmetric discretization of the

derivative

For this choice the lattice action is Hermitian and the dispersion relation is real:

. (35)

36

Unfortunately a new problem has arisen: although (35) has the correct continuum limit,on the lattice there is fermion doubling: (0 = \1 at p = 0 (low momentum) and co = \i atp = MI2 (high momentum). The appearance of these spurious fermion states on thelattice renders invalid the numerical calculations of the Green's functions of the theory.

The method of finite elements totally eliminates the problems of lattice fermions.The method of finite elements gives a unique and unambiguous prescription fordiscretizing (29). Following (27) the discrete Dirac equation becomes

° 2h ( ¥ m - l i n + V m ' n V m-1-»-1 VmiB-i)iyi

+ ~^j- (Vm,n + Vm,n-1 ~ ¥m-l,n " Vm-U-l)

+ - J (Vm-U + Vm,» + Vm-U-1 + Vm.n-l) • (36)

Equation (36) has the following five nice properties:

(i) the equal-time anticommutation relations are exactly preserved in time;

(ii) the associated action is Hermitian;

(iii) there is no fermion doubling as one can see from the dispersion relation

(iv) the difference equation (36) is local (only nearest-neighbor terms appear);

(v) Equation (36) is psi symmetric in the massless limit.10

The no-go theorems discussed by Karsten and Smit, Nielsen and Ninomiya, andRabin have been avoided because the Hamiltonian operator is not local.11

ABELIAN GAUGE INVARIANCE

Having solved the problems associted with lattice fermions, we now examine alattice gauge theory. We consider quantum electrodynamics in 1 + 1 dimensions. Thefield equations are

, (37a)

, (37b)

O . (37c)

where, classically, the electric current is /** = ey-fy. (In field theory it is necessary todefine J^ as a limit of a point-split current.) The system (37) is invariant under aninfinitesimal local gauge transformation

(38a)

37

(38b)

To obtain a discretized electrodynamics we begin with (38b). The finite-elementlattice transcription of (38b) is

n = ~

(&4 , ) m > n = -^-

5Am>#I+1 - 5Am+l/l - 5Am „] ,

- 8Am,B] . (39)

Under (39), the lattice transcription of (37a) is gauge invariant.

Next we write down the lattice transcription of (38a)

8ym>n)/4

8Am>n)/4]

Vm,n+1 + ¥,»,„ 4]

and solve the equation for 8\j/:

.> n - l fm-l M

n'=0 |m'=l m'=m

x (_ i

(40)

where we have imposed the boundary conditions

YO,n •

Now that we have solved for dymn we can perform an infinitesimal gaugetransformation of the form i y}d^ and '"/ôV terms in Dirac equation (36).

We then determine an interaction term (/ : ) m „ with the property that if we vary I±with respect to A and use the free Dirac equation (36), terms of order 8Am „ cancel. 1\has the form

=~~n'=l

2 - 2m'=l m'=m+l

38

Next we determine a term fox,, so that if we vary 12 with respect to A and J^ withrespect to A and vf and use the Dirac equation with I x included, terms of order 8Am n

cancel. We continue this process and obtain a sequence of interaction terms I1J4, . . .,which can all be summed to give the gauge-invariant interaction term of the Diracequation:

Z Bm,n'n"=n'+l

(e"*-*' -

\ieh T B,n"=l

m,rf

xexp

sec

iekIf

4- Y, c 'M

MX sgn(m"-m)(-iy"-mX-ir+m"

iekIf- S sgn(m'"-m)sgn{m'"-m")sgn{m'"-m)Cm^m'"=\

where

The Dirac equation (36) with this interaction term is a gauge invariant lattice fieldequation.12

THE ANOMALY IN THE SCHWINGER MODEL

The Schwinger model (two-dimensional massless quantum electrodynamics) isobtained by setting |i = 0. This model is interesting because it has a chiral anomaly:The divergence of the vector current vanishes

d^ = 0

but the divergence of the axial current is proportional to an anomaly:

3R/£ = -(anomaly )£ ,

where

anomaly = e2/n ,

for the continuum model.

39

One can solve the finite-element discretized version of this model exactly12 and oneobtains

a n O m a l y = Afsinfr/M)

+ O(1/M2)]—71

Observe that corrections are of order I/A/2, just as in the case of classical differentialequations. The result in (40) is a major success of the finite-element approximation.

RESULTS FOR INTERACTING SCALAR HELD THEORIES

Our most recent results involve the determination of the mass gap (renormalizedmass) in interacting scalar quantum field theory.13 For the theory whose Hamiltonian is

we find that the approximate renormalized mass is

m2 2+(2K)" - 1

InAmT

For the quantum sine-Gordon equation whose Hamiltonian is

we find that

2 2 g

= H

This is the characteristic power-law renormalization found in the conventional treatmentsof the sine-Gordon model14'15 Note that our treatment is non-perturbative: If g2/8rt issmall compared to 1, then we obtain the perturbative renormalization result ofColeman.16

FUTURE RESEARCH

There are many directions that future research on the finite-element approximationmay follow. The simplest generalization of the work described in this talk is to higher-dimensional field theories. This generalization is not conceptually or technicallydifficult. It merely requires that the operator difference equations expand in size and thatthe fields carry more spatial indices. We have not yet examined the massrenormalization in these more elaborate equations but we believe that it would notsignificantly deepen our understanding of the finite-element approximation.

40

A second and extremely important area that must be examined involves errorestimates. From studies of models in one-dimensional space-time (quantum mechanics),we have learned that the relative error decays like N~2, where N is the number of finiteelements in the time direction. (This result is true whether or not the differentialequations involve operator or c -number variables.) As mentioned above we also haveone definitive result for a theory in two-dimensional space-time, namely the Schwingermodel. Here too, the error decreases like the square of the total number of linear finiteelements. However, for nontrivial two-dimensional interacting field theories where wedo not know the exact answers, we are unable as yet to determine how the errordecreases as the number of finite elements increases. A deeper analysis of errorestimates is crucial to the further development of this program.

Finally, there is the question of how to obtain a sequence of increasingly accurateapproximations to physical quantities. There are two possible directions. Either, onecould use higher-order finite elements (quadratic, cubic, ...), which would involve adramatic increase in algebraic complexity, or one could increase the number of timesteps, which would probably require the use of computers. Although, we havesuccessfully implemented both approaches in quantum mechanics4-5 it is still not clear tous how to improve the field theoretic approximations in this talk. This is probably themost important topic for future research.

Ultimately, of course we hope to use the method of finite elements to obtainaccurate numerical calculations of the spectra of nonabelian gauge theories.

I thank the U.S. Department of Energy for financial support.

REFERENCES

1. Strictly-speaking, we are using the collocation method, a technique closelyresembling the method of finite elements.

2. The inverse function g"1 is unique if V"(x) > 0 (that is, if V is a single potentialwell). The case of double wells for which g~l is not unique is an extremelyinteresting one deserving further investigation.

3. C. M. Bender, L. M. Simmons, Jr., and R. Stong, Phys. Rev. D 33, 2362 (1986).

4. C. M. Bender, K. A. Milton, D. H. Sharp, L. M. Simmons, Jr., and R. Stong,Phys. Rev. D 32, 1476 (1985).

5. C. M. Bender and M. L. Green, "Accurate Determination of Spectra in Discrete-Time Quantum Mechanics," to be published in Physical Review.

6. C. M. Bender, F. Cooper, J. E. O'Dell, and L. M. Simmons, Jr., Phys. Rev. Lett.55, 901 (1985).

7. C. M. Bender, L. R. Mead, and S. S. Pinsky, Phys. Rev. Lett. 56, 2445 (1986).

8. C. M. Bender, K. A. Milton, S. S. Pinsky, and L. M. Simmons, Jr., Phys. Rev. D33, 1692 (1986).

9. C. M. Bender and D. H. Sharp, Phys. Rev. Lett 50, 1535 (1983).

41

10. C. M. Bender, K. A. Milton, and D. H. Sharp, Phys. Rev. Lett. 51, 1815 (1983).

11. Equation (36) was also discovered by R. Stacey; see Phys. Lett. 129B, 239 (1983)and Phys. Rev. D 26j 468 (1982) and the finite-element result was generalized toarbitrary dimension by Matsuyama (1984 preprint).

12. The finite-element approximation to the field equations of the Schwinger model isgiven in C. M. Bender, K. A. Milton, and D. H. Sharp, Phys. Rev. D 31^ 383(1985).

13. C. M. Bender and K. A. Milton, "Approximate Determination of the Mass Gap inQuantum Field Theory Using the Method of Finite Elements", to be published inPhysical Review.

14. R. F. Dashen, B. Hasslacher, and A. Neveu, Phys. Rev. D lh 3424 (1975).

15. S. Coleman, Phys. Rev. D 11, 2088 (1975).

16. S. Coleman, ibid, Eq. (2.12).

43

NEW CHARM RESULTS USING HIGH PRECISION VERTEX DETECTORS

Presented by Roilin J. Morrison

For the Tagged Photon Spectrometer Collaboration

J.C.C. dos Anjos, J.A. Appel, S.B. Bracker, T.E. Browder, L.M. Cremaldi,J.R. Elliott, C.E. Escobar, P. Estabrooks, M.C. Gibney, G.F. Hartner,P.E. Karchin, B.R. Kumar, M.J. Losty, G.J. Luste, P.M. Mantsch, J.F. Martin,S.F. McHugh, S.R. Menary, R.J. Morrison, T. Nash, U. Nauenberg, P. Ong,J. Pinfold, G.D. Punkar, M.V. Purohit, J.R. Raab, A.F.S. Santoro, J.S. Sidhu,K. Sliwa, M.D. Sokoloff, M.H.G. Souza, W.J. Spalding, M.E. Streetman,A.B. Stundzia, M.S. Witherell

University of California, Santa Barbara, California, U.S.A.Carleton University, Ottawa, Ontario, Canada

Centra Brasileiro de Pesquisas Fisiaas, Rio de Janeiro, BrasilUniversity of Colorado, Boulder, Colorado, U.S.A.

Fermi National Accelerator Laboratory, Batavia, Illinois, U.S.A.National Research Council, Ottawa, Ontario, Canada

Universidad de Sao Paolo, Sao Paolo, BrasilUniversity of Toronto, Toronto, Ontario, Canada

ABSTRACT

The first results from the charm photoproduction experiment E691 at the

Fermilab are presented. Using a silicon microstrip vertex detector (SMD),

a very large sample of clean charm decays has been recorded. The use of

SMD's for isolating clean signals and for measuring lifetimes is discussed.

From the 15% of the data so far analyzed, the lifetimes of the Dc and D

mesons are found to be .44±.02±.02 10"12 sec and 1.09**Q| ± .06 TO"12 sec,

respectively, and the lifetime ratio is 2.5±.2±.l. The F+ meson is ob-+ + 1 ?

served in the $v mode with the lifetime found to be .40 'no ± .06 TO"12

+ '-08 +1 3

seconds. The F has a cross section times branching ratio which is 2.4_gg

times that for D -+<tnr . Charm meson lifetimes are reviewed and future pros-

pects for fixed target charm and for SMD detectors are discussed.

44

I. INTRODUCTION

A. Motivations for Fixed Target Charm Experiments

The motivations for fixed target charm experiments fall more or less

into two categories. One is that photoproduction and especially hadro-

production have the potential for very high rates of detected charm. Many

of the interesting charm physics questions involve rare processes where

large data samples are required. In weak decay studies, for example, there

are the questions of D°-D° mixing and double Cabibbo suppressed rates.

The isolation of the different types of charm mesonic decay amplitudes need

much more work, especially with regard to F decays. Charm lifetimes are

very important, and have not been well measured. In addition to weak decay

physics, there is the spectroscopy of charm baryons and meson resonances.

The characteristic of the above studies is the need for lots of clean data,

with the production mechanisms of little importance.

There are also important charm studies which are unique to the fixed

target environment. Here an understanding of production dynamics is the

goal, and these questions can be isolated by using appropriate beam par-

ticles and experimental targets. In photoproduction, for example, there is

some hope of isolating the photon gluon mechanism and measuring the gluon

structure function.

B. The Fixed Target Problem

While fixed target experiments hold the promise of high charm rates

they have, so far, not been very productive. The reason is that while

charm cross sections are large, background cross sections are 200 times

and 1000 times larger for photoproduction and hadroproduction, respectively.

The most fundamental consequence of this dilute charm signal is that the

signal can not be isolated from the background. Furthermore, since a good

trigger has not yet been devised, very large quantities of data must be

recorded and processed.

C. Experiment E691

The goal of the tagged photon spectrometer collaboration (E691) was toisolate the largest possible sample of clean charm events. In order to dothis, advantage was taken of three technological advances to solve the fixedtarget problem.

45

CT120

80

40

ALL CUTS

To separate the signal from background the experiment relied on silicon

microstrip detectors (SMD's)2'3 to provide a high precision measurement of

the location of the charm decay vertex. Since charm decays weakly, these

vertices are separate from the primary production vertex, providing a power-

ful signature for charm events. In addition, the tracks from the decay ver-

tex are identified, greatly reducing combinatorial backgrounds. In Fig. 1

a mass plot of the D ->-K~TT TT (particle and antiparticle data are combined

throughout this paper) is shown where

vertex cuts have been applied. These

cuts have reduced the background by a

factor of about 300 with a loss of

^30% of the signal. This state is,

for practical purposes, unobservable

without the vertex detector.

The second important techno-

logical advance, from which this ex-

periment greatly benefited, was the

Tevatron. The high proton energy

was essential for achieving a suffi-

cient flux and energy in the tagged

photon beam. Combined with the su-

perb duty factor of greater than 33%,

this enabled us to record a data

sample of about 103 events. This

data was recorded between March

and August, 1985.

Finally, to process all of thisdata, we plan to use the fast, cost-effective, computing power availablewith the Fermi lab Advanced ComputerProgram (ACP).

D. Charm Lifetimes

J I1.76 1.84 1.92

K7T7T MASS (GeV)2.0

Fig. 1. Mass histogram of KTTTTusing Cerenkov and vertex cuts.

The vertex detector, which solves the problem of reducing background,is also ideal for measuring lifetimes in the range 1 0 " 1 3 < T < 5 10"la seconds.The lifetime resolution is given very approximately by,

46

where CK is the proper time resolution of the detector, T is the particle

lifetime and N is the number of events (assumed to be background free).

Past experiments have suffered either from a poor a., or from a small N.

In E691 at is .04 10"12 seconds so that a^. T//N and the statistics from

the 15% of the data which has been reconstructed so far is adequate to mea-

sure Tp and to make very good measurements of TDe and T +.

The remainder of the presentation will involve a very brief discussion

of the experiment, with the emphasis on the vertex detector. A discussion

of our experience in utilizing SMD's will be given, followed by our lifetime

results. Then a brief review of previous charmed meson lifetime measurements

will be given. Finally, I will make some observations on the future of fixed

target charm and SMD detectors.

II. EXPERIMENT E691

The experiment made use of the tagged photon spectrometer shown in

Fig. 2. The spectrometer has been improved by the addition of more Cerenkov

01

a|H

Be target

-,

\

D2

\

«SMDPlanes

Hodrofi Calorimeter

35 Drill Chamber \ / F l n t l y S e g m e n t e d

Planes \ / Electromagnetic2 Gas Cerenkov Calorimeter

2 Large Aperture CountersMagnets

•n.K/p s.p«r«iMi > eGiv Muon IdentificationTT. K . P > 20 G«vTT/ tc .p >37G«v

Fig. 2. The Tagged Photon Spectrometer.

47

cells and drift chamber planes, and by 9 SMD planes just downstream of the

5 cm Be target. The spectrometer has a mass resolution of about 10 MeV at

the D mass and separates IT'S from K's from 6 to 37 GeV.

The 260 GeV electron beam provided ^1.5 107 tagged photons in the range

from 100-225 GeV during each Tevatron spill. The experiment made use of a

calorimetric based trigger which led to the recording of about 2000 events

per spill (with a 60% livetime) with a transverse energy greater than 2 GeV.

This trigger accepts 40% of the total cross section and is about 80% effi-

cient for charm. There is one Tevatron spill per minute, and each corres-

ponded to the recording of 25 charm events. About ~\% of these events decay

to advantageous modes and are cleanly reconstructed with low background.

t5 cm

I5 cm B»Torgtt X Y V X V XV

0 x -20.5 oeg

25 cm

Acceptance - 100 mrad

Fig. 3. Layout of the silicon microstrip detector system.

A layout of the 9 SMD planes is shown in Fig. 3. The planes are ar-

ranged in 3 views as indicated. The first three planes are each 1" square

and are composed of 512 strips spaced 50 microns apart. The latter 6 planes

are 2" detectors with the same strip spacing. The middle three planes were

only 75% instrumented giving a total of 6840 readout channels.

A minimum ionizing particle leaves about 25,000 ions in the 300 micron

detector thickness. This signal is amplified by a preamp located close to

the detector and then coupled to a discriminator-shift-register based readout.

The discriminator thresholds were set just below half of minimum ionizing so

that the efficiency of 95% is dominated almost completely by the fraction of

functioning channels. The strobe signal for the system was 50 nanoseconds

wide, which resulted in a rate of electronic noise hits of about one per plane.

48

III. USE OF THE VERTEX DETECTOR

The vertex cuts are made in terms of the ratio, AZ/oz where AZ = yvt is

the measured vertex separation, a' is the error on this separation, and t

is the proper decay time. The error o' is proportional to the error a^ in

the location of the decay vertex az oy/9, where or is the transverse posi-

tion error in the location of a track ( 20 microns) at the vertex, and 9 is

-UP

200-

210

160

80

0

1

-I\ .• Kflj

•

(b)

a typical opening angle of the decay. Since 9 m/E = 1/y, AZ/az is in-

dependent of y and is typically %15t for our experiment, where t is in pico-

seconds. Similarly, the proper time resolution, cr. = a /vy - a /c, is also

independent of y and is about .04 picoseconds. In practice these quantities

are computed for each event and in-

clude the effect of multiple Coulomb

scattering, which has a large effect

for tracks of less than a few GeV.

The signals are cleaned up by

accepting only those decays where

AZ/az is greater than a cut, a,

which is chosen to be between 5 and

10 depending upon the particle life-

time and backgrounds. To illustrate

the effects of the AZ/c' cut, histo-

grams of K-rr masses are shown in Fig. 4.

In Fig. 4a the cut, I/a'z > 3 has al-

ready been imposed. With no cut this

signal would be barely visible. The

effect of increasing the cut is shown

in Figs. 4b, 4c and 4d. We note that

the background below 1.7 GeV is at

least partially due to the decay Km"

where the IT3 is unobserved. In Fig. 5

1.6 1.8 ZD Z2K-PI MASS. GeV

1.6 1.8 2.0 22K-PI MASS, G«V

1.6 1.6 2.0 2.2K-PI MASS,G«V

Fig. it. The K~TT mass spectrafor different vertex cuts.

49

we show a display of a typical D°

event in the three x plane detectors,

where the X and Z scales differ by a

factor of 10 to exaggerate the angles.

A blowup of the vertex region is shown

in Fig. 6 for the same view as shown

in Fig. 5. The ellipses shown indi-

cate the 3 standard deviation bound-

ary of the found vertices. Tracks 1

and 2 are the two tracks from a D°->-KTT

decay. The power of three views is

illustrated by Fig. 7 where track 5

appears to be associated with the

decay, although it is clearly separa-

rate in the other views. These fig-

ures also illustrate a problem which

must be dealt with in lifetime mea-

surements. In about 20% of the events

- 4 0 A 8 12 16 202-COORDINATE (cm)

Fig. 5. The hit pattern for theX SMD's in a typical charm event.

-1.4 -1.4

-2.2-0.15 -0.14 -QI3 -0.12

X-COORDINATE (cm)

Fig. 6. Blowup of vertex regionin the X view for the same eventas Fig. 5.

-2.2

I I I

0.19 0.20 0.21 0.22 023V-COORDINATE (cm)

Fig. 7. The V view of thesane event as Fig. 5.

50

more than one possible primary

production point can be found.

In Fig. 8 we see a I)0 decay from

a D with the IT from the pri-

mary vertex. This figure also

shows a common feature; the

event appears to have a second

charm decay. This aspect of our

data has not yet been analyzed,

but will soon have a high pri-

ority.

The data in the SMD's is

very clean. As a consequence we

have rewritten our track recon-

struction programs so that tracks

are first found in the SMD's, with

angular errors of v ! 5 mrad, and

then projected through the Drift

Chamber System. Unused Drift

chamber hits are then used to

find strange particles which de-

cay downstreams of the SMD's.

-1.04 -1.02 -1.00Y-C00RDINATE (cm)

Fig. 8. Vertex_blowup of eventwith D*~-»DoTr , 5°-+K+ir"". Eventcontains possible second charmvertex.

IV. LIFETIME MEASUREMENTS

Charm meson lifetime measurements are of great importance. The first

indication that charm decays proceed through other than the external spec-

tator diagram was first given by the observation of unequal D+ and D* life-

times. The measurement of the ratios of charm meson lifetimes is important

in determining the different amplitudes from the measured branching ratios.

The ratio T D + / T D O has been determined from the ratio of semileptonic

branching ratios of D° and D . This method depends, however, on ignoring

the Cabibbo suppressed non-spectator contribution to the D+ decay. It is

therefore important to measure this ratio directly.

The charm particle lifetimes are measured by doing a maximum likelihood

fit to the proper decay time distribution. In order to avoid the large back-

bround region and to reduce the problems in primary vertex identification,

51

the proper time is computed from the distance of the secondary decay from a

locatn

amount

location z m i n, which is chosen to be downstream of the primary by the

VJ7 "

zmm=a<rz'

In order to avoid biases and to minimize systematic effects we use the

following procedure:

a) The candidate charm particle forms a good decay vertex with a

chisquare per degree of freedom of less than 3.5.

b) All possible primary vertices within ±80 microns of the charm candi-

date flight path are found.

c) In about 20% of the events there is more than one such primary, and

if it is not obvious which is correct, the most downstream possible primary

is chosen. No knowledge of the secondary vertex z location is used in

this choice.

d) For the D° and F case it is determined from the charm candidate

momentum whether the particle would have passed the first SMD plane before

a proper decay time of 4 lifetimes from the primary vertex. If so the event

is excluded without using knowledge of where it actually decayed.

In this procedure the major mistake to be avoided is the situation in

which the particle is actually produced downstream of z m 1 n.

In order to understand the systematic effects, and to make corrections,

we have done a thorough Monte Carlo study by subjecting many simulated

events to the full reconstruction and analysis chain. This process takes

into account possible z dependent acceptance effects in the SMD system, the

absorption of the charm particle or its decay products, possible primary

vertex problems and detector resolution. From these Monte Carlo studies we

have evaluated a correction function, R(t) = 1 + at. Since the corrections

are small in all cases the Monte Carlo studies indicate that the results are

insensitive to the form of R(t). The data are then fit to the function

N-R(t) e" 'T + B(t), where N and T are free parameters, and the background

function, B(t), is determined from the proper time dependence of the side-

52

OB 1.2 IJBT(IOH2sec)

TT with the D° *+Fig. 9. Lifetime plots for D°-»-K TT with the D° associated with the DIn Fig. 9a the number of events is shown vs. the proper time, with thebackground shown by the lower dashed line. The mass distribution is shownin the inset. The upper dashed line is the fit described in the text.In Fig. 9b, background subtracted data is compared with the relevant fiton a semilog plot.

0.6 1.2

T(IO"'2sec)0.6 1.2

T(lO"l2sec)

Fig. 10. Lifetime plots for D°->-K~TT -TT~TT+ with the D° associated with the D +.The information is the same as described for Fig. 9.

53

bands of the mass distribution. In all cases the fit is made to a region

extending to 4 lifetimes. In Fig. 9 the proper decay time distribution is

shown for the mode D°-+K"TT+ where the D° is required to come from a D decay.

The mass distribution for this case is seen to be essentially background free.

For the linear plot the data is fit to the sum of background + foreground as

described above. For the semi log plot the background has been subtracted

from the data. The results of this fit are given in Table I.

In Fig. 10 the data are shown for the decay D°-H<~7T TT'TT , again using

the D*+ trick. For this mode the corrections due to a z dependent acceptance

and for absorption are larger, vio% as indicated in Table I. The result,

however, agrees well with that for the KIT mode.

The data for mode D°-»-K~TT+ is shown in Fig. 11, where those events used

in Fig. 9 are excluded, to have a statistically independent sample. Here

the background is significantly larger but again the results, as seen in

Table I are in good agreement. The simultaneous maximum likelihood fit to

all these modes gives a result,

T D O = .44+.02±.02 10"12 seconds,

where the second error is systematic and has been obtained by a careful

Monte Carlo study of the various effects. The net correction of -.02 10"12

sec. has been determined from a fit with R(t) set to unity.

TABLE I

Summary of Prel iminary D° L i fe t ime Results Based on15% of the Data

a Signal Bckgnd Corr TDO 10" 1 2 sec

D*++D°7T+ 5 198 7 - .00 .43±.O4

D*++D°TT+ 7 173 17 - .04 .42±.O45

D°-*-K"TT+ 8 351 168 - .03 .45±.O3*+

(Excluding D )

Combined 672 192 - .02 .44+.02+.02

54

ISO

120

80

1

T(IO~l2sec)

o2

10

1

i \ i ^

•

—

i i i I

DP-

(b)

1

• K "

i

mm

-

0.6 1.2

T (I0"12 sec)

1.8

Fig. 11, Lifetime plots for D°-*K~TT where the events of Fig. 9 have beenexcluded.

150

100

50

0

1

-

11

-1

_

-

\11

\

Mn

\\

1

1 - .

\ -

1

120

60

an

o

1

1.76

]

i

1 '

1 ALU CUTS'

-

•

-

-

-

_

1*1 1.92 2.0 -K7T7T MASS IGeV!

(a )

2r : :L<:-

_

M i

I ~—

D+-*K~7r+-7T+_

(b)

_ j I I I I I I

T(IO~'2sec)Fig. 12. Lifetime plots for D ->-K~Tr ir

T(IO"l2sec)

55

The procedure for determining the D+ lifetime is the same, except for

the treatment of the cases where the D+ might decay after the first SMD

plane. In the D+ case the event is kept if the first plane is at least 2

picoseconds downstream of z m i n, similar to the D° case above. While our

acceptance for decays after the first plane is still large, we avoid system-

atic errors associated with a changing acceptance by not using events decay-

ing downstream of the first plane. An analytic correction is made for lost

events with decay times between 2 and 4 psec, which explains the non-exponen-

tial shape of the curve in Fig. 12. We find the D lifetime,

T D + = 1-09*-°7 + .06 10"12 sec,

based on 475 events. The correction in this case is -.14 10" 1 2 sec.

It is interesting to compare our lifetime ratio,

TD+/TDO = 2.5 ± .2 ± .1,

with the ratio of semileptonic branching ratios,

Br(D+V"X) = 2 3+.5Br(D°-HS+X) " -.4 '

measured by Mark III. The directly measured lifetime ratio is approaching

sufficient precision so that a better measurement of the semileptonic branch-

ing ratios would set limits on the Cabibbo suppressed contribution to the

semileptonic decays.

We study the state F in the (j>ir mode. In Fig. 13 a typical inclusive

4H-K K" mass spectrum is shown. A very weak cut is applied to clean up the

F signal. For the spin parity sequence, 0"-*l"+0~, a cut on |cos0|» .3

keeps 97% of the signal where 0 is the angle between the K and ir in the <f>

frame. This cut eliminates 30« of the background. In Fig. 14a we see the

F -+<J>TT as well, as the Cabibbo suppressed D+-H}>TT+ (none of our mass plots

include an approximately .2% mass scale correction). In Fig. 15 the data+ + 1 ?

is plotted vs proper time. We determine an F lifetime of Tp+ = A0_'Lg ±

.06 10~ 1 2 sec based on 19 events with 4 background.

In Fig. 14b events are plotted in which the decay time is longer than

.4 picoseconds; it is clear that the F lifetime is significantly less than

that of the D+.

56

From the data shown, and cor-

recting for the F+ and D events

lost because of short decay times,

we find the ratio of cross sections

times branching ratios,

p»Br(F -

V. REVIEW OF CHARM MESON LIFETIMES

The current situation with D

lifetime measurements is shown in

Table II. This plot does not in-

clude past measurements with very

large errors or results in which

the identification of the charm

particles was ambiguous. My selec-

tion also indicates a bias toward

12-

1.80 1.88 1.964>7T MASS (GeV)

2.04

Fig. 14a. Mass spectrum for+ + and + +

1 1 1 r— 1

1.00 1.04K+K~MASS (GeV)

uoe

Fig. 13. Inclusivespectrum.

mass

130 1.88 1.96 2.04<t>TT MASS(6eV)

Fig. 14b. Mass spectrum forD+-*<Jnr+ and F+-+<(nr+ for propertimes greater than .4 15~*2 sec.

57

results which have appeared in published

form. The open data points indicate ei-

ther new measurements, or final results

from old measurements, made available since

the Kyoto Symposium in August 1985. The

plotted errors are statistical and system-

atic added in a quadrature.

It is interesting that these results

are made by very different techniques.

The first group employs high resolution

bubble chamber technology coupled with ex-

ternal equipment. The e e~ measurements use

high resolution ( 90 microns) vertex drift

chambers. The new Cleo results were just

presented at the Washington meeting. This

group has made a breakthrough in their reso-

lution and they expect to soon reduce their

errors significantly. Experiment E531 has

just published their final results using a

4-

2-

2.0

TOO '"sec)Fig. 15. Lifetime plot for

the F+. The lower dashed

line is the background.

TABLE II

World Data on D° and D Lifetimes. The Crosses Representthe Averages Computed for the 1985 Kyoto Symposium

* • ' - 0 . 9

4.4l°J±0.26.1 ±0.9 ±0.3

; ! ±0.5

4.5 + 1.4 +QB

«±'*1&4.4 ±0.9 ±0.5

+0.7 +0.1- 0 . 5 - 0 . 2

, 7 + I . O -°-' -0.7 "4.4 ±0.2 ±0.2 O

4.35+0.32 •*• KWA

2 4.rH3

BCNA 16 LEBCNA 27 LEBC

BC 72-3-5

E*E~DCMARK IIHRSDELCOCLEO

EM SPECTE 531

SMDNA II

TPS

BAt\%1 1 . 6 1 " ±0.6

•12.1 ±4.0 ±2.0

KWA -*• 9.01+075

l -2.9

10.611510.9 l p "

sec.4 8 12 16

sec.

58

hybrid emulsion-spectrometer technique.

The SMD measurements were pioneered by the ACCMOR collaboration in Exper-

iment NA11. They have more data and new results should be available soon.

The new TPS measurement of T n 0 is comparable in precision with the pre-7vious world average (4.35±.32 TO"13 sec) given by Thorndike at the Kyoto

meeting and is in excellent agreement. The TPS value for Tp+is slightly

larger than the Kyoto world average of 9.01+.74 TO"13 sec.

The data on F+ lifetimes8 is not as abundant or as precise, as is seen

in Table III. The E531 value is their final result just published. The HRS

and TPS values are determined exclusively from the 4>TT mode while NA11 uses

the K+K"TT+ final state. Since these results are all dominated by statistical

errors I have computed a combined average of Tp+ = 3.5_'g.

VI. CONCLUDING COMMENTS

A. Future Direction for the E691 Analysis

In Table IV are shown the projections of the total number of events in

some clean modes for the E691 data sample. The numbers are larger if less

stringent cuts are applied. With this data we plan to address the follow-

ing problems:

1. Measure D° and D lifetimes to a precision of a few percent.

2. Search for A and measure its lifetime.

3. Look for D°-Da mixing using the

sample of D^KTT from D*'s. We note that

mixing has a characteristic proper time

dependence <vt2e" 'T which can be used to

distinguish it from double Cabibbo sup-

pressed decays. We estimate a sensitiv-

ity of < .5%.

4. Search for double Cabibbo sup-

pressed decays.

5. Search for other F decay modes.

6. Look for charm resonances and

other aspects of charm spectroscopy.

7. Production studies. We will

measure ratios such as D°/D+, D°/D*,

TABLE I I I

World Data on F Lifetimes

F+ LIFETIMES

E53I 2 .6 ! i |DIFFERENT MOOES

NAII 3.l!i;|F*-»K+K~ir*

HRS 3.5tf£±o.»

TPS4.Oti|±o.«F+-» + 7T+

COMBINED

°-D -0.51 1 1

59

D+K"- + +TT TT

- +TT

*vD°+K~Tr+

F+->-<i>T

HC"ir T

+r

(loose

(tight

r IT

cuts)

cuts)

3000

4500

1800

1000

1000

125

TABLE IV

Projected Signals from Full Data Sample

Channel Signal Background

900

1000

300

35

200

30

0°/D°, D /D" and study the Xp and PT dependence of various quantities.

8. Study correlations between the two charm particles in the same

event. Hopefully this will help isolate the different production mechan-

isms. If nature is kind we may be able to measure the gluon structure

functions.

9. New good ideas.

8. Future Fixed Target Charm

Given the luminosity limit of SPEAR, fixed target experiments appear

to offer the only possibility for collecting the much larger charm samples

needed. So it is worthwhile to see what is possible at the Tevatron.

We note first that E769 (which includes some members of the TPS col-

laboration) has been approved to use the same equipment but with incident

pions and kaons. To compensate for the factor of 1/5 in richness of charm

in hadroproduction, the data acauisition will be speeded up by a factor of

about 4. This data could be written directly to tape but the experimenters

Intend to use ACP based computing in the data acquisition system to filter

the events to be written to tape. This filter would depend upon sensing an

impact parameter from the SMD detectors.

With the same system, but going back to the tagged photon beam, an ex-

periment could be done in one running period in which ^40,000 clean charm

events could be collected. This represents the flux limit in that beam.

60

The new Fermilab wide band beam has about a factor of 5 more flux, so

one could contemplate a run there producing ^200,000 clean charm events.

This would require further cleverness in the trigger and the electron pair

flux might present problems for the drift chambers.

Hadron beams do not have the pair flux to contend with and have much

higher possible charm rates. On the negative side, the multiplicities tend

to be larger and the intrinsic signal to background is worse. The major

problem, however, is still that of achieving a trigger which is open for re-

constructable charm while having a high rejection of non-charm events. With

sufficient ingenuity, I believe that such a trigger can be developed and

that data samples of millions of clean charm events will be recorded.

C. Creativity with SMD's

The E691 SMD system was built with 1983 technology. A striking feature

is the enornous ratio between the volume of associated PC boards, cables

and readout electronics, and the volume of the actual detector planes.

Smart people are working hard to circumvent this problem, which now severely

limits the use of SMD arrays, by developing special integrated circuits to

be located at the edge of the silicon plane. With this problem solved,

there will be great latitude for creativity in the uses of SMD's in experi-

ments. One could contemplate dramatic new approaches like all-silicon micro-

spectrometers and "silicon bubble chambers". It should be lots of fun.

We wish to acknowledge the assistance of the staff of Fermilab and of

all the participating institutions. This research was supported by the

U.S. Department of Energy, by the Natural Science and Engineering Research

Council of Canada through the Institute for Particle Physics, by the National

Research Council of Canada, and by the Conselho Nacional de Desenvolvimento

Cientifico e Tecnologico de Brasil.

61

REFERENCES

1. See for example the talk at this conference by John Brown. There are

many theoretical papers on the weak decays of charm mesons. Some of

the more recent ones, J.F. Donoghue, Phys. Rev. £33, 1516 (1986),

M. Bauer and B. Stech, Phys. Lett 152B, 380 (1985), I.I. Bigi, Phys.

Lett. 169B, 101 (1986), L.L. Chau and H.Y. Cheng, Phys. Rev. Lett. 56,

1655 (1986).

2. Silicon microstrip detectors were developed by Erik Heine and co-workers

at CERN and by J. Kemmer and co-workers at the Technische Universitat,

Miinchen. They were first used in High Energy physics by the ACCMOR

collaboration in experiment NA11 (refs. 6 and 8). Use with MWPC read-

out for this experiment is described in ref. 2.

3. P. Karchin, et al., IEEE Trans, on Nucl. Sci. NS-32, 612 (1985).

4. See, for example, K. Sliwa, et al., Phys. Rev. D32, 1053 (1985) and

references therein.

5. R.M. Baltrusaitis, et al., Phys. Rev. Lett. 54, 1976 (1935).

6. The references for D lifetime measurements are the following:

NA16 M. Aguilar-Benitez, et al., Phys. Lett. 123B, 312 (1983).

NA27 M. Oori, Bari Conference (1985).

B672-3-5 John Butler, SLAC-290, UC-34D (1986).

MARK II L. Gladney, Ph.D. Thesis, Stanford.

DELCO H. Yamamoto, et al., SLAC-Pub-3628 (1985).

HRS P. Barringer, et al., Contribution to the 1985 Symposium on Lepton

and Photon Interactions at High Energies, Kyoto (1985).

CLEO P. Haas, et al., Washington APS meeting (1985).

E531 N. Ushida, et al., Phys. Rev. Lett. 56, 1767 (1986), and N. Ushida,

et al., Phys. Rev. Lett. 56, 1771 (1986).

NA11 R. Bailey, et al., Z. Phys. C. 28, 357 (1985).

7. E.H. Thorndike, Proceedings of the 1985 International Symposium on Lep-

ton and Photon Interactions at High Energies, 406 (1985).

8. The references of r lifetimes are the following:

NA11 R. Bailey, et al., NIKHEF-H Report 85-5 (1985) and Proceedings of

the Conference on Hadron Spectroscopy, College Park, MD, USA (1985).

HRS C. Jung, et al., Phys. Rev. Lett. 56, 1775 (1986).

E531 N. Ushida, et al., Phys. Rev. Lett. 5J5, 1767 (1986).

63

Review of Charm Quark Physics

John S. Brown

Dept. of Physics

University of Illinois

Urbana-Champaign,Illinois,61801

Abstract

A review of recent developments in the field of charm physics is presented.

Measurements of the mass of the F* and F* provide tests of our understanding

of the charmed meson spectroscopy. The recent results on the lifetime measure-

ments of the D and F mesons are reviewed. The latest results on the production

cross-sections and inclusive and exclusive decays of the D mesons are discussed.

Finally, the latest results on J / 0 exclusive decays and their implications are re-

viewed with emphasis on the status of the ((2240) and the glueball candidate

0(1720).

64

1. Introduction

Twelve years have passed since the discovery of charm.' In that time a rich

body of physics has been uncovered on the charm quark, its spectroscopy and

its decays. The discovery of the ip family and the charmed mesons firmly estab-

lished the quark picture and was a stunning confirmation of the GIM mechanism

which later became one of the fundamental postulates of the standard model. *

Throughout this period, the e+e~ machines have played an essential role in devel-

oping our understanding of charm physics. At these machines the 1 members

of the charmonium family (bound states of cc) are copiously produced with very

small background. Since the produced charmonium state decays at rest in the lab

frame, the final state particles tend to be scattered evenly over the entire solid

angle of 47r and thus place less demands on detector technology. In contrast, at

fixed target machines and even at hadron colliders the final state particles tend

to be scattered at a small angle relative to the incident beams. Another benefit,

arising from the relativistic kinematics of the e+e~ annihilation, is that the 1

charmonium state has its angular momentum parallel to the collision axis. This

information is useful in spin parity analyses. Finally, because of their copious

production, narrow width and multiple decay channels, the J/if> and ijt have

proven to be factories for the production of light hadrons, and are an important

tool for understanding the hadron sptctroscopy below 3 Gev.

2. Charmonium Spectroscopy

One of the first impacts of the 1974 charm discoveries was to establish the

validity of the quark picture. Since the charm quark is so massive compared to

typical hadronic binding energies non-relativistic potential models could be used

to accurately explain the charmonium spectroscopy. The potential models were

then extended to include the u, d and s quarks. Later with the discovery of the T,

these simple phenomenological models were successfully extended to the b quark-

bearing mesons. At about the same time, Quantum Chromodynamics (QCD)

65

was emerging as a viable theory of the strong interactions. QCD was then used

to motivate some of the potential models. Figure 1 summarizes our experimental

knowledge of the charm quark-bearing states. The most prominent member of

the charmonium family which remains to be discovered is the IP 1 state. This

state is difficult to produce at «+e~ machines since it must be produced from the

vector state via $ —* n°lPl with an expected branching ratio of ~ 10~3 or via

V> —* IVc with an expected branching ratio of ~ 10~8.

The latest tests of the theory are the F+ and F* mesons. The F+ is par-

ticularly interesting. The early measurements of the F+ mass centered about a

value of 2040 Mev, which was in contradiction to the potential model predictions.

However, the latest measurements are now ~ 1971 Mev and are in reasonable

agreement with the predictions of the potential models. The F* is the most

recently discovered charmed meson. Seen by the HRS and TPC collaborations

as a narrow state which decays to a photon and an F+ meson, the F* has also

recently been seen by the MARK III collaboration in the associated production

channel e+e~ —* FF*. The F* is found to have a mass ~ 130 Mev higher than

the mass of the F + which is in agreement with the predictions of the potential

models.

3. Charmed Meson Weak Decays

Just as for the strange quantum number, the charm quantum number only

changes in weak interactions, thus charmed meson decays provide important tests

of our understanding of the electrowcak sector. Recently, some fundamental

issues in the area of charm decay have been re-examined with surprising results.

New measurements of the production cross section for the JD+ and D° have been

performed. Several new measurements of the lifetimes of the £>+,£>° and F+

mesons have been completed and also the ratios of the lifetimes of the D+ to /?°

have been studied. In addition, the first measurement of the D form factor has

66

Charmonium Family Charmed Mesons

4.5 -

O

enen

4.0 -

3.5

3.0

V»(4.

1—

h -

i>, \—

Vc

j/n

i—Vc

' 1 !

41)

H

16)

H

1—I—

f—

1

1 1

H X2•1 X l -

i Xo

i

IS0 ZSl3Fn 3D1

cu cd cs

Charmed Baryons

cuu cus esscud edsedd

Figure 1. Spectroscopy of charm states.

67

been completed and recent measurements of rare D meson decays have improved

our understanding of charmed meson decay mechanisms.

The measurement of the production cross-section for the D mesons is im-

portant not only for normalizing D branching ratios, but is also important to

other areas such as B meson research. Previous measurements have relied on a

measurement of the cross-section of the V* anQ" have assumed that the ip de-

cays exclusively to D's. A recent measurement by the MARK III collaboration

uses a double tagging method to absolutely measure the cross-section. The

technique uses three DQ decay modes (K~ir+, A'~7r+7r"7r+, and K~ir*ir°) and

four £>+ decay modes (K~ir+it + , K~it+n+iroyK°Ti+ and K^n+ir°). By compar-

ing the number events with a single reconstructed D(OT D with the number of

events with both a reconstructed D and D the cross-section can be inferred. The

MARK III collaboration finds oDo - 4.48+;^ ± -37 nb and oD+ - 3.35+;^ ± .24

nb where the first error is statistical and the second error is systematic. These

are substantially different from previous results (cr u = 7 - 12 nb and apt = 6 — 9

nb). If these results are correct it may imply that ^ has substantial non-Z? decay

diodes. This issue is currently under investigation.

Early measurements of tho D+ and D° lifetime indicated a large difference

between the lifetime of the D+ and the D° . ' This was surprising since in the

naive spectator quark mode] the lifetimes should be determined by the coupling

of the charm quark to the weak current and, hence, should be equal for the £?+

and the D° as well as for the F mesons. Recently two precise determinations of

this ratio have been performed. The TPS collaboration has performed a direct

measurement of the lifetimes of the D+,D° and the F+ mesons using a silicon

microstrip detector at a fixed target machine. These beautiful results have

been presented at this conference and I refer the reader to the accompanying-

article in this conference report. They have measured the following lifetimes:

rm = 1.09+;$ ± .06 x 10" 12s

TDO = .44 ±.02 ± .02 x 10" 12s

68

TF+ = .40i;£|± .06 x 10 "12s

from which they find:

The MARK III collaboration have also performed a measurement of the ratio

of the J5+ to D° lifetimes using an indirect method. Measuring the inclusive

semileptonic branching ratios for the £>+ and the D° and assuming that Cabbibo-

suppressed decays are small the ratio of lifetimes should be equal to the ratio of

the inclusive semileptonic branching ratios. The MARK III collaboration finds:

£(£>+ -* e+AT) = 7.5 ± 1.1 ± 0.4 %

B(D° -> e+A') = 17.0 ± 1.9 ±0.1 %

from which they infer:

_ 2 3 + o . srDo

Both lifetime ratio measurements are in reasonable agreement with the previous

world average of 2.5 ± 0.6.

Certainly the lifetime of the D+ is different from the lifetime of the D° by,

a factor of ~ 2. One can add corrections to the naive spectator model, but most

corrections preserve the equality of lifetimes. Some of the possible corrections

which could lead to unequal lifetimes are illustrated in Fig. 2. The first possibility

(compare Fig. 2a and 2c with Fig. 2b and 2d) is that there may be destructive

interference between the external W emission diagram and the internal W emis-

sion diagrams. Since this only applies to the D+ meson, the relative lifetimes

between D + and D° could become different. Internal W exchange (see Fig. 3)

69

Figure 2. £» meson weak decay inteference. Interference between diagrams

(a) and (c) can alter the lifetime of the D+ relative to the D°.

u

Figure 3. W exchange diagram.

70

which applies only to D° decay could lead to smaller D° lifetimes, but this dia-

gram should be Cabbibo-suppressed. To substantially change the lifetimes, this

suppression would have to be lifted. Which of these mechanisms are occurring?

To study this the MARK III collaboration has examined several exclusive decays.

Examining D+ decays they find:

= .29 ±.08 ±.05B{D

This is rather large and is suggestive that destructive interference is at work.

Many theorists have proposed that the decay channel D° —> K°<f> would be solid

evidence for the presence of the internal exchange diagram, however, other

theorists have proposed that quark rescattering may also lead to large branching

ratios for the above process. Several groups now claim to have detected this1

mode. The ARGUS collaboration has measured B(D° -> K°4>) = 1.4 ± 0.4%,

while the CLEO collaboration has measured B(B° -+ K°4>) = 0.9 - 1.3%, and

the MARK III collaboration finds B(D° -* K°4>) = 0.7 ± 0.5 ± 0.2%.'"" These

measurements are at quite large levels and are larger than expected for a purely

Cabbibo-suppressed W exchange diagram.

4. Charmomum and Light Hadron Spectroscopy

The J/ip and t/» are both produced below the threshold for strong decay to

charmed mesons. They also are copiously produced with little background at

e+e~ machines. In addition, their narrow widths enable the use of constrained

kinematic fits. This analysis tool can provide significant improvements over the

intrinsic experimental resolution of the momenta and energies of the final state

particles in any particular exclusive final state. We believe that we understand the

structure of the J/i/> and ip so well that we now use these particles as probes of the

hadron spectroscopy below 3 Gev. Both these states have been studied intensively

since their discovery, but in the last few years there has been a dramatic increase

71

in the size of the world collection of J/i}> events. The DM2 collaboration now

has 8.6 x 10° produced J /^ ' s and the MARK III collaboration now has 5.8 x 106

produced J / ^ ' s . This increase in statistics allows a more accurate determination

of mass spectra and the spin-parity certain final states, and the examination of

rare decay modes.

The fundamental diagrammatic decay modes of the J/if) are shown in Fig. 4.

The largest decay amplitude is the 3 gluon diagram (see Fig. 4a). This diagram

leads to pure hadronic, isospin-symmetric decays. The electromagnetic decays

(Fig. 4b) produce both leptonic and hadronic final states and can violate isospin.

The radiative decays (Fig. 4c) will always have a final state photon as a signature

of the decay. The fourth diagram (Fig. 4c) is a special case of the radiative

diagrams where the T)C, the ground state member of the charmonium system, is

produced and decays. Each of these diagrams contains possibilities for probing

hadron spectroscopy. By studying the overall pattern of the J/ip decays to other

hadrons, information on the quark and gluon contents as well as the dynamics of

strong decays can be learned. By studying the Dalitz plots of the produced final

state particles, previously unknown states can be uncovered.

cC fiOOrons

(a) 3 Gluon

c

( c )

yhadrons

C hadrons

lb) Electromagnetic

haclrons

( d ) V i o 7} 5 B 4

' c

Figure 4. Lowest order Jji> decay diagrams.

72

QCD is currently an excellent candidate for the theory of the strong force

and of the hadron spectroscopy. Some rather unusual predictions arise in QCD.

Since the carriers of the color field (called gluons) themselves carry charge, there

is a possibility that gluons can be constituent members of QCD bound states.

Indeed, bound states composed of only gluons, the so-called glueballs, should

exist. Other possibilities are composites of quarks and gluons which have been

labelled meiktons or hermaphrodites, and the cryptoexotic states composed of 4'do]

or 6 quarks. Some of the signatures of these exotic states would be an excess

of hadronic states which could not be fit into the usual quark nonets, states

with quantum numbers which are forbidden to a bound state of 2 fermions (i.e.

quarks) such as Jpc = 1~+, and states with flavor-symmetric decays (but this

latter requirement is quite controversial).

Since the radiative decays of the J/V> are thought to be excellent hunting

grounds for 2-gluon bound states, this has been the most active area of J/if>

research in the past few years. In that time at least 2 candidates for glueball

status have emerged, the t and the B. In addition, a host of new unexplained

structures have been discovered. The most controversial of these new states is the

$(2240) which is a narrow state claimed to be seen by the MARK III collaboration

in the channels J/ij> -* iK*K~ and J/ij> —» ^KtKt.

As a first example, consider the decays of the t]c . Since the tjc decays via

annihilation of the charm quark into either 2 gluons or 2 photons, the resulting

hadrons should be flavor-symmetric, just as for glueballs. The MARK III collab-

oration has recently completed a study of the 1 1 decay modes of rjc. The

results are summarized in Table 1. Also shown are the reduced branching ra-

tios B normalized to the <f><f> reduced branching ratio. The predictions for SU(3)

symmetry are also shown. The measured pattern indicate a large violation of

SU(3) symmetry. Final states containing strange quarks seem to be favored over

non-strange quark final states. The lowest order graphs for the decay of the »?c

to gluons is shown in Fig. 5. The pp,uu and 4>4> decays can be produced by all

three mechanisms, while K*K* can only arise from the first and third diagrams

73

Table 1. T)C -*

Decay B(r?e -» )0

"1

B(,B(n

decays.

SU(3)

^(^ 0.8 ± 0.2

K'K* 0.9 ±0.5

pp < 1.4

wu < 0.31

CJC5 < 0.10

1 1

0.85 ± 0.47 4

< 1.08 3

< 0.24 1

<0.10 0

Table 1. IJC vector-vector decays. The measured brandling ratios B and

measured reduced branching ratios B relative to ^ are shown plus the prediction

ofSU(3).

( a )

nnrn

7 - 8 5 ' 5 1 7 O A 1 O

Figure 5. Lowest order TJC graphs.

74

and oj(f> can only be produced via the second mechanism. Clearly the K*K* indi-

cates that there is a substantial presence of the second mechanism, yet it if it were

dominant then it has been estimated that B[rjc —* <jj<f>)/B(rje -* <l>4>) = 0.60±0.05

which is clearly not the case.

We now turn to a similar analysis of the glueball candidate 8. The 0(1720) is

a prominent structure in Jji> radiative decays. It decays preferentially to final

states containing strange quarks. We consider the decay modes J/rp —* ^Xt <f>X

or uX where X is always the same. From the radiative channel we infer that X

is flavor symmetric. From the OZI rule, we infer that one of the quarks in the

<i>[u>) must share a world-line with one of the anti-quarks in X. Therefore, the

4> and u> sample the quark content of X. In Fig. 6 the mass spectra of the KK

system recoiling against i,u and <f> are shown. These results are from MARK

III but DM2 also has similar results. The peak at 1.525 Gev in Fig. 6a and

6c is consistent with an / while the broad peak at 1.720 Gev is interpreted as

the 5(1720). The 0(1720) is quite apparent in Fig. 6a and 6b and its presence

is suggested by the shoulder in Fig. 6c. Similar spectra for the TCK system are

shown in Fig. 7. Here, the broad peak at 1.27 Gev is interpreted as the / and

is quite apparent in Fig. 7a and 7c. The smaller 0(1720) peak is also present

in Fig. 7a and 7c and does not appear in Fig. 7b (but may be overwhelmed by

background). The large peak at .8 Gev is background from J/V> -+ pir and the

peak at .975 in Fig. 7c is probably the S*. Assuming that the peaks near 1.73

Gev are due to the 8, implies that the 8 decays are more flavor symmetric than

are the / or / .

The narrow peak at 2.2 Gev in Fig. 6a is the controversial £. It is seen

by the MARK III collaboration in both of the channels J / ^ -* iK+K~ and

J/if/ -* qKtK3 as shown in Fig. 8. The narrowness of this structure is most

intriguing. Narrow resonances are often a signal of new physics. The extreme

narrowness of the J/ip was the first hint of a new conserved quantum number.

The measured width of this structure is ~ 20 Mev. While exotic, this width does

not rule out an ordinary hadronic state. Possible interpretations of this state

75

c\>

0.9 1.3 1.7 2.1

S3/9A2 rn(K*K-) (GeV/c2) 4-«6

1.2 2 .0

~) (GeV/c2) *-8

Figure 6. The KK invariant mass

spectrum in the channel: a)

b) J/V -^ u/K+Jf-.

c) J/V- - • <f>K+K~.

Figure 7. The irn invariant mass spec-

trum in the channel: a) J/V> —*• f7r+jr~.

c)

76

are either A glueball or hybrid," a high spin qij meson,' or something else.

Unfortunately the state has not been seen by the DM2 collaboration and has

not been claimed in other channels. Clearly more experimental work is necessary

to establish the validity of this new state.

The above examples are only a small sample of the research currently active

on the 7/V> decays. Other areas currently under investigation are the patterns

of baryonic decays, the vector tensor decays, the vector scalar decays as well as

others I have not mentioned. With the large collection of J/i> data many areas

can be explored, yet till now only a fraction of these areas have been scrutinized.

5. Summary

In the twelve years since the discovery of charm, the energy frontier has

moved from the 3 Gev region of charm to the 100 Gev region of the W and Z°.

Still the charm region remains an actively pursued region of research. In part due

to charm research, the standard model has come to be established as the current

explanation of the electroweak and strong forces, yet important questions remain.

In particular, the tests of bound-state QCD states must be calculated and mea-

sured in order to establish quantitatively the validity of QCD. The calculations of

lattice guage theory are quite promising, yet they require further refinement and

strangely enough, better hardware (in computing capability). Our understand-

ing of the charmonium spectroscopy is primarily phenomenological and awaits ab

initio calculations of the form of the potential. Our understanding of the decay

of charmed mesons requires theoretical as well as experimental clarification. The

spectroscopy of the light hadrons and the predictions of glueballs and hybrids also

require careful theoretical calculation and experimental verification. Very little

is known about the charmed baryons, and only recently has much information

on the charm-strange mesons become available.

The future should bring improvements in our experimental understanding

of the charmed mesons and baryons as the experimental program at SLAC is

77

200

01

O

O

tr

1.0 1.5 2.0 2.5 3.0

t-B5 MASS (GeV/C2) SZ1SBS

Figure 8. Experimental evidence for the £(2240) state. These are the KK

mass spectra from MARK III from the channels: Jjij) —> ^K+K~ and J/ip —*

lKtKt.

78

continued, while the e+e~~ collider under construction in Beijing promises to

open a new frontier in ".harmonium research. The charm region continues and

will continue to be an excitir.£ ?.nd important area of elementary particle research.

Acknowledgements

I would like to thank Bob Panvini and the organizers of the Vanderbilt Confer-

ence for their hospitality and efforts to provide a warm and intimate atmosphere.

79

References

1. J.J. Aubert et al., Phys. Rev. Lett. 33, 1408 (1974).

J.E. Augustin et al., Phys. Rev. Lett. 33, 1406 (1974).

2. Many reviews of the standard model have been published. Eg. see:

H. Harari, Weak Interactions of Quarks and Leptons (Theory), Proceedings

of the Twelfth SLAC Summer Institute on Particle Physics,(1984)264-304.

3. For a review see:

C. Quigg and J. Rosner, Phys. Rept. 56 C,167(1979).


J. Lee-Franzini, Surveys H.E.Phys. 2,173(1981).

5. J. Rosner, Comm. Nucl. Part. Phys. 13,117 (1984).


K. Johansson, USIP Report 86-01.

7. H. Albrect et al., Phys. Lett. 146 B,lll(l984).

H. Aihara et a/., Phys. Rev. Lett. 53,2465(1984).

8. G. Blaylock et al., Contributed Paper to 23rd International Conference on

High Energy Physics (1986).

9. M. Frank and P. O'Donnell.Phys. Lett. 159 B,174(l985).

10. I. Peruzzi et al., Phys. Rev. Lett. 39,1301(1977).

D. Scharre et al., Phys. Rev. Lett. 40,74(1978).

R. Schindler et al., Phys. Rev. D24,78(l98l).

11. R. Baltrusaitis et al., Phys. Rev. Lett. 56,2140(1986).


K. Nui,Proceedings of the Europhysics Conf.(l984).

13. R. Morrison, these proceedings.

14. R. Baltrusaitis et a/., Phys. Rev. Lett. 54,1976(1985).

15. For an excellent review of D meson physics see:

D. Hitlin, D Meson Studies at the ip , Proceedings of the Twelfth SLAC

Summer Institute on Particle Physics,(1984)524.

16. S.P. Rosen.Phys. Rev. Lett. 44,4(1980).

M.Bander,D.Silverman,and A.Soni.Phys. Rev. Lett. 44,7(1980).

H.Fritzsch and P.Minkowski.Phys. Lett. 90B,455(1980).

I. .1. Bigi and M. Fukugita.Phys. Lett. 9lB,12l(l980).

A. .N. Kamal.U. of Alberta Preprint THY-3-85,(l985).

17. J.Donoghue.U. of Mass. ,UMHEP-241,(1986).

18. H. Albrect et al, Phys. Lett. 158B,525(1985).

P. Avery et al., —985 Int. Symposium on Lepton and Photon Interactions

at High Energy,(Kyoto 1985).

R. Baltrusaitis et al., Phys. Rev. Lett. 50,2136(1986).

19. For a general review of glueballs and other exotica see:

T. Barnes,The Exotic Atoms of QCD: Glueballs,Hybrids and Baryonia. In-

vited Lecture at the School of Physics of Exotic Atoms,Erke,Italy, (1984).

20. D. Scharre et al., Phys. Lett. 97B,329(l980).

C. Edwards et al., Phys. Rev. Lett. 48,458(1982).

21. W. Lockman.Invited talk presented at the Second Conference on the Inter-

actions between Particle and Nuclear Physics.Canada (1986).

81

22. H. Haber and J. Perrier.Phys. Rev. D32,296l(i985).

23. U. Mallik, Invited talk presented at 21st Rencontre de Moriond: Strong

Interactions and Gauge Theories, Les Arcs, Franco (1980).

24. B. Jean-Marie, Invited talk presented at Int. Symp. on Production and

Decay of Heavy Hadrons, Heidelberg, West Germany (J98G).

25. R. Baltrusaitis tt al., Phys. Rev. Lett. 50,107 (1986).

26. M. Chanowitz and S. Sharpe, Phys. Lett. 132B, 413 (1983).

B. Ward, Phys. Rev. D31, 2849 (1985).

2V. S. Godfrey tt al., Phys. Lett. 141B, 439 (1984).

28. M. Shatz, Phys. Lett. 138B, 209 (1981).

S. Pakvasa tt al., Phys. Lett. 145B, 134 (1984).

S. Pakvasa, et al., Phys. Rev. D31, 2378 (1985).

83

Production of Hadrons and Leptons at High p and Pairs at High Mass

Daniel N. KaplanFlorida State UniversityTallahassee, FL 32306

1 Introduction

The study of particle production at high transverse momentum (p )and pair production at high mass in energetic collisions betweennucleons has been a fruitful area of research for over a decade [1-3].The approach goes back to Rutherford [4] and is based on the notionthat scattering at high momentum-transfer should reveal the internalstructure of the scatterers. Nowadays these processes are analyzed interms of the parton model and Quantum Chromo-Dynamics (QCD). Previousexperiments by this collaboration confirmed the parton-scattering modelof large-p. and high-mass production [2] and discovered the T particles[3] and the fifth quark. The present experiment extends thesemeasurements to higher beam energy and improves resolution, particleidentification, and luminosity. Besides addressing QCD issues, thedata also allow limits to be set on the mass and lifetime of the axion.

2 Apparatus

Experiment 605 at Fermilab uses a large spectrometer designed todistinguish accurately pions, kaons, protons, electrons, and muons andmake precise measurements of their trajectories in the region near 90°in the center-of-momentum frame of the colliding nucleons.Measurements extend from a few GeV/c transverse momentum out to nearthe kinematic limit. The large "SM12" magnet (see Figure 1) deflectshigh-p charged particles around the beam dump and into the sensitivevolume of the detectors, while neutral particles produced in the targetare absorbed in the dump or in the magnet walls and shielding.Charged-particle trajectories are measured at three detector stationsby proportional and drift chambers, and consistency of the trajectoryupstream and downstream of the "SM3" magnet verifies that the particlewas produced in the target. Scintillation-counter hodoscopes at thethree stations furnish a crude measurement of the trajectory fortriggering purposes. Particle identification is provided by thering-imaging Cherenkov counter [5], the electron and hadroncalorimeters, and the muon proportional tube arrays located behind the

84

calorimeters and additional shielding. The large p kick of SMI2 (8GeV/c at full excitation) combined with the good resolution of thedrirt chambers (200 um r.m.s) yields mass resolution better than 0.2$r.m.s. at m - 10 GeV/ca.

MUONPROPORTIONAL

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10

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ELEVATION SECTION E-605MTTCHAMKH

PROPORTIONAL CMAMKR

COUNTER SANK

FIGURE 1 : Plan and elevation of the apparatus, showing Pbabsorber and Station 0 chamber which were added for the 1985run.

3 Rate Limitations and Chronology of Runs

Luminosity was limited by counting rates in the detectors. Themain problem was production of neutrals in the walls of SM12, whichcould then illuminate the detectors (see Figure 2). During our firstrun, in the Spring of 1982, this background limited our luminosity to 3x 10^ cm s~ . The next run took place in the Winter of 1984; this wasthe first run of the Tevatron, but at a beam energy of 400 GeV. Inpreparation for this run we lined the inner walls of SM12 withcarefully designed Pb and W absorbers and were thus able to operate at10-" cm~"s~ . Finally, in 1985 we erected a 4'-thick Pb wall at theexit of,SM12 and concentrated on dimuon measurements at a luminosity of3 x 10-* cm s~ . Data were taken using a variety of targets in orderto study nuclear effects. Table 1 gives the integrated luminositiesfor each run and target. To date, only the 1982 data have been fullyanalyzed [6,7], but preliminary results from the 1984 and 1985 runswill also be presented.

85

target

FIGURE 2: Schematic diagram of apparatus illustrating photonbackground problem.

TABLE 1 : Data Recorded

Integrated Luminosity/Nucleon (10J cm )

1982

1984

»

1985

0

1

12

Be

.2

.5

.9

Cu

0.3

2.2

2800

target

W

0.3

3.5

2.2

Lfc

0.

0.

7

8

/i"(GeV)

LD2

27.4

2.6 27.4

38.3

38.8

aperture

open

open

open

closed

86

H Nuclear Effects

The differential cross-section vs. p has been observed to dependin a complicated way on the atomic weight (A) of the target nucleus.The dependence might be expected to be exponential in A, with exponenta - 2/3 if the nucleons on the surface of the nucleus shadow nucleonsin the interior, or with a - 1 if there is no shadowing. The formercase would be expected (and has been observed) at low p (a GeV/c),where interaction cross-sections are large and so there is significantabsorption of the incident nucleon as it penetrates a nucleus, but athigh pt (>1 GeV/c) one is sensitive to processes involving hardscattering of partons and small interaction cross-sections, so a 3houldapproach 1.

The observation [1] of a > 1 at p > 2 GeV/c suggests thatcollective behavior of nucleons in the target nucleus is beingobserved. Multiple hard scattering of partons is capable of explainingthese results, at least at a qualitative level. Figure 3 shows oursingle-hadron data [7] (from the 1982 run) and data from theChicago-Princeton [1] and Columbia-Fermilab-Stony Brook collaborations[8], along with predictions of the constituent multiple scattering(CMS) model of Lev and Petersson [9J. The model is seen to reproducethe trend of the data, though there is some disagreement in detail.

A further prediction of the CMS model is independence of a on massfor symmetric hadron-pair production, since symmetric hadron pairs tendto arise from single hard scatters. This prediction is borne out bythe data, as shown in Figure 4. For fixed mass, a should rise as thenet p of the pair increases. Our acceptance for net pt * 0 is smallin the (approximately vertical) production plane, however we can defineP t as the momentum component of one hadron perpendicular to the planedefined by the beam direction and the momentum vector of the otherhadron. According to the CMS picture, a should rise with increasing

P ., since multiple scatters are required to give a momentum componentout of the plane. Figure 5 bears out this prediction.

87

rtloliv*normoHiolion §uncertainty forIhn tip.

• This Experiment- CP(R«f. I )« CFS (Rtf. 4 )

PT(G«V/c

FIGURE 3: The exponent o of the A-dependence ofpositive-hadron production cross-sections at 400 GeV vs. p t;the curves indicate the predictions of the constituentmultiple scattering model for ir and K+ proivetion.

88

pair

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1.40 -

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FIGURE 5: The exponent a of the A-dependence of thehadron-pair production cross-section at 400 GeV vs. p

89

5 Cross-Sections vs. Pt and 6

The magnitude and shape of hadron production cross-sections atp vs. pt and scattering angle 6 are calculable from QCD, givenf t i b t h th

large p t

some information about how the scattered partons fragment into theobserved particles. We have used the Lund monte carlo [10] to performsuch a calculation, using the PYTHIA (4.2) and JETSET (6.2) routines tomodel parton scattering and fragmentation. Figure 6 shows theinclusive invariant cross-section vs. p to produce positive hadrons,compared with the Lund monte carlo prediction. The shapes are seen toagree well, however the magnitude of the Lund prediction is too low bya factor of 2.6.

-38 ~i I i i t

•O<Cos0

forFIGURE 6: Inclusive invariant cross-section vs. jpositive hadron production off of Be at 400 GeV; the^curverepresents the Lund monte carlo prediction, multiplied by2.6.

The dependence of the cross-section on 6 has not been measured byany previous experiment in this range of p and 6. Figure 7 presentsthe power a of the atomic-weight dependence vs. cos 6, as measured inour 1982 run using Be, Cu, and W targets. The data are consistent witha constant value of a in our range of cos 6. Figures 8 and 9 presentthe invariant cross-sections vs. cos 8 for positive and negativehadrons from the three targets. We show also an extrapolation to A - 2(labeled "deuterium"), compared with QCD predictions from the Lundmonte carlo and from a calculation to leading-log order by J.F. Owens[11]. The Lund prediction has been multiplied by 2.6 to facilitate thecomparison, but the leading-log prediction agrees in magnitude with theexperimental results.

90

06

-0J

FIGURE 7: The power a of the A-dependence of positive- andnegative-hadron production cross-sections vs. cos 6.

91

ro

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FIGURE 8: The invariant cross-section vs. cos 6 for positivehadron production at 400 GeV off Be, Cu, and W targets, andits extrapolation to A = 2 ("Deuterium").

92

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FIGURE 9: The invariant cross-section vs. cos 9 for negativehadron production at 400 GeV off Be, Cu, and W targets, andits extrapolation to A • 2 ("Deuterium").

93

For positive hadrons, both the data and the QCD predictions showan enhancement at angles forward of 90°, but the data show a strongerenhancement than either calculation. This forward enhancement arisesin the QCD models due to the presence of neutrons in the target, asfollows: At these high values of x - 2p. / /s, the crc.3-section isdominated by scattering of valence quarRs off of each other and off ofgluons; also u quarks tend to fragment into positive hadrons, whereas dquarks tend to fragment into negative hadrons. Since the u-quarkstructure function is harder in the proton and the d-quark structurefunction is harder in the neutron, in proton-neutron collisionspositive hadrons tend to be produced in the proton direction (forwards)and negative hadrons in the neutron direction (backwards).

Note that the results heretofore presented are all based on the1982 run. Once the analysis of the 1984 data is complete we will havebetter statistics by an order of magnitude, as well as betteracceptance and better control over systematic errors. Some preliminaryresults from the 1984 data are presented below.

6 Particle Ratios

Figure 10 presents preliminary measurements of particle productionratios at 400 GeV using the LH target, along with results from theChicago-Princeton collaboration ana Lund monte carlo predictions. Thetwo data sets are in agreement where they overlap, and both agree withthe Lund prediction for ir+/ir~, however the Lund mcr.te carlo is seen tounderestimate production of kaons and overestimate baryon production.These predictions are sensitive to two parameters in the fragmentationmodel: the ratio of s to u quark production and the ratio of diquark tosingle quark production. These parameters were determined frome+e -annihilation data [12] to be 0.3 and 0.1 (respectively); our dataprefer the values 0.5 and 0.05. Similar problems have been noted bytwo ISR experiments [13] (at lower values of x ). Note that both thedata and the monte carlo runs suffer limited statistics so far.

94

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FIGURE 10: Invariant-cross-section .-atios for pions, kaons,and protons prccuced in 400 GeV F"P_coIlisions: a) w /» , b)K*/it+, c) K~/T~, d) p/iT , and e) p/ir~. The shaded bandsrepresent the Lund monte carlo predictions.

95

7 800 GeV Data

7.1 Open-Aperture Run

Figure 11 presents preliminary results on the yields vs. p ofpositive hadrons and hadron pairs at 800 GeV off of Be. The resultsshown represent the first 3% of data taken and serve to indicate thequality of the results expected once the analysis is complete.

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FIGURE 11: Yield of a) positive hadrons vs. p and b)opposite-sign hadron pairs vs. mass at 800 GeV off Be forfirst 3? of data taken.

Figure 12 shows the dimuon and dielectron yields vs. mass. The Tstates are clearly resolved, and the yields in the two modes are equalto within 20$. No large opposite-sign ue signal is seen; the yield isless than 1? of the dimuon and dielectron yields.

96

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FIGURE 12: Yield of opposite-sign a) muon pairs and b)electron-positron pairs vs. mass at 800 GeV.

7.2 High-Lumincsity Dimuon Run

In 1985 we added a k '-thick Pb absorber at the exit of SMI 2 inorder to eliminate our photon background (see Figure 13)- We were thusable to increase our luminosity by a factor of 30. We retain good massresolution (0.2J r.m.s. at the T) in the presence of the absorber,since SM3 provides a good measurement of momentum and we trace thetrajectory back through the field of SMI 2 in order to determine theproduction angle, allowing the track to have a kink due to multiplescattering in the absorber. To improve the momentum determination weadded a station of proportional drift tubes ("Station 0") justdownstreaoi of SM12, which we successfully operated at rates in excessof 100 MHz (2 MHz on the hottest wire). Using Station 0 SM3 provides0.1{ momentum measurement. Table 2 gives expected contributions to themass resolution at the T.

97

large

detedor

FIGURE 15:installec

Schematic diagram of apparatus with Pb absorber

TABLE 2: txpected Contributions t"Resolution

Closed-Aperture T Mass

Contribution o (MeV/c2)

target size

dE/dx fluctuations

multiple scattering

in targetin lead absorberin detectorsin helium

chamber resolution

other

6.3

3.0

9.47.86.53.7

7.0

TOTAL 18.0

98

Table 3 sumr 2es rates at various stages in the apparatus anddata acquisition. In order for data acquisition not to be the limitingbottleneck, we used a two-stage trigger. The first stage consisted ofa trigger matrix which looked for triple coincidences of hodoscopespointing back to the target in the bend plane. The second stage was afast parallel-pipelined trigger processor [I1*], which foundwire-chamber tracks in the bend plane pointing back to the target andfiring the muon proportional tubes and required two opposite-signtracks with mass exceeding a threshold. The trigger processor not onlyreduced the trigger rate oy an order of magnitude, but gained anotherorder of magnitude in required off-line computing for those eventswritten to tape, since chamber hits inconsistent with processor trackscould be ignored in the rff-l;ne trackfinding. (Due to the nigh beamintensity there were typically 10 to 20 accidental hits per chamberPlane per event.) Figure 1 shows trigger processor efficiency; theinefficiency is consistent with that expected from chamber inefficiencyand dead time.

lAELi. i: Hates per I x 'I 1- Prcter. 3 on Tarzet

{Closed Aperture, "00 GeV

station 0 5 x 1 0 ^

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99

Mass (GeV/c2)

FIGURE Trigger Processor Efficiency vs. mass.

Figure ^5 shows event yield in the T region with half of the dataanalyzed. The mass resolution has not yet been optimized, but thethree T states below 3-meson decay threshold stand out clearly and withlittle background. Table M gives preliminary measurements ofcross-section times branching :iatio for production of T's. Using valuesmeasured at e e colliders for leptonic branching ratios [15], we canextract differential cross-section ratios for the three states, shownin Table 5. These have been predicted by Eaier and Ruckl [16] assumingT-production in 800-GeV pN collisions is dominated by gluon-gluonfusion into P states, which subsequently decay into the observed Sstates. Their predictions are also indicated in Table 5 and are inreasonable agreement with our result. Barger, Keung, and Phillips [17]and Childress et al. [18] used models based on local duality tocalculate the sum of cross-section times branching ratio for all threeT states. In these models the cross-sections are strongly sensitive tothe shape of the glaon structure function. The T data pin down thegluon structure function to within one power of (1-x): Barger et al.find the exponent to be 5 or 6, while Childress et al. (who includeqq-annihilation in their analysis) find 7.6 ± 1.

100

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FIGURE 15: Yield of opposi te-sign muon pa i r s vs . mass in theT region at 800 GeV off Cu for 112 of the closed aper turedata.

TABLE 4: T Cross-Sections (Preliminary)

p • Cu + X a t 800 GeV

state B 1 ° -dy

y=0(pb)

T ( I S ;

T (2S)

T (3S)

1.32 + 0 .08

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101

TABLE 5: T B £idy

Ratios (Preliminary)

p + Cu - •/u~ • X at 800 GeV

ratio

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Figure 16 gives the dimuon yield over the mass range 8 to 16GeV/c2. No new resonances are in evidence. Figure 17 shows95S-confidence-level upper limits for the production of new resonances,expressed as a ratio to the Drell-Yan cross-section. These limitsshould come down a factor of two when the mass resolution has beenoptimized and the remainder of the data has been analyzed. Also shownare expected levels of signal for the Higgs [19] and the technipion[20], assuming they have masses in our accessible range. The Higgsproduction cross-section increases with the number of quarkgenerations, assumed here to be four, and a plausible "k-factor"enhancement of two has also been put in.

102

10

• t

f • • • •

FIGURE 16: Yiela:-eV off Cu for "

-;f opposite-sign dimuons vs. mass at 800- zf the closea-aperture data.

103

FI'J'uRE '7: i5«----.n.fi-ience-Ievel ipper limi". vs. mass forc'.muor, resonance production cross-section times branchingratio, .-.orxal ;zec tc trie Dreli-Yan cross-section, andcompared to predicted cross-sections for the Higgs and theTecrmipicn.

104

7.3 Search for "Axions" [21]

Recently interest in axiona has been renewed due to theobservation of monoenergetic electrons and positrons produced inheavy-ion collisions [22], suggesting the production and decay of aparticle with mass - 1.8 MeV/ca. Our relatively short (5.5 a) Cu beamdump, located within the field of SMI2, followed by a spectrometer withgood electron identification turns out to give excellent sensitivity tosuch a particle, produced in a ir°-initiated electromagnetic shower atthe upstream end of the Cu beam dump and decaying downstream of thedump.

We took a sample of data triggered only on energy deposition inthe calorimeter during the 1984 800-GeV run, and for U x 10 ^ protonson target we find 74 e*e" pairs which reconstruct to a vertex at thedownstream face of the dump. These pairs are all consistent with zeromass. Figure 18 shows the distributions of the exit angles of thepairs in the vertical and horizontal planes at the downstream face ofthe dump. During the same data runs we also recorded a prescaledsample of the copious flux of muons emerging from the downstream faceof the dump- These muons were produced by meson decay in the initialhadron shower and were then deflected in the vertical plane due to the3.1 GeV/c magnetic kick over the length of the dump. The angulardistributions of the muons were identical to the distributions of thee*e~ pairs in Figure 18. Axions, traversing the dump as neutralparticles, would be expected to have narrow angular distributions inboth x and y. The e+e~ angular distributions are consistent with muonbremsstrahlung in the last radiation length of the beam dump, and atmost one pair is consistent with the decay of a neutral particleproduced at the upstream end of the dump.

Using a phenomenological fit to the flux of ir°'s in thick targets[23] and an axion production formula due to Tsai [24] (assumingpseudoscalar coupling of the axion to e e ), we can compute90j-confidence-level limits on the mass and lifetime of the axion,shown in Figure 19. Also shown are limits vs. mass and lifetimederived from the anomalous magnetic moment of the electron [25], whichwould receive a large contributibution from axion loops if theaxion-electron coupling becomes large. (These limits are not muchdifferent for other possible axion couplings.) Together the twomeasurements exclude a large region in mass-lifetime space, and a1.8-MeV axion appears to be ruled out (unless it interacts strongly andis absorbed in the beam dump).

105

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mFIGURE 19: Limits on mass and lifetime of an axlon-likeparticle from a) this experiment, and previously publishedlimits from b) KEK, Konaka et al., c) FNAL E613. and d) SLACE56. Also shown is the lower limit from g-2 measurements.

106

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0

T. Akesson et al., Nuci. Phys. 52H 6 , ^G8 ;19a^;.

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16. R. Baier and R. Ruckl, Z. Phys. CJ_9. 251 11983).

17. V. Barger, W.Y. Keung, and R.J .N. P h i l l i p s , Z. Phys . C6_, 169( 1 9 8 0 ) .

18. S. C h i l d r e s s e t a l . , "Produc t ion Dynamics of the T and the GluonStructure F u n c t i o n , " unpub l i shed , 1983-

19. J . P . Ruther foord , p r i v a t e communication.

20. C. Quigg, FERMILAB-PUB-85/1^-T.

2 1 . C.N. Brown e t a l . , "A S e n s i t i v e Search fo r the Axion," submit ted toFiiys. Rev. L e t t . ( 1 9 8 6 ) .

22. J . Scr.weppe e*. a l . , Phys . Rev. L e t t . 5 1 , 2261 (1983) ;

M. Clemente e t a i . , Phys . L e t t . 1373, 41 (1984) ;

T. Cowan e t a l . , Phys . Rev. L e t t . 54_, 1761 (1985) and Phys. Rev.L e t t 56_, 444 (1986) .

23 . A.J . Malensek, Fermi lab p r e p r i n t FN-341, FN-341-A.

24. Y.S. T s a i , SLAC-PUB-3926, Apr i l 1986.

25- S . J . 3roCsKy e t a l . , San ta Barbara p r e p r i n t NSF-ITP-86-17.

109

b PHYSICS

Richard WilsonHarvard University

on behalf of the CLEO collaboration*

*Carnegie-Mellon University, Cornell University, University of FloridaHarvard University, Ithaca College, Ohio State University

University of Rochester, State University of New York at Albany,Syracuse University. Vanderbilt University

Introduction

b physics has the principal subject of enquiry for the e+e" ring,CESR, at Cornell and now for the DORIS ring at DESY. It has thereforebeen reviewed regularly. The last systematic review was by Thorndike atthe Kyoto Conference and in Annual Reviews (Thorndike, 1985a; 1985b). Iwill build upon these.

I note firstly that while theorists would like to know what Is thephysics of the b qu-i • all that experimenters can tell them are theproperties of the ob states, the upsilon particles, and the bu and bdstates, the B— and B° mesons. This talk is an experimenter's talk andis primarilyARGUS data.

about the B mesons. I will review new CLEO data and some

Eighteen months ago, the following improvements were made in CLEO:

(i) a beam pipe of thin beryllium was made;(ii) the inner proportional chamber was replaced by a precision

vertex chamber;(iii) some dE/dx measurements are now possible in the drift chamber;

and(iv) an integrated luminosity on the 4S has now added another

78 pb"1 to the 1983 data sample.

The standard model puts a b quark in a right handed doublet as shownin Table I and the relationship between the real d, s, and b quarks andthe d', s', and b' is by the Kobayashi-Maskawa matrix, also shown inTable I. One important question of interest is then to determine therelevant elements of this matrix, V- u and VTDC. The upsilon 4S state isa broad resonance and it has been conventional to assume that it decaysentirely into BB mesons, because there is no other reason suggested whyit should be broader than the upsilon 3S state.

TABLE I

( M. U ) t + + 2/3• 1/3

d's'b'

Vud Vus VubVcd Vcs VcbVtd Vts Vtb

110

Earlier studies suggested that the B meson decays almost entirelyinto charm states so that V^/V^c or (b -» u)/(b -* c) is small. However,when the branching ratios of the D mesons were redetermined by theMK III group last year (Baltrisatis, et al., 1985), and found to be 1.5times as large as previously believed, the branching ratios of B to Dmesons had to be correspondingly reduced, and our understandingreexamined. This reexamination is still in progress.

The mass of the b quarks comes from the measurement of the mass ofthe upsilon particle, combined with a nonrelativistic calculation. Theupsilon particle is a bb state. The fact that the simple potentialmodel correctly gives the mass differences and decay parameters of thevarious upsilon states gives us some confidence in the calculation.

The masses of the upsilon states, of course, given the sum of theelection and positron energies at the peak of the resonance. The energyof the circulating beams is determined by the magnetic fields and theorbits. The fields are measured by NMR, but the scale of themeasurement is given by making a resonance method. The beam polarizesby synchrotron radiation, and the polarization is destroyed by shiftingto a g-2 resonance. There have been no new data at CESR, and Itherefore quote from the old paper by MacKay, et al. (1984) and list thenumbers in Table II. The masses of the T(5S) and T(6S) massesare less reliable because there are open coupled channels and the fit tothe cross section curve may not be correct.

The diagrams which might describe the decay of the B particles areshown in Figure 1. Figure la is the spectator model where the spectatorquark, d or u, is unchanged in the decay. Other possibilities are the Wexchange diagram, lb and the diagram of 1c.

B Meson Mass

The B meson was definitively located In 1983 by measurement of itsdecay products in 1983 (Giles, et al., 1984). This came when it waspossible for a few events to fully reconstruct the B particle throughits decay into D°7r, DO7r7r, D*TT , or D*TTK . The D° was located by requiringthe K"TT+ decay, to give a mass within 40 Mev of the D° mass and the Dwas located by requiring the K-KIT - K.ir (or D*+ - D°) mass difference tobe within 3 Mev of 145.4 Mev.

The energy of the B meson was constrained by the beam energy, andsince this was set to be on the T(4S) resonance, the analysis reallymeasures the difference between the T(4S) and twice the B meson mass.If the energy scale changes, the b mass as measured by the energy of theT states, changes in the same way. Therefore, it is this differencewhich is of most importance. It might be appropriate to list only thismass difference, but I keep to the usual practice here of listing themass of the B meson Itself. In presenting these data in Table II, Iincrease the masses by 2.3 Mev because of a recently discovered error inassigning the energy scale.

ARGUS have recently reported (.ARGUS, 1986) measurements of the Bmesons. In principle there are 5 different B decay channels into Dmesons and 4 channels for D decay, making 4 x 5 = 20 total

111

possibilities. I shown in Figures 2 and 3 the Argus data and list themasses derived therefrom in Table III.

There have also been new CLEO data using these channels (Read, 1986)and, as I report later in this talk, data on B -* i/>K and tpK. (Jan Guida,1986), which I also list in Table IV. In each of these cases, thecharge of the B is determined so that it is possible to determine themass difference Am = mg± - mgo. In this difference, some of thesystematic error in the determination of the energy scale cancels.

TABLE 11

Masses of T States (Mev)

CESR Novosibirsk

T(lS.iT(2S)T(3S)T(4S)T(5S)T(6S)

9a59 a~10021 .610353.210577.51086811019

±0

±3±0±6±5

.11

. 0

.07

±0

±3±5±7

.07

.0

94601002310355

.6

.8

. 5

±0±0±0

.4

.5

. 5

DESY

1002 3.1 ±0.4 ± 0.5

TABLE III

B Masses and Am = mgo - mg±

Units of Mev

(Actual Measvrement Ej->oam - m

CLEOOLD

(Giles, 1984)

CLEONEW(Read, 1986)

ARGUS '1986)

CLEO

(Jan Guida, 1986)

MEAN

<B>

5275.5±1.6±2

5278.5±1±3

5275.0±0.8+ ?

B±

5273.5±2.4±2

5277.2±1.4±3.0

5273.8±1.3+ ?

5280.1±1.7±3

B°

5277±1.9±2

5281±1.2±3.0

5276±1+ '/

5281±1±3

Not meaningful

.5

.0

.2

.2

Am

4±2.7±2

3.8±1.8±2.0

3.8±1.6±?

1.1±2.1±2

2.6±1.1±2?

112

The data in Table III are inconsistent; the new CLEO data givemasses 4 Mev higher than the old. The reason for this is unclear. Oneclue to a possible reason lies in the high branching ratios to two bodystates found in the old CLEO study. (See Table IX infra). Thebranching ratio B -• D*TT was originally found to be 2.7%- -higher than the1% found by looking at the inclusive IT spectrum and higher than found inrecent ARGUS studies. This might have been a high statisticalfluctuation; initial discoveries of particles are often associated withupward statistical fluctuations for obvious reasons. But it might also

Figure 1

W Exchange

figure Figure 3

6.2,

Gev

have been that a pion was missed in some cases and the measuredbranching ratios could have included some events where B decayed to D%TTTas well as the intended DTT states. This would have the effect ofproducing coo low a B mass. This new data has better resolution andthus it is less likely that an extra IT meson was missed. We arestudying this carefully and urge ARGUS to study it as well.

113

The higher value of Che B mass gives a value for the differencem(T4S^ " 2mB = 2G Mev instead of the previous 32 Mev. This will haveseveral implications. Assuming that Am = mgl - mg = 3 Mev as suggestedboth by calculation and experiment, the fraction of B° produced in T(4S)decays is likely to be less than the 40% previously assumed ( f 0 / ^ <2/3). Since the width of the T(4S) is about 20 Mev, it may be possibleto change this ratio by runs on either side of the T(4S) peak.

Leptonic BranchinE Ratio

The liLCO £,roup (Pal, et al . , 19861 have published their finalleptonic branching ratio

Br(B - 14.9 -1.9

I list this in Table IV which replaces Table 4 in Thorndike's review.The mean barely changes.

TABLE IV

B Semileptonic decay branchinE ratio measurements

Group

Branching ratio (%)

B - Xeu B -

CLEO (Kowalewski, 1986)CUSBT(4S) combinedMark IIMAC

DELCO (Final)TPCMark JTASSOCELLOContinuum, combined

10.9±0.7±0.513.7+0.811.4

11.13.5+2.6+2.0

+2.214.9+ _ 1 - 9

11.011.811.0

11.113.414.014.1+5.8+3.0

12.3+0.9

10.7±0.6+1.011.2+0.911.0

5+0.612.6±5.2+3.012.411.8+2.2

15.211.911.210.5+1.511.311.7+2.8+1.08.8+3.4+3.5

I note that the branching ratio measured at CLEOassuming that the T(4S) decays entirely through BB.true, the branching ratio would havewould be destroyed.

b Lifetime

to be increased,

is calculatedIf that is notand agreement

At both PEP and PETRA quark jets are produced from the continuum bythe reaction e+e" -» qq. At the cm energies 2 E b e a m = 3 0 - 4 0 Gev, onlyabout 1/11 of all events come from bb" production because of the lowcharge of the b quark. It is therefore necessary to enhance the bbevents in the total event sample.

All methods of determining the b lifetime except one (MK II, secondmethod) have followed this b enrichment by a measurement of the impact

114

parameter of all, or most, tracks from the b decay.

Since last vear, there have been two changes. TASSO have finalizedtheir measurements ^Venkatamania, 1985) and MAC (Nelson, 1986) bothhave an enlarged data sample and an improved enhancement procedureThe MAC result is preliminary and may change.

The impact parameter of a track does not always have the same sign.A negative sign impact parameter can arise from either of two causes:the resolution of the drift chamber is larger than any individual impactparameter; and an individual track from a b jet does not exactly followof the b jet direction. Therefore it is not only possible to measure ashift of the center-of-gravity of the impact parameter distribution fromthe expected value, calculated on a study of all ha.>ons.

In enhancement use is made of one of two facts caused by the highmass of the b quark:

i Semileptonic decays of bottom hadrons produce high pj leptons.This is illustrated by the Monte Carlo calculations of Figure4. It is clear that for p^ > 1 Gev/c most of the leptons comefrom b -* civ: and

(ii) b quark jets are "fatter" than other jets andsphericity.

have a higher

Different groups have used slightly different procedures; JADE usedonly high p-j- electrons and v mesons to identify the b events. TASSOused all charged tracks. In Figure 5 I show the impact parameterdistribution for TASSO events, using their new vertex chamber, showing ashift to the right of the distribution for the b enriched sample. Thisshift is a measure of the b lifetime.

Figure 4 Figure 5

• — \

MONTE CARLO j

U £U

0,15

0 10

n

—'—i—"—i—•—;—>—i—'——r-feit

-

I

m

'—i—i—i—'—i—'i—^

Vertex • Drill Chca.iDer !

ES b enriched

C b depleted

a -

-as -at -as -a.2 -0.10 D.I

81cm)

oj as ax as

MAC, in their new analysis, which they prefer, use high p-pto identify the b sample. Applying this method to both olddata, they increase the lifetime from the previous value of 0.1.07 psec. (See Table V).

leptonsand new185 to

115

Averaging these data is difficult, and Thorndike (1985a) pointed outa few small details. I use his procedure and find an improved average

rb = 1. 30 ± 0 . 16 psec

This is not a big change from previous numbers.

TABLE V

B lifetime experiments

Statistical Systematic

SLAC

DESY

MACMK IIMK IIDELCO

JADE

TASSO

Mean

(method(method

1!2'

1 .0.1.1

1

1

1.30

078325.16

.80

.57

± 0.16picoseconds

±0.±0.±0.±0.

±0.

±0.

14

2323

45

32

10.31±0.21±0.37±0.35

±0.-4

±0.35

192*"2vub "" + fps •'cb I

Leptonic Decay Spectra

The leptonic decav spectra for B -* IJ-V'K and B -* ei/jL have been furthermeasured at CLEO (Figures 6 and 7) and compared to theoreticalcalculations (Jan Guida, 1986; Kowalewski, 1986). The muon spectrum is

cut orr below = 1.25 Gev because or the need for the muon topenetrate shielding to be identified. Below E e = 1 Gev electrons fromsubsequent D leptcnic decay enter and must be sutracted.the thec-v is not as good as we had at one time thought.

Unfortunately

The important question at issue is whether the decay proceedsentirely by b -* c transitions, or partly by b -* u. This would show upas a difference in trie shape of the leptonic decay spectrum. Inparticular, if the decay proceeds by b -* c, the mass of the recoilingobject(sj X, must be at least the D° mass, and the maximum lepton energyE^ < 2.2 Gev, wh = reas if it proceeds by b ->• u. X could be a i or p mesonand the êpton energy could Le greater than 2.2 Cev 'Figure 8).

The data in Figures 6 and 7 clearly show no Isptons (after back-ground subtraction) above 2.2 Mev, confirming the dominance of b -• c.To obtain more precise limits on V-û/V^c [= (b -+ u ~ -> c)] the data werefitted either to a constituent quark model (.Alt. arel!* , et al. . 1982), orto a varying mass My. However, last year, another itidel becameavailable (Isgur, Grinsteir. and Wise, 1985). In this model, explicit

116

states X - D, or D were used with their form factors (1 form factor forD, 3 form factors for D*). The spectra for b - u decays with either X -n, p and A were calculated. These calculations show that X - 7r and pare relatively suppressed and therefore that the spectra, particularlyfor b •* u, were softer (more leptons at lower energy) than previouslyassumed. Another model used is the CLEO Monte Carlo model.

We have attempted to fit the data parametrically with the b -* cassumption, and varied the adjustable parameters. In Figure 9 are thespectra for b - c for the Altarelli constituent quark model for twovalues of the Fermi momentum of the quark, and in Figure 10 are shownthe spectra for b -» c and b ->• u for the best fit. In Figure 10 thespectra according to the Isgur model are shown for D and D separately.

Figure 6 Figure 7a'.tim- 5qa SEC'a. n*

Figure 8 Figure 9

x 5- ft -e • «e ;.m ;.a ; t,

Table VI shows the best fits and Table VII shows upper limits for(b -+ c)/(b -* c) from these fits. Also shown are the upper limits usinga limited part of the spectra, assuming that the spectra for b -> u decayare the same as Altarelli calculates. The most model insensitive upper

117

limit comes from examining the data above 2.4 Gev only. However, if theb -» u spectra are those given by Isgur and Wise, B -* irti/ and B -» plu aresuppreseed relative to the Altarelli model. An upper limit of (b -*u)/(b -• c) of 11% is reached if it is assumed that the calculatedspectra for B -• TTJSI/, w£i/ and A£N are adjusted upwards to match theexpermental branching ratio, or 20% if it is assumed that other highermass states also contribute.

Figure 10 >^p\. li

\ ' \b~c/ -|

CC« 0.06 0.08

F -d:.e • ra--ir.**a ty K -.«. ir.at r i x e lement s '*' . end V , showing" e ; : ? r i s a i l c - e a by t.-.e ypps : i ^ n i ' . j ?n '. b-u) ,•' [L^c J , and byn e i j u t t ^ e n l s y £ tr.e a I - ; * ; ;_me, semi lepc^nic decay branch—

t. .e :o*«r Doviida.-y ot tr>e :ea:cn ccn=l = Cent wilh the F.e ( t)measurement. !here rc^ - 4C GeV 13 assumed.)

(Thorndike, 1985a)

We therefore see that the experimental data on leptonic B decay canonly be used to give tight values on (b -» u)/(b -* c) by use of theory.

These changes in the b lifetime and in the leptonic branching ratiosince Thorndike's review are small and I therefore make no change fromhis analysis for the values ofsemileptonic decay gives:

and Vcjj. The calculation for the

BrfB - Xit/)

lvub! + fps cbl

The phase space suppression factor, f, was calculated using physicalmasses in B - Dif. The value of m^ to put in this formula is stilluncertain. The consistent mass, obtained from putting the upsilon massof Table III into a Schrodinger equation is over 5 Gev, but it has beensuggested, without much theoretical guidance, that a "running mass" of4.25 Gev be used. Thorndike uses 4.8 ± 0.2 Gev, corresponding to themass at an energy scale of 2 Gev.

I copy .from Thorndike his figure 19 as Figure 11. In this he plots

Vct>. Also shown on this plot are the upper limits if the CPviolation in K decay is given by the K-M matrix.

118

TABLE VII

Best fits of parameters in fits to CLEO lepton spectrum

Aitarelli PF = 231 ± 27 Mev

CLEO Monte Carlo ± 0.2 5D ->• D

SINCE THIS CANNOT BE SET TO ZEFO FOR TABLE VI11

DIse;ur & Wise 1 i- t 0.20

D + D

TABLE YII

Calculated Values of i b -> u)/(b -> c) (%)

i.' ;.Assuming, Aitarelli model for b - u):

Fit toFit whole spectrum

I - 2 .6 2.4-2.6Mev Mev

Aitarelli

CLEO Monte Carlo

Tve - _ rahem

Additional statisticalerror oi da t a

2.2 ± 1.1

-0.1 ± 1.6

-0,1 ± 1.2

1.4 + 0.4 -1.8 ±0.1

1.2 ± 0.6 -1.8 ± 0

1.4+0.3 -1.810.1

± 1.7 2.9

sgur la point including s t a t i s t i c a l error

Isgur 2o point using Isgur b' norrriai lr e L • ;see text)

calculation

7Dint assumir.g b -i^.adi jf higher -jiass) (assumingir, p, A exact and highermass X contribute)

16%

119

Dileptons

Since both a B meson and its antiparticle are produced in the sameevent, two leptons can often occur. There are two interestingparameters to learn from a study of dileptons: a study of leptons ofunlike sign can tell us the ratio of the charged and neutral lifetimes(or strictly speaking a ratio of the branching ratios) and a study ofleptons of the same sign gives an upper limit on B°B° fixing. CLEO hasanalysed the new data sample for both of these (Bean, 1986).

The data are found to be much cleaner by making a cut on the angleand between the two leptons. Data where the cut |cos 6\ < 0.8 have beenlooked at, but are not yet completely understood. The number ofresirtual leptons (after the cut) are in the first line of Table VIII.The numbers must be corrected for V decays, particles which areincorrectly assigned as leptons (fakes), and for those lepton pairswhere one lepton cones from B decay and the other from a subsequentdecay of the D. These dileptons are not of interest here. Continuumdata are used as a check of background subtraction.

TABLE VIII

DILEPTONS

CUTS: hadronic eventlepton identification1.2 < ?£ < 3.0 GeV/c| c o s < 0 . 8 22 $i

Like Sign Unlike Sign

M " M " i e A1 i e'î") e /J" , e'v )

(e+e+, e"e

Raw Data on T(4S)

•0 Decays on T(4Sj

Fake Leptons on T(4S)

Leptons on D Deca]/ on T(

Background subtracted on

Corrected for angle cut

4S;

T(4S)

32

N/A

8

N/A

4 ±

4.3 ±

5

5.6

172

8

12

10

147

193 ± 19

120

The number of leptons (N^) from B decay is given by.

Nl a ^foô) + ^ f+ T + )

The number of dileptons (N2) is

N 2 « (foro2) + (f+r+

2)

We can therefore form the ratio

N2N g ;1 + (fo/f+)(ro/r + .r; (1 + fQ/f+)

N 2 4 [1 + (fo/f+)(ro/r+).'

where g is a factor correcting for slightly different efficiencies forsingle leptons and dileptons.

For -he 1985 data, N, = 193 ± 1.8; Nx = 8272 ± 9 4 ; N = 85800;g = 0.98. If we assume fo/f+ = 0.4, and include 1983 data, we find

0.5 < T O /T + < 1.9 (90% confidence)

If fo/f+ is less than 0.4, as suggested by the new B mass, theselimits will r ise sl ightly.

For B°B0 mixing, the upper limit on the number of like-sign leptonpairs (divided by the number of unlike-sign pairs gives the mixingparameter, y:

2+ + 1 [ (r+/ro) f+ + fo

+ i")

Inserting the values from Column 2 of Table IX and folding in the1983 data gives the latest value

y < 0.18 (90% confidence)

B

The decay B -* \j>X is particularly interesting because it probablyproceeds by the W exchange diagram of Figure l(c). It has now beenmeasured both at CLEO and ARGUS. \j> is easily identified by the decayinto muons or electrons. Once identified, precision with which the massis known is dominated by the i{> mass and the beam energy.

Figure 12 shows the e+e" or M + M " mass distribution from Argusshowing a peak at the ij> mass. There is a hint of a peak, the rj>' mass.The i/>' peak does not look very convincing, but the mass plot for \brjr(Figure 13) shows a much clearer peak, and suggests that 20% of i> from Bdecay comes from iji' .

121

Figure 12Figure 13

Mass Gev

The momentum distribution of the \j> mesons, as measured by ARGUS(Figure 14) shows the peak at high p^ for two body decay, \j>K or $C*Both CLEO (Jan Guida, 1986) and ARGUS (1986) have identified the twobody decay by reconstructing the B mass. The ARGUS data are in Figure15 and those of CLEO are shown in Table III. No numbers are quoted yetfrom the ARGUS data and so none are shown in Table III. The branchingratios are listed in Table X infra.

Figure 14 Figure 15

5.20 5 JOMass (ev)

122

B -» F -» d>

CLEO has measured (Bartoletto, et al., 1986) the inclusiveproduction of <j> mesons from the B; the 4> peak is shown in Figure 16.The products of the branching ratios becomes

B r ( B - F x ) B r ( F - <£x) - 0 . 0 2 3 ± 0 . 0 0 6 ± 0 . 0 0 5

We do not know Br(F ->• >x) , but estimate it to be about 20%. ThenBR (B -» Fx) becomes 10-15%. The momentum distribution of the <j> is hard(Figure 17) and is consistent with them all of the <j> being observed fromthe W -* cu decay identified in the spectator diagram of Figure la. Thisis calculated to be 0.15 per B.

Figure 16 Figure 17

- i . c i c - c h . . * ^ .IM--.! /•• !' • M >l,(l - •! \ i - 1 % a n d

B - D°. D +, D*+ /.•»• - . . • • : ' . * • > • • • > . - , n - r .

CLEO has remeasured the inclusive branching ratios B -»• D°, D+, D*+

using the improved data sample and apparatus. The D° was identified bythe decay D° - K'ir+. The mass plot (Katayama, 1986) is shown in Figure18 and the background is subtracted in the usual way. No effect is seenon the continuum. The D + was identified by the 3 body decay D + -+ K7r+7r+

as shown in the mass plot of Figure 19. Finally the D*+ was identifiedmaking a mass plot for KTT decays for those events where the D*+ - D°mass difference is 145.4 Mev to within 3 Mev (KTTTT - KTT mass < 3 Mev).The D° peak is evident. The mass plot for D° is shown in Figure 20.

The efficiencies were estimated by the usual Monte Carlo analyses.

The actual quantities measured are products of branchingratios--again assuming that the T(4S) decays entirely by BB.

Br(B - D°x) Br(D° - K~ir)+ = 0.021 ± 0.002Br(B - D+x) Br(D° -» K'JT+TT") = 0.019 ± 0.004Br(B -• D*+x) Br(D*+ -* TT+D0) Br(D° -• K"TT+) = 0.0076 ± 0.0010

123

We take the D° branching ratios from Mark III (which we note areconsiderably larger than the older Mark II ratios)

Br(D°Br(D+

= 0 . 0 5 6 ± 0 . 0 0 4 ± 0 . 0 0 3- 0 . 1 1 6 ± 0 . 0 1 4 ± 0 . 0 0 7

and the D* branching ratio from the older Mark II data

Br(D*+ - TT+D°) = 0.6.0 ± 0.15

From these data we find two quantities: the ratio of directproduction of D and production through D

D

D + D= 0.17 ± 0.15

+0.12-0.21

(assuming. . . )

We also derive the total branching ratio

Br(BBr(B

D°x) = 0.39 ± 0.03 ± 0.04D+x) = 0.17 ± 0.04 ± 0.04

where the first error is the CLEO error--almost all statistical, and thesecond the error on the MK III branching ratios.

The momentum distributions of the D° and D+ are compared with (a) aphase space model; (b) the spectator model; and (c) a leptonic decaymodel as shown in Figure 21. The spectator model agrees quite well andtends to support our initial supposition.

CLEO has previously measured A and P from T(4S) (Bowcock, et al.,1985) . An upper limit to the production of Ac can be obtained byassuming that all the P and A come from the decay of Ac. This gives Br(B - Ar) < 0.05.

Figure 18

0000

BOOO

6000

«0OO

•dOOO

0

1500

4000

3500

^ 3000

V500

\ ^V

-

1 f

l-B 1.9 2D-

""••. A

1.3 2.3

Figure 19

150

0 GeV< P D . - * H 5 GeV

- ON T (13)— SCALED CONTINUUV

I K J\\ vI i i

I ? 19 2 1

' N'.BSS ( C e v l

K'TT' MiSS(GeV)

124

Figure 20 Figure 21

aoa

1=

1

m

°S

q

10.0

CD

6.0

Q

O

' I i

b—t

- Phase Space

- V/o- •' /- / A

[ y v

v///

1

1 1

1 /1 /

1

1 ' 1

-

b-c-F. "

\\

\

\ \ •

\ \

. \ \

\ •

q o

t

o

aICD

0.5 1.0 1.5 2.0

Moment urn (GeV/c)

Where Do the B's Go?

In Table X I add the different branching ratios discussed in theearlier sections. The expected number is the fraction (b -* c/b -* all)plus 15% at the W vertex. The measured and identified total is about30% less than expected, whereas a year ago, as noted in theintroduction, there was excellent agreement.

There are several possible explanations between which we cannot nowdistinguish . Nor.e are attractive .

(1) The B branching ratios measured by CLEO may be wrong.

(2) The D branching ratios measured by Mark III may be wrong.

TABLE IX

Br (B - D°x)Br (B -Br (B -Br (B -

• D + x)* D t o t a l )* F)

Br (B - V)Br (B -Br (B -Br (B -

Total

* Ac)+ A)+ noncharm s ta tes )

(B -» to charm)Expected (B •* to charm)

0.390.170.560.150.010.05

= ?= ?

0 . 7 71.15

CLEOError

±0.03±0.04±0.05

MK I I IError

±0.04±0.04±0.06

- Br(B -» noncharm)

125

(3) T(4S) may decay to BB only 70% of the time, and decay tononchann states the rest of the time.

(4) There may be a much larger branching b -> u than previouslybelieved.

(5) None of the above.

Explanation (3) is interesting; the Mark III group have argued thatij)' does nw decay to DD all the time, and this explains the (smaller)Mark III D branching ratios. However, if it is possible that ip' doesnot decay into DD', a similar explanation for T(4S) also seems possible.Alternatively, the c and c quarks in the D and D might instantlyannihilate.

The major problem with such an explanation is that the V> has a smallwidth and it is hard to understand the increased width of the ij>' unlessthe decay is almost entirely to DD.

Partial Reconstruction

There is another possible approach to some of the issues here. Itwould be very attractive to identify definitely one group of B° mesonsand another group of B + mesons and search for the accompanying B° andB" mesons respectively. This would enable us to measure separately theleptonic branching ratios and just as in the Hark III experiments, abranching ratio can be determined independent of the assumption thatT(4S) decays through 'BB and that the normalization is correct.

Unfortunately the number of totally reconstructed B mesons are toosmall to carry out this program. For this reason, the idea of partialreconstruction was developed. This takes advantage of the slowness ofthe B meson produced in T(4S). There are two applications. Firstly thereconstruction of B from B° decay to D*+ir". The soft n+ from D toD°JT+ and the hard TT~ were both detected and the angle between themmeasured. The D*+ is opposite to the hard ir" (Figure 22). It isassumed that the D° is in the same plane as the two TT mesons, the eventcan be reconstructed to give a mass slightly above the B mass. Althoughformally a (- 1) C fit, it does give a good B peak.

Figure 22

Measure

Measure

High Energy if

B decay

Unobserved

126

The problem with the method is the background. Initially it wasevaluated by reversing the direction of the soft pion and recalculatingthe apparent B mass. Due to the energy constraint, there is still apeak near th<= B mass, and the subtraction is necessary. This led to abranching ratio

Br(B - D*+»T) = 0.021 ± 0.OU5 ± 0.005 (Giles, et al., 1984)

A correction of the beam normalization changed this to

0.017 ± 0.005 ± 0.005 (Chen, et al., 1985).

A more detailed look at backgrounds led to a revised value

Br(B° - D* +TT) = 0.010 ± 0.007 (Hempstead, 1985; Thorndike, 1985a)

One problem is determining whether or not an extra undetected pionis present in the decay. If Lhere is an undetected pion, the measuredtwo body branching ratio could be too large. It also prevents us gettinga clean sample of B° mesons. I note here that ARGUS have measured abranching ratio of 0.004 ± 0.002 which lends support to the idea thatCLEO, in the early data, was including extra pions.

The method has also been used to identify a measure

Br(B° - D*+p) = 0.08 ± 0.04

Another use of partial reconstruction actually predates its use inmeasuring Br(B° - D*+TT~). This is to study B° -* D*+ lv, where the £'and the n+ from D + are both detected. Since the u is undetected, thefit is even less constrained than in the previous example. Nonetheless,the background seems tractable, probably because a high energy lepton ismore unique than a high energy 7r.

Using this technique, CLEO (Word, 1986) find

+_,. +0.009Br(B - D + i'u N(TT)) = 0.033 ± 0.007 _0

If we assume that the number of accompanying pions N(TT) — 0, thenthis becomes a branching ratio of B° mesons, not charged mesons. and canbe used to find a B° leptonic branching ratio independently of themechanism of production. However, this is not yet definite.

Mutiplicity

A new look at the charged multiplicity in B decay (Riley, 1986)lends some credence to the idea that the number of extra pions in theobserved events is less than 1/2 (probability of an extra pion less than1/2). This is shown in Table IX. The raw charged multiplicity isunfolded using a Monte Carlo calculation. This is for a BB decay. Thecharged multiplicity for semileptonic decays is lower. From thismultiplicity per BB event, the multiplicity per B decay is calculated.

127

TABLE IX

Charged Multiplicity

Observed Unfolded

per BB _ 9.00 ± 0.02 10.66 ± 0.09 ± 0.10

per semileptonic BB 7.85 ± 0.07 9.21 ± 0.20 ± 0.10per leptonic B 3.84 ± 0.20per hadronic B 5.7 5 ± 0.1less - D multiplicity 2.7 ± 0.20less -» charged lepton 1.00extra pions in leptonic decay 0.14 ± 0.28

If we assume that 25% of B decays go to D and 75% to D the chargedmultiplicity of D's can be calculated.

Two Body Decays of B

(i) b -> u states

One of the ways of understanding the ratio (b -» u)/(b -* c)might be to compare the two body decays such as B -• pir with similartwo body D decays. No new data are available since last summer, andupper limits for these decays are listed in Table X. They are of theorder of 2 x 10" , and by comparison with D decay probabilities intosimilar states of a few percent, suggest that (b -* u)/(b -* c) is lessthan a few percent. But reliable theory is nonexistent. For example,Isgur and Wise as noted above calculated a relatively small contributionfrom B -• vlv and piu, and B -• p-n might be correspondingly suppressed.

(ii) In Table X is also a set of upper limits of the B particleinto various exotic states. I list no ARGUS numbers in this table, butunpublished numbers for two body decays are lower:

B° - D*TT- = 0.%4 ± 0.1 ± 0.1

This suggests that much of the earlier CLEO data may be contaminated byan extra pion--as previously mentioned.

Conclusions

B physics depends upon theory to tell us about b physics. Thisparticularly applies to B leptonic decay.

The B mass is probably a few Mev larger than previously believed:T(4S) - 2mB = 20 Mev instead of 32 Mev.

Mark III branching ratios for the D lead to difficulty inunderstanding the total B decay probability.

A number of new measurements give some promise of increasing ourunderstanding, but we are looking forward eagerly to the completion of 7detection and measurement in CLEO II, so that many more B mesons can beidentified and charged and neutral B mesons definitively separated.

128

TABLE X

Branching, Ratios in Percent

(corrected for new D -* Kix branching ratios)

Charged B"

K°xu-

CLEO

2.2 ± 1.1

1.0 ±0.4 ' average with V*n-

0.11 ± 0.07

2.5 ± 1 6(a)

<0.02

<0.08

<0.04

<0.02 1000 < VLy. < 1600

<0.016

<0.017

<0.017

<0.024

T •= 100

Neutral B

B° - D*H

•71— X -

CLEO

1.0 ±0.7 (partial reconstruction)

1.4 ± 1.0â^

0.40 ± 0.16

*(ie

8.1 ± ;

7.0 ± 4.8

<0.02

<0.24

<0.20

<0.07

<0.01

<0.07

<0.04

<0.04

<0.013

<0.008

<0.0008

-2.4

1000 < < 1600 100

129

Unspecified

B -• D° (cr D*)?

B - D°X

B -

B -

• D+X

* 0X

r 2.

0.

0.

2.

1.

CLEO

1 ±

39 ±

17 ±

3 ±

05 ±

0

0

0

0

0

.4

.03

.04

.6

.19

+

+

+

+

+

0.

0.

0.

0.

0.

3(a)

04(b)

5

22(c)

References

Altarelli, et al. (1982), Nucl. Phys. B208. 365.

ARGUS (1986), 21st Recontre de Moriond "Electroweak Interactions andUnified Theories," Les Arcs, France.

Baltrusaitis. R.M., et al. (1986), Phys. Rev. Letts. 5£, 2140.

Bean, L. (1986). Bull. Am. Phy. Soc. 31, 790.

Bortoletto, D., et al. (1986), Phys. Rev. Letts. 5£, 800.

Bowcock, T., et al. (1985), Phys. Rev. Letts. H , 923.

Chen, A., et al. (1984), Phys. Rev. Letts. 52, 1084.

Chen, A., et al. (1985), Phys. Rev. D31, 2386.

Giles, R., et al. (1984), Phys. Rev. D30, 2279.

Guida, Jan (1986), Bull. Am. Phy. Soc. 31, 790.

Hempstead, M., et al. (1985), Ph.D. Thesis, Harvard University,Cambridge, MA.

Isgur, Grinstein and Wise (1985),

Katayama, B.N. (1986), Bull. Am. Phy. Soc. H , 790.

Kawalewski, R.V. (1986), Bull. Am. Phy. Soc. 31, 790.

MacKay, W.W., et al. (1984), Phys. Rev. 29, 2483.

Mueller, J.A. (1986), Bull. An. Phy. Soc. 31, 790.

Nelson, H. (1986), 21st Recontre de Moriond "Electroweak Interactionsand Unified Theories," Les Arcs, France.

Pal, T., et al. (1986), Phys. Rev. D33, 2708.

Read, K.F. (1986), Bull. Am. Phy. Soc. 3JL, 790.

Riley, D.S. (1986), Bull. Am. Phy. Soc. 31, 790.

Thorndike, E.H. (1985a), Ann. Rev. Nuc. Sci. 15, 195.

Thorndike, E.H. (1985b), Kyoto Conference.

Venkatamanian (1985), DESY Report 85-115.

Word, G.B. (1986), Bull. Am. Phy. Soc. 31, 790.

131

HEAVY QUARK PRODUCTION AND MISSING ENERGY STUDIES AT THE CERN pp COLLIDER

UAl COLLABORATION

presented bv

Anne Kernan

University of California, Riverside

ABSTRACT

The cross section for strong bb production is inferred from the flux

of high p,_ muons observed in pp collisions at the CERN collider. Like-sign

dimuon events give evidence for B° -B° mixing. Events with jets and

missing transverse energy are due mainly to W -* TI/ with hadronic decay of

tau. These results come from 120 nb"1 of data at 7s of 546 GeV and 600

nb"1 at 7s of 630 GeV.

132

1. HEAVY QUARK PRODUCTION

The UAl experiment has observed charmed D mesons in jets via theJL t .1

decay sequence. D ~ -* D°ir~, D° -» Kn [1] . Heavy quarks may also be

detected through their semileptonic decay: Q -• Q' + i + i/«. In fact it

has long been anticipated that the dominant source of high p_ leptons at

collider energies would be QCD produced heavy quarks. In semileptonic

decay of the top quark the leptons are expected to be isolated; for

semileptonic c- and b- decay the leptons are close to or within the

accompanying hadronic jet.

In this report I will discuss strong production of charm and beauty.

The UAl experiment has reported the observation of six isolated e/ji events,

the kinematics of which are consistent with W -* tb or strong tt production

[2]. Further studies of events with jets and isolated leptons are in

progress.

1.1 High p_ Muons and bb Production [3]

The UAl detector has muon detection and momentum measurement

capability over 75% of 4?r, with almost complete coverage in azimuthal angle

for rapidity range 0 < | r? | < 2 [3,4]. Within this rapidity range the 10%

or so of c- and b- quarks which decay muonically can be recognized by the

resulting "muon in jet" configuration. (The corresponding electron

configuration is not generally identifiable).

The data discussed here comes from the 1983 (Js = 546 GeV) and the

19H, 1985 (7s = 630 GeV) runs. A total of 108 nb"1 (/s = 546 GeV) and 584

nh~l{J~s - 630 GeV) were recorded with an inclusive muon and dimuon trigger.

A total of 1158 dimuon events met the requirement of p_ > 3 GeV/c for

each muon. A visual "muon validation" scan reduced this sample to 861

events. Rejected events included cosmic ray muons (9), K -* fii/ decays in

flight (63) and events in which a hadron reached the muon chambers through

a crack in the apparatus (56).

After the application of loose track quality and matching criteria,

the single muon trigger yielded 76,000 events with P_(M) > 5 GeV/c from the

1984 data and 22,000 events with p_(^) > 6 GeV/c from the 1985 data.

Scanning all of these events would not be practical or appropriate. To

reduce the amount of routine work to be done by physicists, and to

eliminate the subjectivity inherent in scanning, an automatic computer

selection procedure was devised. This program applies a set of routines to

perform the scanner's tasks of rejecting cosmic rays, leakage through

cracks in the detector, kinked tracks caused by decay in flight of charged

kaons, and mismatches between the track in the central drift chamber and

133

the muon chamber track. The surviving sample contains 20,000 events with

pT(M) > 6 GeV/c.

The following discussion is mainly based on the 512 events with

M > 6 GeV/c2. This condition is designed to eliminate muon pairs

resulting from the decay chain b •* c/ii/, c -* spv.

A substantial background exists to the "prompt" muons from heavy

quarks, T, J/V>, Drell-Yan etc. The primary background is "non-prompt"

muons from K/tr decay in flight. This background is estimated by applying a

Monte Carlo procedure to high p_ data. Pion and kaon decays in flight are

simulated for charged hadrons, assuming a charged particle content of 58%

charged pions and 21% charged kaons [5]. This gives an estimate of 95

events for the decay in flight background in the 512 event dimuon sample.

A similar study for the single muon sample is in progress; preliminary

background estimates vary from 50% at p_(^) of 6 GeV/c to 20% at p^C/O of

15 GoV/c.

Punch-through background is typically two orders of magnitude smaller

than the background from 7r/K decays in flight. Another background arises

from association of the track in the outer muon chambers with the wrong

track in the central tracking chamber. For dimuon tvents this background

is estimated from scanning to be (5±5) like-sign muon events and (5±5)

unlike-sign events.

We classify the dimuon events according to whether the muons are

"isolated" or accompanied by hadrons. In general we expect muons

originating from J/i/>, T and Drell-Yan processes to be isolated. The

isolation criterion is defined as S < 9 GeV2 by reference to observed

W - pi/ decays; the variable S = [XEî^)}2 + [ZET(/i2)]2 where 2ET(/J) is the

sum of the transverse energies deposited in calorimeter cells in a core of

Ar — (A»72 + A4>2) < 0.7 about the muon. The 512 events divide as follows:

An examination of W -» pu events indicates that about 18% of Drell-Yan

events fail the isolation cut; similarly the presence of isolated same sign

events suggests that some muons originating from heavy flavor decays meet

134

DIMUON MASS

10 100

GeV/cz

1000

O.-* 0.8 LZ 1.6 ZX> 2.4 2-E

Fig. 1: Mass distribution for pairs of opposite sign isolated muons.

The M > 6 GeV/c2 is relaxed in this plot.MM

10'

10 -

10"

to"3

ALL PROCESSESLOWEST ORDER ONLY

o SINGLE MUON DATA IT,I < 1.5• NON-ISOLATED DIMUON DATA

0 2 4 6 8 10 12 14

MUON TRANSVERSE MOMENTUM GeV/c

Fig. 2: Inclusive, background subtracted, muon p_, distr ibutions for

single muon and non-isolated dimuon events. The curves are

QCD predictions according to the Eurojet Monte Carlo program

[6] for cc and bb production via 2 -• 2 processes (broken

line) and 2 - 2 , 2 - 3 (solid l ine ) .

135

the isolation criterion.

Figure 1 shows the dimuon mass distribution for all isolated

unlike-sign events. The expected peaks in J/\6, T and Z° stand out.

Figure 2 shows da/dp_ for single muon and non-isolated dimuon events.

The smooth curves are QCD expectations for c- and b- quark production

computed by the EUROJET [6] Monte Carlo program for a2 and a3 processes.

b-Quarks are the dominant source of muons owing to the harder

fragmentation function of beauty compared to charm. Beauty decays

constitute 90% of the predicted dimuon events. The QCD predictions are in

reasonable agreement with the data.

As seen in fig. 2 approximately half the single muon production is

predicted to come from higher order (2 -* 3) processes; the gluon splitting

diagrams (g -• cc.bb) are particularly important. As expected the relative

component of higher order processes in the dimuon sample is reduced by the

mass cut M > 6 CeV/c2 .

The component of muon p_ relative to the jet axis is sensitive to the

flavor of the decaying quark. The distribution in thif parameter is given

in fig. 3 for the subset of 175 dimuon events which v.ave a well-defined

charged particle jet. (Because of the large calorimeter modularity the jet

axis is measured less precisely by the calorimeter). After background

subtraction the data is fit with a mixture of bb:cc in the ratio 5:1.

Comparison of the QCD predictions for cc and bb production with the

dimuon data leads to the following cross section estimate for bb

production:

a (pp - bb; pT(b) > 5 GeV/c, |>j| < 2.0) = 1.2 ± 0.1 ± 0.2Mb.

The systematic error reflects uncertainties in detector acceptance and

luminosity.

Halzen et al. [7] have suggested that the decay B -+ J/\6 + X which

occurs at the 1% level [8] may be the dominant source of 3/TJ> production at

large p ,. Figure 4 shows da/dp_ for J/\6 measured in the UAl experiment

[9]. The smooth line in fig. 4 shows the J/V> spectrum expected from beauty

decay according to reference 7. The distribution has been scaled to agree

with the bb cross section measured in this experiment. The good agreement

between prediction and data provides additional evidence for bb production

at the level estimated in this experiment.

1.2 Like-Sipn Dimuons and B°-B° Mixing [10]

The possibility of observing mixing in the B°-B°system has been widely

discussed. In particular mixing is expected to be almost complete for the

B° s mesons. Defining e as the fractional probability for the transition

136

24 -

Fig-

Fig.

0.4 0.8 1.2 1.6 2.0

»„ x J (GeV/c)

2.6

Proiection of muon p_ perpendicular to the axis of the

accompanyinr barged particle jet fcr unlike-sign

noil-isolated dirauon events. After background subtraction

the data is fitted vith a variable mixture of cc and bb

events.

100 -

c

bT3

UAI 1984 DATA

HALZEN ANDHERZOGb* J/ty + X

2 4 6 8 10 12 !4 16TRANSVERSE MOMENTUM 6eV/c

Transverse momentum dis t r ibut ion of J/rj>• The curve is a QCD

prediction '71 scaled to the measured bb cross sect ion.

137

B°(bq) -» B°(bq), Barger and Phillip have estimated (for Mt - 40 GeV/c2)

that £ < 0.25 and e. « £ [11]. Ignoring b-baryon production and assuming

meson production with semi-leptonic decay to contribute in the ratio

bu:bd:bs - 1:1:0.5, they find that the probability for a single B to give a

"•wrong-sign muon" through mixing is t - 0.2c. < 0.05. The Hark 2 exper-

iment has recently measured e < 0.12 at the 90% confidence level [12].

As outlined in section 1.1 the predominant source of non-isolated muon

pairs appears to be strong bb production. The 142 like-sign muon pairs in

the sample of 399 muon-in-jet events may be evidence for B°-B° mixing. To

test this hypothesis we compare the experimental value of R - N(±±)/N(+-)

for the muon-in-jet events with Monte Carlo predictions.

The measured R value is:

R _ N(++)/N(+-) = (142-45)/(257-49) - 0.46 ± 0.07 + 0.03

where the systematic error is associated with the background estimates.

Table 1 lists the R values predicted for B° -B° mixing fors s

f - N(bs)/SN(bq) ranging from zero (no mixing) to 30%. The range of

values within a given column is indicative of the systematic error on these

predictions.

Reference

Barger et al.

Halzen et al .

Isajet [15]

Eurojet [6]

[13]

[14]

0

0

0

0

0

00

.25

.25

.26

.21

0

0

0

0

0

s

10

.31

.33

.34

.28

0

0

0

0

0

.20

.36

.-+1

.42

.36

0.

0.

0.

0.

0

30

42

48

50

43

NcNF+NS+NC

0.23

0.11

0.10

0.15

Table 1: Monte Carlo estimates of R - N(±±)/N(+-) for a range of f =

N(bs) /ZN(bq) values and maximal B° -B° mixing. NF, N,, ar.a N_ are

respectively the number of dimuons from first and second

generation decays of bb and from cc. Only the ISAJET calculation

uses the full detector simulation.

138

We compare the experimental value of R with the ISAJET [15] prediction

and assign an uncertainty to the prediction of ±0.03 due to possible errors

in decay branching ratios and the relative cc, bb production rates. The

measured R value is consistent with full B° -B° mixng for f - 20% or 30%;s s s

it is 2.5 standard deviations from the no mixing (f - 0) hypothesis.

1.3 D in Jets - An Update

A copious signal of D mesons in jets was observed in the 1983 data

for events satisfying the trigger: electron • E_ > 60 GeV [1]. The

magnitude of the signal, N(D*±)/N(jet) - 0.65 ± 0.19 ± 0.33, and the

observed soft jet -» D fragmentation led us to conjecture that the

underlying process was gg -» gg, g -» cc. Mueller and Nason [16] have

calculated that p - N(cc)/N (jet) =0.10 for g -> cc in the same Q2 range,

considerally lower than the experimental number (N(cc) ~ 4/3 N(D ")). They

have also emphasized that the measurement of p is a clean test of QCD

because non-perturbative contributions to the gluon splitting can be shown

to be negligible.

We have repeated the measurement in the 1984 data, this time for

events with a simple inclusive jet trigger [17]. Figure 5 shows the

distributions in AM - MCKTTTT) - M(KTT) and (b) M(K?r) . The measuredI t

N(D ~)/N(jet) - 0.08 ± 0.02 ± 0.04; the combined peaks cons t i tu te a 4.9 a

effec t . The corresponding p value i s seen to be in good agreement with the

Mueller and Nason predict ion shown in f ig . 6.

The magnitude of the D signal reported in ref. 1 i s s t i l l not

understood. Possibly the electron • high E,_ tr igger enriched the sample in

heavy quarks. Monte Carlo studies to invest igate th is question are

current ly in progress.

2. MISSING TRANSVERSE ENERGY [18]

The hermeticity of the UA1 detector was an essent ia l factor in the

discovery of U -1 ei/. Calorimeter coverage extends to within 0.2° of the

beam direct ions , providing a resolut ion:

a = 0.5 ,/ETX 'y (GeV)

in each component of total transverse energy. This hermeticity has been

exploited to search for other processes involving the emission of neutral

non-interacting particles. In the 1983 data five events were observed in

which missing energy is balanced by a jet [19].

Additional results on "jets + missing E_," are reported here. These

results are based on 715 nb"1 of data recorded between 1983 and 1985: 118

rib"1 at 7s of 546 GeV in 1983 and 597 nb"1 at 630 GeV in 1984, 1985. The

139

M.rr

.9 2.1

(GeV/c2)

Fig. 5: a) AM distribution for 1.83 < M(K.TT) < 1.89 CeV/c2

b) H(K7r) distribution for 144 < AM < 146 MeV

.I6r

o

.02

300 600 900 1200

Fig. 6: Heavy quark content of gluon jets for two extreme values of

the charm quark mass [16]. The UAl measurement for

inclusive jet trigger events is shown.

140

events were obtained with one of the following triggers:

1) electromagnetic E > 10 GeV in two adjacent electromagnetic

calorimeters elements;

2) a jet with E T > 25 GeV;

3) t r a n s v e r s e energy imbalance defined as a j e t with ET > 15 GeV and

miss ing ET > 17 GeV (630 GeV data on ly ) .

2.1 Event Select ion

Events were se lec ted having

1) one or more j e t s with ET > 12 Gev,M

2) missing transverse energy E_ > 15 GeV and more than four standard" M Mdeviations from zero: E~. /o(E_, ) > 4.

Cuts were applied to remove contributions from "jet fluctuations" i.e

multijet events in which variations in detector resolution fake missing

energy. Events with electrons and muons were excluded to avoid W -* ei/,/ii/

decays. Additional cuts removed background from cosmic rays, beam halo and

a variety of instrumental effects; the remaining background due to these

effects was removed by a visual scan in which 30 events were rejected.

A total of 56 events remain. All but three are "monojets". The

instrumental background is estimated at less than one event. The

background due to "jet fluctuations" is estimated by a Monte Carlo

procedure utilizing UAl jet data to be 3.8.

2.2 Conventional Sources of Missinp Energy

In the Standard Model framework a variety of processes can give rise

to high p_, neutrinos. The number of such events in our data has been

estimated using a version of ISAJET [15] in which the properties of beam

spectator fragments was modified to agree with UAl data. The program

includes full detector and trigger simulation. The predicted contributions

are:

The decay W -• TV followed by T -* hadrons - - - - - - - - - - - 36.7

w -» ei//iiv + jet, e/fi being unidentified, and Z - vis + jet - - - 11.5

Strong and weak production of heavy flavors - - - - - - - - - - 0.2

Adding in 3.8 events expected from jet fluctuations leads to an

estimate of 52.2 ± 6.9 events expected from conventional sources. We note

that the contribution from heavy flavor events is miniminal because events

in which missing E_ is close to a jet are rejected in order to exclude jet

fluctuation background. Figure 7 shows that the predicted jet and missing

Ey distributions are in good agreement with experimental observations.

141

>a>

ID ^0

I-

UJ>UJ

5 -

0

I O -

5 -

00

Fig.

JET ET (GeV)1

-

J

1

I////,

i

i i i

B

\ , r — H ADRONS]r/ )

1 1 / NON-TJ

m/

20 40 60

MISSING ET (GeV)80

(a) E_ of the j e t i s j and (b) missing E_ for 56 4CT missingenergy events. The curves are the sum of ISAJET predictionsand je t fluctuation background.

142

24

20

t c

n

LU 12

UJ

8

4

0

r —7 '! i

T - HADRONS

MONTE CARLO -

UAI JET DATA 1

(ARBITRARY LNORMALIZATION) / \

A/ \' M

/ V1 }

1 \1

1 /

1J 1y/ _^s —

\\

-A\\\

-

TB%

— \ I^' i ^<"^ l 89% 11% \1

-16 -8

Fig. 8: Distribution of L , the tau likelihood function for UAl jet

events and foi" Monte Carlo W -» TU events

20

O 16CO-v

EV

EN

T!

as

ro

4

n

UAI56 EVENTS

-

-

r — HADRONS ,

NON - T —

\1t^zz^-i—-

1

i/\

-16 -12 -4

Fig. 9: Experimental and Mor.te Carlo distributions in L for 56 4a

missing energy events.

143

2.3 Separation of the W -> TW Decay Signal

The predominant component of missing energy events is expected to be

W -* TV decay with hadronic decay of r. The decay fragments of r may be

distinguished from a QCD jet by their low invariant mass and restricted

charged particle multiplicity. We define a likelihood function L which

quantifies the "r-ness" of a jet on the basis of three variables:

1)

2)

F - 2ET(Ar < 0.40) / SET(Ar < 1.0) where Ar (Ar?< The

variable F measures the narrowness of a jet;

angular separation between the leading charged particle and the jet

axis ;

3) charged particle multiplicity

Figure 8 shows the measured L distribution for QCD jets and the Monte

Carlo expectation for r. Figure 9 compares the experimental distributions

in L^ with Monte Carlo predictions. Figure 10 shows L versus jet E for

the 56 missing energy events.

70

Fig. 10: Tau likelihood function L

missing energy events.

versus ieti':r J E for the 56

144

Based on the data in fig. 8 we define the tau sample by requiring

L > 0. Figure lla shows one such event. There are a total of 32 tau

candidates, the kinematics of which are quite consistent with the process

B •> ri/. For example fig. 12 compares the experimental transverse mass

distribution M_(riO for L > 0 events with the distribution expected for

My - 83.5 GeV/c2.

The non-tau events having L > 0 are calculated to amount to 2.3 ± 0.6

events. The net tau signal of 29.7 ± 5.9 events gives:

CJ-B(U - TV) - 610 ± 130 ± 115 pb

B(W - TI/)/B(W - eu) - 0.97 ± 0.22 ± 0.10

confirming e-^-r universality ^t Q2 - 2y-

2.4 Z° -> w Events (L < 0)T

A total cf 24 events have L < 0. Figure 11B shows one such event.

The corresponding Monte Carlo expectations are:

W -* rv, T -> hadrons - - - - - - - - - - - 8 . 0

Zc + j e"' 2° -* vv .............. . . _ 7 _•_

W + jet. V - leptons - - - - - - - - - - 2.0Z' ~ TT ...... - - - - _ - - . . - . 0.1Heavy flavors (cc, bb) - - - - - - - 0.2

QCD jets - - - - - - - - ],4

Total 20.8 ± 6.1

The predicted and experimental distributions in jet E_, for L < 0

events are shown in fig. 13. We note that apart from the residual r signal

the major contribution is from the neutrino decay of Z° recoiling off a

gluon jet. This observation provides a limit on the total number of light

neutrino species:

N < 10 (90% C.L.)

2.5 Limits on Supersynunetric Particle Masses

The decay of squarks and gluinos is expected to have the topology:

jets + missing energy. The present search is not optimized for such events

because selection criteria, designed to reduce QCD jet background, also cut

away the multijet states expected in squark and gluino decays. On the

basis of two events observed with L < 0 and two jets of E_ > 12 GeV we

obtain the mass limits shown:

Mq > 7° G e V' c a (90% C.L.)M- > 60 GeV/c2g

145

(a)EVENT 11673/449

ET (jet) = 21 GeV

ET (miss)= 19 GeV 1

til

I«:

/

V.7t \ •

-

— — —

(b)EVENT 18167/942

ET (jet) = 48GeV

ET(miss)=53GeV

Fig. 11: (a) digitizings in central drift chamber for r candidate

(L^ > 0) event. The invariant mass of the charged particle

je t is 0.99 ± 0.1 GeV/c2; (h) LT < 0 event

146

" r SAMPLE"LT>0

FOR Mw=83.5GeV/c2

T — HADRONS

NON-r

0 40 BOMT(GeV/c2)

Fig. 12: Experimental and Monte Carlo d i s t r i b u t i o n s for t r ansve r se

mass M_ (TW) for tan candidate events (L > 0 ) . The curve

i s ca lcu la ted for My •= 83.5 GeV/c2.

MISSING TRANSVERSE ENERGY

7

6

% 5

bJ

UAI24 EVENTS

-

/

I /

i

;

i

\

\

\

\

<

L T <0

ALL EXPTCTEDCONTRIBUTIONS

\\

s.

1 1 - -

2 -

I -

10 70 8020 30 40 50 60MISSING E T (GeV)

Fig. 13: Experimental and Monte Carlo distributions in je t E_ for

non-tau (L < 0) events.

147

using the supersymmetric model of Barnett, Haber and Kane [201. The number

of two-jet events expected from conventional sources is 2.8 ± 1.7 ± 0.3.

3. CONCLUSIONS

At the CERN pp Collider the dominant source of high pT niuons

(excluding isolated ones) is c- and b- quark production. The production of

c- and b- quarks at high p T is in good agreement with QCD predictions.

The rate of like-sign dimuons is consistent with substantial B° -B°_

mixing.

The rate and kinematics of jet events with large missing transverse

energy are explicable in terms of the Standard Model. The largest source

of these events is V - ry decav with hadronic decay of tau. The other

major source is neutrino decay of a high transverse momentum Z°.

148

REFERENCES

1. G. Arnison et al., Phys. Lett 147B (1984) 222.

2. G. Arnison et al., Phys. Lett 147B (1984) 493.

3. For additional info see G. Arnison et al., Beauty Production at the

CERN Proton-Antiproton Collider, submitted to Phys. Lett. B.

4. G. Arnison et al. , Phys. Lett. 134B (,1984) 469.

5. M. Banner et al., Phys. Lett. 122B (1983) 322.

G.J. Alner et al., Nuc. Phys. B61 (1973) 62.

6. A. Ali, E. Pieterinen, B. van Eijk, "Eurojet, a Monte Carlo Program

for Jet Simulations", presented by B. van Eijk, 5th Workshop on

proton-antiproton Collider Physics, Saint Vincent (1985).

7. Halzen et al.. Phys. Rev. D30 (1984) 700.

8. H. Albrecht et al., Phys. Lett. 162B (1985) 395.

P. Hass et al., Phys. Rev. Lett. 55 (1985) 1248.

9. A detailed account of the study of J/ij> production is in preparation

10. For additional information see G. Arnison et al., Search for B°-B°

Oscillations at the CERN proton-antiproton Collider, submitted to

Phys. Lett. B.

11. V. Barger and E. Phillips, Phys. Rev. Lett. 55 (1985) 2752.

12. T. Schaad et al., Phys. Lett. 160B (1985) 188.

13. V. Barger and R. Phillips, preprints HAD/PH/ 155,239,266.

14. F. Halzen and A. Martin, preprint DTP/84/14.

15. F. Paige and S.D. Protoposescu, 1SAJET Program Version 5.20, BNL 38034

(1986) .

16. A. H. Mueller and P. Nason, Phys. Lett. 157B (1985) 226.

17. R. Frey (UAl Collaboration), presented at the Division of Particles

and Fields Meeting, Eugene, Oregon, Aug. 1985.

18. For additional details see G. Arnison et al., "Events with Large

Missing Tranverse Energy at the CERN Collider", papers I and II,

submitted to Phys. Lett. B.

19. G. Arnison et al., Phys. Lett. 139B (1984) 115.

20. R.M. Barnett, H.E. Haber and G.L. Kane, Nucl. Phys. B267 (1986) 625.

149

COLLIDER PHYSICS

V. Barger

Physics Department, University of Wisconsin

Madison, Wisconsin 53706

ABSTRACT

QCD shower simulations of W production are compared with UA1 data; two re-cently observed W —* lu events with pr(W) > 50 GeV and dijets are shown to bemarginably compatible with expectations. The status of the search for a charged fourthgeneration heavy lepton in pp collisions is discussed. The implications of CERN dimuonevents for B°-B° mixing are considered. Trimuon events may aid in future pp collideridentification of i-quark contributions. Superstrings offer interesting new possibilitiesfor phenomenology, such as an extra neutral gauge boson [Z') and exotic fermions be-longing to 27 representations of EQ. Prospects for finding these particles are evaluated.

1. INTRODUCTION

The W, Z, jet and heavy quark data from the CERN pp collider have providedimportant tests of perturbative QCD. The success of these QCD predictions instillsconfidence that reliable calculations can be made in other contexts in the search fornew physics. This report considers several areas of current interest in the search fornew effects or new particles. Two recently reported W —* tu events at exception-ally high pr{W) are compared with the tail of the QCD distribution and found to bemarginally compatible with it. The missing pr plus jets signal for a fourth genera-tion charged heavy lepton is compared with standard model backgrounds; the UA1limit on monojets from new physics sources gives a (preliminary) lower bound of or-der 42 GeV on the heavy lepton mass. Expectations for dimuons from heavy quarkproduction are compared with UA1 data; the observed ratio of same-sign to opposite-sign dimuons seems to require B°-B° mixing effects at or above the maximal valuepredicted by the standard model. Trimuon events are now reported from the CERNcollider; these may potentially aid in the search for the t-quark. The richer particlespectrum possible with superstrings enlarges the scope for collider searches. The as-sociated phenomenology of Z and Z' boson and exotic fermion production and decaysis surveyed.

150

2. GLUON SPLITTING IN W+ DUETS EVENTS

High statistics W data have been accumulated at the CERN pp collider. The UAlcollaboration alone has reported 298 W —» ev events and 78 W —» fiu events. Ofthese, two dijet events are found at remarkably high pr{W): a W —* eu event withpr{W) =S 85 GeV and a W -> (xu event with pr[W) = 66 GeV. Can these high pr{W)events be explained as the tail of the QCD distribution or do they represent new physics?

QCD shower monte carlo simulations allow complete predictions to all orders in9

aa. Figure 1 compares shower predictions "with the UAl data. The predictions forpx(W) S 15 GeV are sensitive to resolution smearing, assumed here to be 3.5 GeV. Theagreement with the data is reasonably good, with the possible exception of the two high

events noted above.

5o

c

BU

6 0

40

20

0

1 1 '

A w~eVe

i I—-QCD Shower

\

A

I

M.C.

1

Data

aJ

1

298

]

1 1 '

Events)

—

—

—

i 1 _20 4 0 60 80 100

PT(W) (GeV)

T ^ I ' I

(UA! Data 78 Events)

QCD Shower M.C.

20 40 60PTIW) (GeV)

80 100

F'.g. 1 Shower Monte Carlo predictions of Ref. 2 comparet with preliminary UAl datafrom Ref. 1.

151

At high PT{W) the leading order diagrams are expected to be dominant. Thepaxton level showers can be combined into jets using the UAl jet algorithm applied topartons. Dijet events arise from both independent radiation of two (or more) gluons andfrom time-like daughters which split into two gluons. The gluon splitting componentis significant: <J(2 jet)/<r(l jet) = 0.7 (0.4) is obtained with (without) this splitting.With gluon splitting effects included, dijets are almost as likely as single jets, so theobservation of two dijets at high pr(W') is not yet a problem for a standard QCDinterpretation.

In comparing event rates at high pr{W) involving low statistics it is better touse the integrated rate above a threshold value p^ . Figure 2 shows such a compar-ison of the shower predictions with the data.

100 -

0

100

1 to"1

in

,o2

40 60 60 100p t( i (GeV)

to" 3

i '

Wo

l\ ,

1 '

n

1 i

1 ' 1

ULV %/?= 630

78 Events

No

1

GeV

—

20 40 60p .h (GeV)

80 100

Fig. 2 Cross section for W-production with pT{W) > plft from Ref. 2 compared withpreliminary UAl data from Ref. 1.

152

At high pr{W) the integrated cross section falls exponentially or faster with p^. Still,the observation cf only one W —> ei/e event and one W —» p^v^ event at pr(W) > 50 GeVis not in major disagreement with QCD expectations.

3. HEAVY LEPTON SEARCH

The search for a possible fourth generation of leptons (VL, L) and quarks (a, v) isa priority task for colliders. For light UL, the most promising L-signal at pp colliders isW —* LVL decay with subsequent L —• uiud and vi,cs decays, which would give eventswith large missing transverse momentum [fiT) and jets; the lep tonic L-decay signalsare obscured by the larger W —* tvt and W —> ruT contributions.

The rfT signal and backgrounds are shown in Fig. 3. The large W —> TUT backgroundis identifiable from the narrow hadronic jet of the T. In a recent UA1 search (based on381 nb~l integrated luminosity) a total of 14.9 ± 2.1 events were expected from non-r

o

monojet sources (assuming Nu = 3 neutrinos) whereas only 13 events were observed.This gives an upper limit of 4.5 events due to new physics sources and a preliminaryheavy lepton mass bound m^ > 42 GeV (at 90% confidence level, but systematic errorsnot included).

120

80

40

0

\ \

\ \L(25)

L{40) \

- \ > \L(60) \ \

\ \ \- • • N \

tvS.. \ N

b b . c C '••••--'?

> -i.

530 GeV

—

—

\ \ -

50 20 30 40pf (GeV)

Fig. 3 Heavy lepton cross section for rfT > ptfi compared with backgrounds (fromRef. 7).

153

4. DIMUONS AND B°-B° MIXING

The UA1 collaboration9now has 433 events with m(fj.fj.) > 6 GeV. The observedratio of like-sign to unlike-sign dimuons is unexpectedly large. Can this observation beexplained in the standard model with large B°-B° mixing? To answer this question, theproduction, fragmentation and semileptonic decays of heavy quarks must be calculated.

In evaluating the cross section for heavy quark production the 2 —> 2 and 2 —> 3

paxton subprocesses are included in a truncated QCD shower that is justified by the

validity of an analogous approximation to the W-production shower. At each rn(QQ)

a py-cutofF on the divergences of the 2 —• 3 cross section is chosen such that (ignoring

possible If-factor enhancements)

= / a(2 -* 3) = a{2 — 2)O'TOTAL

In this Poor Man's Shower approximation, the shower is represented solely by the 2 - » 3

subprocesses.

Fragmentation of heavy quarks to mesons is carried out a la Peterson et al. Weakdecays are evaluated in the V — A spectator quark approximation.

Dimuon events of heavy quark origin usually have jet activity nearby the muons.To separate heavy quark contributions from Drell-Yan and T, ib sources it is useful tointroduce an isolation criteron. The parton pr is summed within cones AR = [(A<£)2 +(AT?)2]1/2 < 0.7 around each muon and a Gaussian soft-hadron contribution from theunderlying event is added. An isolation parameter s = { ( X ^ w ) 2 + {

n

denned, where subscripts 1 and 2 refer to cones about muons 1 and 2. Dimuons with

s > 3 GeV are "non-isolated." The non-isolated events are principally of heavy quark

origin, with Drell-Yan and T, if; contributing mainly to isolated (s < 3 GeV) dimuons.

The possible 66 and cc sources of dimuons with m{iJ.fi) > 6 GeV are shown in Fig. 4.

The calculated numbers of non-isolated dimuon events (assuming no B°—B° mixing)

are given in Table I. The comparison with the UAl data indicates that a sizable excess

of same-sign dimuons over expectations is observed. This suggests B°-B° mixing.

A Bq(bq)-Bg(bq) mixing parameter eq is defined as the probability for B° —> B°

divided by the probability for B° -» fl° or B°. In the standard model the difference ofeigenstate widths AT' is small compared to the mass mixing Am', and eq is approxi-mately given by

where T is the average of the decay eigenstate widths. Note that e, ~ | for maximalmixing. In the standard model short distance calculation, the dominant contribution

154

to Am9 is given by the box diagram with t-quark exchanges; the result is

Am'^/T a Bfldm*U?{t4)

where the bag factor B is the deviation from the vacuum intermediate state approxi-mation and / is the B-meson decay constant. Since the Kobayashi-Maskawa mixingmatrix elements satisfy Utd <S. Uts, the B°d mixing is much smaller than B® (ej <. es).

0

„„(c) ( c )

C—

with B°-B° mixing

[—]B° B°

Fig. 4 The bb and cc sources of dimuons with m{fifj.) > 6 GeV; the signs of the muon

charges are shown.

Table I. Predicted numbers from Ref. 10 of non-isolated dimuon events comparedwith preliminary UAl data from Ref. 9.

Predicted Observed

{no B° - Ba mixing)

66 173 |

; • + - ; cc 68 1 252 216

DY + T 11 J

[±±] bb 60 116

155

12 ,Figure 5 gives the standard model prediction "for tfl versus the i-quark mass, takingfs = fn- For B = 1 and mt > 40 GeV nearly maximal values of is are attained.However, the observable mixing depends also on the production/sernileptonic decayfractions. Assuming meson production only, with oB (semi-leptonic) proportions

5T(6u) :B°{bd) ;B°{bs) = 1 : l : I

the observable mixing I is

I = 0Acd + 0.2es .

As Fig. 5 shows, the resulting standard model upper bound on i is

I £0.14 .

It is the B°{bs),'B'J [bd) ratio that dilutes the mixing effect and it is unlikely that a valuefor it larger than | is realized. The Mark II data13on e+e" production of B-mesonshave placed a limit I < 0.12 at 90% C. L. which is comparable with the above standardmodel bound.

0.5

0 . 4 -

0.1

20 40 60m t (GeV)

Fig. 5 Standard model predictions for e. and e = 0Aed + 0.2es versus mt (from Ref. 12).

156

The dimuon cross sections for mixing t are related to those for e = 0 by

ff(±±,f) = [(1 - t)2 + e V ( ± ± , 0 ) + 2f(l - £>( + - , 0)

a (+- , f ) = [(i - f)2 + e 3 M + - , o ) + 2?(i - f )a(±±,o) .

With only a 66 source, the predicted e = 0 ratio with the UAl acceptance cuts is

<7(±±,0)/<r( + - , 0 ) =0.35

where these like-sign events arise from one 6 —+ fi~ primary muon and one b —* c —> \L~secondary muon. Including all 66, cc, DY and T contributions to non-isolated events,the predictions1 in Table II are obtained. To account for the UAl data a mixingparameter

f - 0 2 4 + 0 - 1 4

is needed.

Table I I . Ratio of like-sign to unlike sign dimuons in pp collisions at CERN collider

energies.

£

e

= 0.0

= 0.1

- 0.2

Prediction

from Ref. 10

0.24

0.34

0.44

UAl

0.48 ± 0.08

157

5. DIMUONS FROM THE t-QUARK

There will also be dknuons of ti and W -» tb origin if the t-quark mass is not toohigh. The dimuon cross sections at y/s - 630 GeV for mt = 40 GeV are as follows:12

I + -] [±±]tb 10p6 lOpb .

ti I2pb Ipb

Thus for the current integrated hminosity of / £dt ~ 0.7p6-1 and dimuon detectionefficiency 0.26, * .:ut 7 events of t-origin are expected. The bulk of these dimuon eventswill be non-isolated.

6. TRIMUONS

Trimuon events are also expected from 66, ti and W -> tb (see Fig. 6) and these canDrovide further information on heavy quarks.15 The UAl collaboration 16has recentlyrecorded the observation of trimuon candidates.

There are distinctive modes to which 66 do not contribute:

• same-sign trimuons (SST)

• mixed-sign trimuons (MST) with both m(/x+/i~) > mB.

MST events with min[m(M+M~)] < 5 GeV dominate at least 40 : 1 over SST events.Although a trimuon search for quarks heavier than 6 is not easy, even one event of thenon 66 modes could provide valuable bounds on the heavy quark mass.

0 © ©. c \ b t y b cs . c \ b t y b c 1/ s

Fig. 6 Diagrams illustrating the signs ± of the charges of muons that can be emitted

at each stage of ti, tb and 66 cascade decays.

158

7. SUPERSTRING PHENOMENOLOGY

11

Superstring theories suggest that E& may be the gauge group of particle interac-1 R

tions at energies below the Planck scale. After EQ breaking, there is the interesting19

possibility of an extra U(l ) symmetry at low energy

En - S t / ( 3 ) • SU{2)L x [.'(l) , { / ( ] ) '

which would imply an extra neutral gauge boson ' * [Z'). Moreover, since fermionswould belong to 27 representations of E& there would be exotic fermions in additionto the usual fermions. The left-handed states of the first generation 27 , labeled bydecomposition into 5c'(10) and SU(5) representations are

(SO(10), SU{5))

ee ( 16 ,10 )

Nc (16, 1)

h ~ [fih) (10, 5)

( 1 , 1)

The exotics are a new charge —1/3 quark k, a charged heavy lepton E, and new neutralleptons N, i/g, Ng, n.

The decays of the Z, Z' and W bosons will include final states with exotic fermionsif they are sufficiently light. Table III gives the partia' widths, under the assump-tion of no phase-space suppression; for exotic ferrnion masses < 30 GeV the resultswould be essentially the same. The exotic leptons E, '/£ a n d NE could be copiouslyproduced by Z and W decays; all of these leptons may well be unstable and decay tothe usual fermions. The Z' boson would be a source of /i-quarks and E, Ng, N, nleptons.

159

Table III . Partial widths in GeV for Z and Z' bosons in E§ assuming no phase spacesuppression for decays to the exotic fermion members of the 27 representa-tion.

hh

EE

WE

NENE

NN

nh

uu

dd

TOTALWIDTH

(3 generations)

T{Z)

.02

.11

.18

.18

0

0

.18

.09

.32

.40

4.22

ftw

.23

.07

.004

.07

.11

.11

.004

.02

.07

.11

2.27

uEE

NEE

Pee

ud

T(W)

.24

.24

.24

.75

4.16

The couplings of the Z' to u and d quarks are smaller than for the Z which makesit more difficult to produce in pp collisions. The branching fraction B(Z' —»• e+e~)ranges from 1% (all exotic fermion decays allowed) to 4% (no exotic decays). Fig-ure 7 shows the limit on the Z' mass imposed by the UAl experimental search forhigh mass electron-positron pairs. For no exotic decays, the limit is Mz< > 143 GeV.Future experiments at the Fermilab Tevatron will be sensitive to Z1 masses up to300 GeV.

160

f£i io~CDb<D

+t '^

CDb

, n 3

I ' 1

N. \

1 . 1

1

V^=630GeV

Al 90% C.L. -

!OO 200. (GeV)

300

100 200M,. (GeV)

300

Fig. 7 Ratio of Z' —>• e+e~ to Z —> e+e~ cross sections (from Ref. 21) at cm. energiesof y/s = 630 GeV and 2000 GeV.

There is a constraint on exotic fermion masses from the measured value of theratio oB{Z -> eJre~)/\crw+JrW" B{W -» «/)] = 0.125 ± 0.023 at the CERN pp collider.Using standard model calculations of az jaw and Y(Z -> e+e~)/T{W —> zv), the widthratio Tw/Tz = 1.11 ± 0.23 is deduced. In the £ 6 model the predicted width ratio for3 generations is

• 0.71 if the neutral exotics are < 30 GeV and charged exotics are > 50 GeV

• 0.80 if all exotics are ss 42 GeV so that they contribute to Z decay but arekinematically suppressed in W decay

• 0.98 if all exotics < 30 GeV or all exotics > 50 GeV

161

The /i-quarks can be hadronically produced via the QCD fusion subprocesses. The/i-quark can decay through mixing with the usual - 1 / 3 charge quark doublet members(though more bizarre decay schemes occur if flavor changing neutral currents are forbid-den by discrete symmetries). It is natural to assume that the first generation /i-quark

25

mixes with the d-quark, with angle a of order md/mh. The weak eigenstates are then

u cos 8c — c sin dc

dcos a — hs'ma' h cos Q + ds'm a

The signature of this doublet-singlet mixing is flavor changing neutral current (FCNC), . . , 2 4decays with

r(/i — dZ'),T{h - uW) ~ 1/2

where the Z', W may be real or virtual, depending on what the /i-mass is. An in-teresting consequence of the FCNC is mixing of neutral mesons containing an /i-quarkconstitutent,2Dvia the Z, Z' exchange diagrams of Fig. 8. The ratio Am/F is indepen-dent of the mixing angle a. For mh ~ 25 GeV the H°(hd) —• fIQ(hd) mixing parametere can be near maximal, as shown in Fig. 9.

Fig. 8 The Z, Z' exchange diagram for H°(hd)-H°(hd) transitions contributing to

Am.

0.5

0 . 4 -

0 . 3 -

0 . 2 -

23 25 30 35mH (GeV)

40

Fig. 9 Mean probability e of H°[hd) -* H°[hd) transitions as a fraction of all H°

decays, plotted versus the mass mjj (from R.ef. 25).

162

The £"6 heavy leptons can be produced in hadron collisions via the W-boson decaysW —* EVE o r ENE (for the first generation states). The exotic-lepton decay schemedepends on the mass ordering:

• for TI%E > JTIJ/JT.,

£• _». yE 4. W*, UE —> e + W* give a final state W —* ee + jets

• for THE < "1| /E ,

the charged current decays UE -* E + W, E — vt +W* lead to a final stateW —* i/P + jets and the neutral current decays UE —> E + W*, E —>• e + Z*give W —»• ee + jets.

If the exotic leptons are very massive, they may be produced at supercollider energiesvia the diagrams in Fig. 10. Typical cross-sections" are given in Fig. 11. Very massiveleptons would decay to real W, Z and Z' bosons.

r.z.z'

q q q q

Fig. 10 Drell-Yan and gluon fusion subprocesses for production of E& leptons atsupercollider energies.

10

1 —

Q.

lO-'L

10r 2

charged

i

ip p -

J

•v^neutrals

1

i

EE + anything

?= 40 TeV

(N, i/p.Nr.n)

0.1 0.5 1.0ME (TeV)

1.5 2.0

Fig. 11 Cross sections for production of E% leptons at y/s = 40 TeV versus the lepton

mass (from Ref. 26).

163

In conclusion there may be many new particles awaiting discovery:

• from superstrings

• from supersymmetry

• from 4** generation

• in standard model

h quarks

E, UE, NE, n, N leptons

!

q, I, H scalars

-7, ill, z, h fermions

!

(a, v) quarks

[uL, L) leptons

f (-quark

[ Higgs scalar

Searches for these particles at new colliders should prove to be interesting!

ACKNOWLEDGEMENTS

I thank R. Phillips and K. Whisnant for collaboration in the preparation of thisreport. I also thank N. Deshpande, T. Gottschalk, W.-Y. Keung and J. Ohnemus forcollaboration on the work presented here. This research was supported in part bythe University of Wisconsin Research Committee with funds granted by the WisconsinAlumni Research Foundation, and in part by the U. S. Department of Energy undercontract DE-AC02-76ER00881.

164

REFERENCES

1. UAl collaboration: S. Wirnpenny, talk at Moriond Conference (1986).

2. V. Barger, T. Gottschalk, R. J. N. Phillips and J. Ohnemus, Phys. Rev. D32, 2950(1985) and to be published.

3. V. Barger, H. Baer, K. Hagiwara and A. D. Martin, Phys. Rev. D30, 947 (1984).

4. V. Barger, H. Baer, A. D. Martin, E. W. N. Glover and R. J. N. Phillips, Phys.Lett. 113B, 449 (1983); Phys. Rev. D29, 2020 (1984).

5. D. Cline and C. Rubbia, Phys. Lett. 127B, 277 (1983).

6. S. Gottlieb and T. Weiler, Phys. Rev. D29, 2005 (1984).

7. V. Barger, J. Ohnemus and R. J. N. Phillips, UW-Madison report PH/275 (1986).

*. I'Al collaboration: M. Mohammadi, talk at Madison workshop on physics simula-tions at high energies (1986).

9. UAl collaboration: K. Eggert. Proc. New Particles 1985, ed. by V. Barger, D. Clineand F. Halzen, World Scientific (1986) and talk at Moriond conference (1986).

10. V. Barger and R. J. N. Phillips, Phys. Rev. Lett. 55, 2752 (1985).

11. C. Peterson et al., Phys. Rev. D27, 105 (1983).

12. V Barger and R. J. N. Phillips (unpublished).

13. T. Schaad et al., Phys. Lett. 106B, 188 (1985).

14. For another recent • aluation of B°-B° mixing in pp collider data by the Eurojetcollaboration see Ref. 9.

15. V. Barger and R. J. N. Phillips, Phys. Rev. D30, 1890 (1984) and UW-Madisonreport PH '283 (1986).

16. D. Cline, talk at Madison workshop on physics simulations at high energies (1986).

17. J. H. Schwarz, Phys. Rep. 89, 223 (1982); M. B. Green, Surveys in High EnergyPhysics 3, 127 (1983).

18. E. Witten, Nuci. Phys. B 258, 75 (1985).

19. P. Candelas et al., Nucl. Phys. B258, 46 (1985); J. D. Breit et al., Phys. Lett. 158B,33 (1985); A. Sen, Phys. Rev. Lett. 55, 33 (1985).

20. J. L. Rosner, Chicago preprints EF185-34, 86-19.

21. V. Barger. N. G. Deshpande and K. Whisnant, Phys. Rev. Lett. 56, 30 (1986).

22. E. Cohen et al., Phys. Lett. 165B, 76 (1985).

23. L. S. Durkin and P. Langacker, Penn. Preprint UPR-0287 T (1985); M. J. Duncanand P. Langacker, Penn. Preprint UPR-0293-T (1986).

24. V, Barger, N. G. Deshpande, R. J. N. Phillips and K. Whisnant, Phys. Rev. B33,1912 (1986).

25. V. Barger, R. J. N. Phillip and K. Whisnant, UW-Madison report PH/286 (1986).

26. V. Barger and W.-Y. Keung, UW-Madison report PH/282 (1986).

165

PHYSICS AT THE Z°*

FREDERICK J . GILMAN

Stanford Linear Accelerator Center

Stanford University, Stanford, California, 94305

ABSTRACT

With the next generation of electron-positron colliders on the immediate

horizon, we review the standard model and the precision tests of it which can be

carried out at the Z° peak. Emphasis is put on the possibilities for discovering

new physics, from additional quarks and leptons to extra neutral gauge bosons.

* Work supported by the Department of Energy, contract DE - AC03 - 76SF00515.

166

1. INTRODUCTION

The cross section for electron-positron annihilation into hadrons is shown in

Figure 1. After the valley following charmonium and bottomonium physics, the

cross section for electron-positron annihilation into hadrons rises to about 40 nb

or 4000 times the "point" cross section for e+e~ —» -7 —• M + ^~ at the peak of the

Z. After struggling in the valley, there is no doubt as to where we want to do

physics next.

There axe two machines designer to do this physics, SLC and LEP. Construc-

tion of both is proceedir? apace. At SLAC, the construction project is in its final

stages. The tunnels are finished and the magnets are being installed. The single

interaction region is also nearing completion, with the first experimental appara-

tus, the Mark II detector, being moved from PEP. Hopefully, there will be beams

in the interaction region by the end of this calendar year and experimentation

can begin next Spring. At the end of the decade, the Mark II will be superceded

by a more powerful detector, the SLD. At CERN, much of the tunnelling for LEP

and its interaction regions is finished. Four experiments are planned: ALEPH,

DELPHI, L3, and OPAL. Data taking is to begin in 1989.

With the era of Z° physics approaching, it is an opportune time to take

another look at what can be discovered at these UZ factories". There have

been rather complete and extensive examinations of this subject. ' The increase

in our understanding since some of the work was done, plus the immediacy of

experiments with well defined detectors, has led to further work. In the following

I will attempt to give a brief overview of what we hope to learn from Z physics.

I start with the standard model and the accuracy with which we can now test it,

and proceed to what new physics will soon be within our reach.

167

2. THE STANDARD MODEL

The standard model for electroweak physics is based on the gauge theory

SU{2) x 17(1), spontaneously broker: BO as to have massive W+, W~, and Z vec-

tor bosons and a massless photon. Within the gauge theory sector itself there

are three parameters, g, the SU(2) coupling; g', the U(l) coupling; and the vac-

uum expectation value, u, of the Higgs field that is associated with spontaneous

breaking of the continuous symmetry.

We usually do not work in terms of these three parameters. After defining

the weak mixing angle through

and identifying the electromagnetic coupling

e = gs'mdw, (2)

and the Fermi effective coupling

it has often been convenient to use a = e2/47r, Gp and sin2 0jy as the three

parameters of the theory. This is related to the very accurate experimental de-

terminations of the first two, a and Gp, leaving sin2 Qw to be pinned down as the

characteristic parameter expressing the unification of weak and electromagnetic

168

interactions. T h e W and Z boson masses are re la ted by

= Mz cos 6W, (4)

and the W mass itself, using Eqs . (2) and (3) in lowest order, is given numerically

by

37.3 GeV ,„.Mw — :—2 • W

While u p to the present it is sin2 Ow t h a t is commonly used as t he third

parameter , Eqs . (4) and (5) make it clear tha t we could use Mw or Mz~ Until

their discovery this made no sense, bu t already the experimental unce r t a in ty on

their masses gives a comparable accuracy in the determinat ion of sin2 &w to tha t

from measurements \v low energy neutral current experiments . In fact, once

we enter the era of Z physics, it is much more appropr ia te to use a, Gp, and

Mz as the th ree parameters of t he electroweak gauge theory, since Mz will be

fairly easily measured to an accuracy which will far exceed its equivalent in other

determinat ions of sin2 dw •

In any case, once these three parameters are all accurately measured , any

independent measurement of a coupling or of Mw will give a test of t he s t anda rd

model. We recall tha t the couplings of the Z to a fermion, / , are given by (where

Qf is the electric charge of the ferrnion in units of t he proton charge) :

QR = —D , (6)cos aw

and

QL = -—3L c o s g

S m — — ' (7)

making explicit their dependence on sin2 flyy.

169

In order to make a precision test of the standard model, we need to take

account of something we have slid over in the previous discussion. The elec-

troweak radiative corrections change the relationship between sin2 &w and the

gauge boson masses. At the same time, we need to be careful to specify at what

momentum scale we define the parameters of the theory. For a and Gp this scale

is taken to be zero, as these two quantities are taken from experiments at zero

momentum transfer (or very close to it). As a result of the electroweak radiative

corrections calculated to one loop level Mw and Mz gel corrected upward by

about (1.07)1''2, so that

38.65 GeV . .Mw = — (8)

sin 6w

and

77.3 GeV

where sin 8w is defined at the scale Mw. For a value of sin2 $w = 0.22 the

corresponding value of Mz from Eq. (9) is 93.3 GeV (as compared with 90.0 GeV

without one loop radiative corrections). The present accuracy of experimental

measurements either of the masses of the gauge bosons or of sin2 &w in neutral

current experiments does not permit an incisive test of the radiative corrections

at the one loop level. Note that the fractional errors in Mz and sin2 6w are

related by:

» £ = -0.36 ' I ™ ' * ' , (10)

BO that a 5% measurement of sin2 6w is equivalent to a 1.8% measurement of

170

Of much higher sensitivity is the polarization asymmetry. If the electron

beam can be longitudinally polarized, we can form the asymmeiry

where aR and aL are the cross sections (integrated over final angles for any

particular final state or sum of final states) for right- and left-handed incident

electrons, respectively. With sin2 $w — 0.22, the polarization asymmetry has a

value of about —0.24. More importantly, since vt is proportional to 1 — 4 sin2 6w,

and small compared to ae,

SApoL^-% 6{sm26w) (12)

Therefore, as seen in Figure 2, with 104 produced Z's and a 5% systematic

uncertainty in the polarization, one can determine the polarization asymmetry

to an accuracy that corresponds to 6(sin20w) = ±0.002. With 106 Z's and

a systematic uncertainty of 1%, the equivalent accuracy in sin2 6w is ±0.0004.

The accuracy here is comparable to that from measuring Mz when the two

measurements are transformed to an equivalent basis. Here is the high precision

test of the standard model; nothing else is so powerful or direct.

There are many other measurements of couplings that can be made from

front-back asymmetries (without a polarized beam), from tau polarization, and

from using longitudinal electron polarization with measurement of particular / /

final states. For both quarks and leptons there is the definite possibility of re-

ducing the present experimental uncertainty in the vector current couplings of

the Z to fermions by about an order of magnitude.

171

4. LOOKING FOR NEW PHYSICS

In the following we review rather quickly many of the possible new physics

areas which can be explored in Z decays. The reader interested in examining

further a particular topic should consult Refs. 1, 2 and 3.

• The top quark should be easy to find if mt < Mz/2. Fairly straightforward

cuts, motivated by the fact that two and three jet events are approximately

planar while weakly decaying top quarks give quite spherical events when one is

not far from threshold, are quite effective in separating out a sample of Z —• it

events- Furthermore, in the semileptonic decays of the t quark, the charged

lepton typically has a rather high momentum relative to the final quark jet,

and additional cuts on lepton transverse momenta produce a fairly clean signal

w % events which are preselected to be aplanar. With 103 to 104 Z's one

should already have a good hint of top quarks if they are present in Z decays,

and with 105 Z's it will be possible to pin down the mass to within a few GeV.

• That brings us to toponium, the bound states of top and anti-top. There

is important mixing between the Z and vector toponium bound states through

the off-diagonal term in the mass-squared matrix:

6m2 = 2v/3 |*(0)| M*/2 vt. (13)

Here 'J'(O) is the value of the wave function of the toponium vector state at the

origin, and fj is the vector coupling of the Z to the top quark. This produces deep

minima at the bare mass of the toponium state in the cross section for e+e~~ —* ff,

as shown in Figure 3. Here the top quark mass was optimally chosen to place the

spectrum of toponium bound states within the Z peak. Unfortunately, even if

172

we should be so lucky, the spread in beam energy at SLC, and to a lesser extent

LEP, washes out much of the beautiful structure (see Figure 4). Still, it should

be possible to delineate the lowest few bound states and make a very accurate

measurement of the top quark mass even with a fairly broad beam energy spread.

• Charged heavy leptons are also relatively "easy" to find. With a branching

ratio of about 3% aside from a kinematic factor plus a clean and simple signature

from their purely leptonic modes, the search procedure would parallel that which

found the tau. Mirror leptons, which couple through V+A to the charged weak

boson, have a characteristic change in sign of the front-back asymmetry which

makes them very distinguishable from the "usual" sequential leptons which couple

through V — A.

• The existence of additional neutrinos can be deduced first from the in-

crease in the total Z width of 180 MeV per sequential neutrino mentioned pre-

viously. Much more incisive "neutrino counting" is achieved by running above

the Z mass and tagging the Z by detecting the radiated photon from the process

e+e~ —* Z + -). This will permit a measurement of the branching ratio for Z

decays into "nothing" once corrections are made for those events with charged

particles or photons from Z decays which manage to escape the detector.

• As for heavy neutral leptons, we should be able to make a rather complete

sweep almost to the kinematic limit. For example, a fourth generation heavy

neutrino which mixes with one of the lighter neutrinos (permitting it to decay;

otherwise it is picked up by "neutrino counting") would be susceptible to detec-

tion if the square of the mixing matrix element was as small as 10~10 and/or its

mass was as large as 45 GeV.

• For quarks and leptons which have a sufficiently high mass that the Z can

173

not decay into them, there is still a sensitivity to their presence in the one loop

electroweak radiative corrections. Figure 5 shows the effect on APOL of a new

quark doublet, lepton doublet, or full generation of quarks and leptons relative

to its value in the standard model with three generations. Unfortunately, the

sizes of the effects are at best only of a few standard deviations significance even

with only a 1% systematic error in the measured polarization of the beam.

• There have been extensive studies of how to detect supersymmetric particles

if they are light enough to be produced in Z decays. Branching ratios are

sizable, if allowed at all, and standard techniques of picking out events with

missing transverse momentum would appear to suffice for at least establishing

the existence of new physics with properties consistent with supersymmetry.

• A similar situation holds for technicolor theories. The characteristic signal

involves production of pairs of light spin zero particles called technipions. If

they are light enough, the Z should decay into pairs of technipions with a sizable

branching fraction.

In both the case of supersymmetry and in the case of technicolor, the effect

of virtual particles on the one loop electroweak corrections is comparable to

that from adding a new generation of degenerate quarks and leptons. For the

case of technicolor the effect may be particularly large, and a many standard

deviation effect in APOL is predicted if the polarization of the electron beam can

be measured to 1%.

o The Higgs boson (like the t quark) should not really be included in a

list of new physics topics, for it is a particle contained in the standard model.

Nevertheless, it is new since it is as yet undiscovered. The standard technique

of looking for Z —» H°l+t~ is quite clean and should be decisive, but requires

174

something like 106 Z\ if the Higgs mass is in the 10 to 30 GeV region. With its

even smaller branching ratio, Z —• H° f requires more events yet. On the other

hand, studies of using the decay Z —<• Hovt>, with about obc times the branching

ratio of Z —* Ho£+£.~, look possible with the SLD and LEP detectors, as well as22

with the Mark II if recent studies are extended and continue to be positive.

• Compositeness is an idea most often considered for quarks and leptons, but

in a more radical form may be taken to include the W and Z as well. In the

former case one looks for a modification of the interactions of the point Dirac23

fermions, excited quarks and leptons, and exotic states. In the latter case, the Z

could itself have an enhanced rate (compared to standard model expectations) for

some decays, such as Z —> 3-7, or new decays, such as those involving associated

composite scalars (if they are light enough).

• The possibility of enlarging the electroweak gauge group beyond the SU[2)x

U(l) of the standard model has had various theoretical motivations over the years.

Grand unified theories, such as 0(10), generally lead to additional gauge bosons,

as do left-right symmetrical theories such as SU(2)L X SU(2)R X 17(1).

The great burst of interest in superstring theories has revitalized research

in this area, as the combined low energy gauge group will generally be larger

than SU(3)C x SU{2)L x U{l)y in these theories.26'27 An early favorite in this

regard is to have SU{3)C x SU(2)L x U{l)y x DT(l) at "low" energies, but this

choice seems to be by no means unique.

Nevertheless, most attention has been focused phenomenologically on the

implications that follow from this last possibility: the electroweak gauge group is

SU(2)L x U(l)y x U{\) and there is just one "extra" neutral gauge boson, a Z'.

We will concentrate or> this case here as well, mostly for definiteness, but also

175

because it serves as a generic model of how electron- positron physics is changed

by the presence of a Z'.

The Lagrangian describing the interaction of the neutral gauge bosons of the

theory with the corresponding currents now has the form

with the last term being new and giving additional neutral current effects. The

weak charges of quarks and leptons which the Z ' "sees" are contained in Jg, and

are well-defined in a particular model. We take those charges which correspond

to the favorite Z' of superstrings, for which these charges have been worked out

elsewhere.

The presence of an extra neutral gauge boson, Z', will generally entail mixing

with the Z of the standard model. The two channel mass matrix has the form

\ 6M2 M%iMT)

and for 6M2 small will be diagonalized by a rotation through an angle

°MIX * M l M l (15)

The physical Z mass will be shifted downward from its "bare", standard model

value, just as the Zl will be shifted upward:

Ml-Ml, „,1MZ

In a given theory, the Higgs content gives restrictions on the elements of the mass

matrix in Eq. (14). There are consequent correlations between &MIX &&<! M\,

if these restrictions are imposed.

176

The constraints which the measured as compared to expected (in the standard

model) Z mass, the neutral current data., and the Higgs content of superstring

models impose have been examined separately or in combination in a number of

papers in order to constrain the values of the Z' mass and mixing angle. As

shown in Figure 6, the region of masses allowed for the Z' which has (unmixed)

gauge couplings corresponding to Zv starts at about 130 GeV and the allowed

mixing angles obey \0MIX\ ^ 0.1. For Z' masses up to several times the Z

mass, it is the neutral current data and/or the measured value of the Z mass

being consistent with the standard model value which provide more stringent

constraints than the Higgs content. The surprisingly low mass value allowed for

the Z' is due to the small (compared to the Z) couplings to ordinary fermions

of the Zq with which we are dealing with here.

Measurements at the Z peak will serve to restrict much more the values of32

&MIX ajid Mz< as compared to the present limits. Figure 7 shows the change

in the cross sections for particular final state fermion pairs in electron-positron

annihilation at the (mixed) Z peak as a function of 6MIX when Mz> is fixed

at 200 GeV. 1 here are changes of roughly 10% for variations of OMIX by ±0.1.

Such a change should be significant, particularly for e+e~ —• Z —* e+e~ (or

equivalently, e+e~ —* Z —<• fi^(j.~), where a 3% measvement of the cross section

seems possible.

Of course the mass of the Z itself, as noted previously, will be very accurately

determined. The impediment to using this information as a constraint is the

accuracy of the prediction of the (unmixed) value of Mz in the standard model

from an independent measurement of sin2 6w (from Mw or couplings). If we

can assume an order of magnitude improvement in the constraint on AMz, the

177

shift in the Z mass from its standard model value, then from Eq. (16) we can

entertain a factor of 3 improvement in the constraint on 6MIX for a given value

of Mz<. Altogether, just the measurement of the Z mass and the peak height

in particular channels will very much improve the limits on the parameters of a

potential Z'.

Far more dramatic yet are the limits provided by the use of a longitudinally

polarized electron beam. In Figure 8 are displayed the changes in ApoL &t the

Z peak due to a Z1 as a function of 8 MIX- NOW we have roughly ±50% changes

for OMIX varying by ±0.1. Even with a 5% uncertainty in the beam polarization

and a modest number of £'s, it should be possible to constrain \6MIX\ ^ 0.01.

There still is the possibility that OMIX — 0. Then the Z is just the good

old one from the standard model, and there is no effect worth speaking about at

y/s = Mz- But now there are still dramatic effects at somewhat higher energies.

Figure 9 shows the front-back and polarization asymmetries as a function of

y/s for several Z' masses and values of 6MIX- Already there are measurable

deviations at y/s = 110 GeV or so if the Z' mass is not many times

178

5. CONCLUSION

I hope to have indicated, if only in a sketchy manner given limited space and

time, the exciting era of physics at the Z which is on the immediate horizon.

With 104 Z's one can already do some very interesting physics: the value of

Mz, the cross section for e+e~ —» Z —> / / , a signal for the t quark if it is at

all accessible kinematically. With 105 Z's plus a longitudinally polarized beam

or 106 Z% we not only have the possibility of making a high precision check of

the standard model and a very thorough sweep of the existence of particles with

masses below M2/2, but we have a window on new physics up to several hundred

GeV.

179

FIGURE CAPTIONS

1. A somewhat schematic view of the electron-positron landscape as a function

of center-of-masE energy.

2. The uncertainty in the longitudinal pola-ization asymmetry, ApoL, and

the corresponding uncertainty in sin2 6w es a function of the number of Z's

detected (from Ref. 11).

3. The cross Bection for e+e~~ —* M+M in units of opt ~ 4na2/3s for m.t = 47

GeV. The dotted curve shows the cross section with the Z present, but no

toponium (from Franzini and Gilman, Ref. 14).

4. Saicne as Figure 3, but smeared using a beam energy spread of OEt — 40 MeV

(roughly characteristic of LEP, solid curve) and O£k — 100 MeV (roughly

characteristic of SLC, dashed curve). The dotted curve again shows the

effect of the Z pole without toponium present (from Franzini and Gilman,

Ref. 14).

5. Change in AIR = — Apoh due to virtual degenerate generations of quarks

and leptons as a function of their mass (from Lynn, Peskin, and Stuart,

Ref. 7).

6. Constraints on the Z prime mass and mixing angle at present following

from the Higgs content in superstring theories (region bounded by the solid

curve), AMz < 3 GeV (region bounded by the darh-dot curve), and neutral

current data and the gauge boson masses (region bounded by the dasher

curve from Durkin and Langacker, Ref. 31).

7. Change in the mass, width, and peak cross sections for e+e~ —* n~*~n~ ,uu

ard dd at the Z (in units r>f opt =• 4?ra2/3s ) as i function of 6MIX f° r

180

mixing with Zr> (from Franzini and Gilman, Ref. 32).

8. Change in APOL *•'•*• t n e Z peak as a function of OMIX f°r mixing with Zv

(from Franzini and Gilman, Ref. 32).

9. The front-back asymmetry, Apg, and the longitudinal polarization asym-

metry, APOL for e+e~ —* /x4fj.~ as a function of y/s for: (a) and (d)

Mzn = 150 GeV and 6MIX = 0 (dashed curve) and -0.2 (solid curve); (b)

and (e) MZn = 200 GeV, BMIX - -0.15 (solid curve) and MZri = 295 GeV,

OMIX = -0.05 (dashed curve); (c) and (f) MZx = 200 GeV, 6MIX = -0.1

(solid curve) and &MIX — 0 (dashed curve). The dotted curve is in all cases

the expectation without a Z' (from Franzini and Gilman, Ref. 32).

181

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29. M. Dine et al., Ref. 25; P. Binetruy, S. Dawson, I. Hinchliffe, and M. Sher,

LBL report LBL-20317, 1985 (unpublished); E. Witten, Nucl. Phys. B268.

79 (1986). See also, H. W. Braden, et al., Phys. Rev. Lett. 56, 2668

(1986).

30. This Z' is a linear combination of the Z$ and Zx defined by P. Langacker,

R. W. Robinett, and J. L. Rosner, Phys. Rev. D30, 1470 (1984) within the

context of symmetry breaking patterns of a grand unified E$ gauge theory.

This combination is often called Zv following Durkin and Langacker, Ref.

31.

184

31. S. M. Barr, Phys. Rev. Lett. 55, 2778 (1985); L. S. Durkin and P. Lan-

gacker, Phys. Lett. 166B. 436 (1986); V. Barger, N. G. Deshpande, and K.

Whisnant, Phys. Rev. Lett. 56, 30 (1986); J. Ellis et al., Ref 28.

32. Effects of a Z' within the context of superstrings on electron-positron anni-

hilation experiments have been considered by G. Belanger and S. Godfrey,

TRIUMF preprint TRI-PP-86-12, 1986 (unpublished); V. D. Angelopoulos

et al., CERN preprint CERN-TH.4408/86, 1986 (unpublished); M. Cvetic

and B. W. Lynn, SLAC preprint SLAC-PUB-39C.1, 1986 (unpublished); P.

J. Franzini and F. J. Gilman, SLAC preprint SLAC-PUB-3932, in prepara-

tion. An early version of this last work was given by P. J. Franzini, invited

talk at the XXIth Rencontre de Moriond, March, 1986 and SLAC preprint

SLAC-PUB-3920, 1986 (unpublished).

33. G. Feldman, Ref. 9 and private communication.

185

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195

To EXPLORE THE l T E V SCALE

C. QUIGG

Fermi National Accelerator Laboratory

P. O. Box 500, Batavia, Illinois 60510

ABSTRACT

I summarize the case for new physics at the TeV scale, and review

speculations about new phenomena which may occur there. I then

discuss the physics prospects of a multi-TeV hadron collider, and

examine some of the processes which may be studied in detail with

such an instrument.

l INTRODUCTION

A great deal has happened since the first Vanderbilt Conference in 1973.

At Vanderbilt, the high-energy physics group has grown in numbers and in

influence, and the department has even taken the radical step of hiring two

new theorists! In physics itself, the changes have been no less dramatic. At

the time of the 1973 Conference, many of the things we now take for granted

as basic elements of our world-view had not yet been established. Quarks and

color were still regarded as vaguely subversive ideas. The formulation of QCD

awaited the recognition of asymptotic freedom. Neutral currents had not yet

been discovered. Large-pj. pions had been observed, but jets of hadrons had not

yet made their experimental appearance. Neither the ip/J nor charmed particles

had been found. The Drell-Yan mechanism was viewed with deep suspicion. The

remarkable progress of these thirteen years, marked by experimental discovery,

theoretical insight, and instrumental innovation in abundant measure, has led

us to a radically new, simple, and far-reaching conception of Nature, which we

call The Standard Model.

The Standard Model is shown schematically in Fig. 1. It is, at least at first

sight, a scheme of considerable economy. We have identified a small number

of fundamental constituents, the quarks and leptons, and have recognized that

the elementary interactions among them all may be described by gauge theo-

196

THE STANDARD MODEL

%%: MATTER & ENERGY

Figure 1: The Standard Model of Particle Physics.

ries. The picture has a pleasing degree of coherence, and holds the promise of

deeper understanding - in the form of a further unification of the elementary

interactions - still to come.

This is an accomplishment worthy of the pleasure we take in it, but if we

have come impressively far since the first Vanderbilt Conference, we still have

quite far to go. The very success of the standard SU{3)C ® SU(2)L <g> U(l)y

model prompts new questions:

• Why does it work?

• Can it be complete?

• Where will it fail?

The standard model itself hints that the frontier of our ignorance lies at ~ 1 Te V

for collisions among the fundamental constituents. In more general terms, the

success of our theoretical framework suggests that a significant step beyond

present-day energies is needed, to see breakdowns of the theory.

Beyond these generalities, there are many specific issues to be faced. There

is, for example, our incomplete understanding of electroweak symmetry breaking

197

and the suggestion (from the "bound" ^Higgs < 1 TeV/c2, for example) that the

1 TeV scale will be crucial to a resolution of this problem. The Higgs mechanism

provides a means for generating quark and lepton masses and mixing angles, but

leaves the values as free parameters. We do not understand what CP-violation

means. The idea of quark-lepton generations is suggested by the necessity for

anomaly cancellation in the electroweak theory, but the meaning of generations

is unclear. We may even dare1 to ask what is the origin of the gauge symmetries

themselves. Such questions - and this is but a partial list - are stimulated by

the standard model itself, and by our desire to find ever simpler descriptions of

Nature, of ever more general applicability.

Beyond OUT search for more complete understanding, there are many reasons

to be dissatisfied with the standard model. A powerful aesthetic objection is

raised by the arbitrariness of the theory, which requires us to specify a multitude

of apparently free parameters:

• 3 coupling parameters a,, a .EM, and sin2 6W,

• 6 quark masses,

• 3 generalized Cabibbo angles,

• 1 CP-violating phase,

• 2 parameters of the Higgs potential,

• 3 charged lepton masses,

• 1 vacuum phase angle,

for a total of 19 arbitrary parameters. A similar count holds for the known ex-

amples of unified theories of the strong, weak, and electromagnetic interactions,

such as 517(5).

198

2 WHY THERE MUST BE NEW PHYSICS ON THE 1 T E V

SCALE

The standard model is incomplete2; it does not explain how the scale of

electroweak symmetry breaking is maintained in the presence' of quantum cor-

rections. The problem of the scalar sector can be summarized neatly as follows.3

The Higgs potential of the SU[2)i ® U{l)y electroweak theory is

V(<j>+<t>)^nl<j,+4> + \\\{4>+4>y . ( l )

With AiJ chosen less than zero, the electroweak symmetry is spontaneously bro-

ken down to the U(l) of electromagnetism, as the scalar field acquires a vacuum

expectation value fixed by the low energy phenomenology,

1/2 « 175 GeV . (2)

Beyond the classical approximation, scalar mass parameters receive quantum

corrections involving loops containing particles of spins J — 1,1/2, and 0:

J = 0 J = j J = 1

( ^ ) W ^ W . . (3)

The loop integrals are potentially divergent. Symbolically, we may summa-

rize the content of Eq. (3) as

A 3

:2 + ---, (4)

where A defines a reference scale at which the value of y? is known, g is the cou-

pling constant of the theory, and C is a constant of proportionality, calculable

in any particular theory. Instead of dealing with the relationship between ob-

servables and parojueters of the Lagrangian, we choose to describe the variation

199

of an observable with the momentum scale. In order for the mass shifts induced

by radiative corrections to remain under control (i.e., not to greatly exceed the

value measured on the laboratory scale), either

• A must be small, so the range of integration is not enormous; or

• new physics must intervene to cut off the integral.

In the standard SU(3)C ® SU{2)L ®U(l)Y model, the natural reference scale

is the Planck mass,

A ~ MPlanck « 1019 GeV . (5)

In a unified theory of the strong, weak, and electromagnetic interactions, the

natural scale is the unification scale

A ~ M y f t 1015 GeV . (6)

Both estimates are very large compared to the scale of electroweak symmetry

breaking (2). We are therefore assured that new physics must intervene at an

energy of approximately 1 TeV, in order that the shifts in /z2 not be much larger

than (2).

Only a few distinct classes of scenarios for controlling the contribution of

the integral in (4) can be envisaged. The supersymmetric solution4 is especially

elegant. Exploiting the fact that fermion loeps contribute with an overall minus

sign (because of Fermi statistics), supersymmetry balances the contributions of

fennion and boson loops. In the limit of unbroken supersymmetry, in which the

masses of bosons are degenerate with those of their fermion counterparts, the

cancellation is exact:

-f-boson>

If the supersymmetry is broken (as it must be in our world), the contribution of

the integrals may still be acceptably small if the fermion-boson mass splittings

AM are not too large. The condition that g2AM2 be "small enough" leads to

the requirement that superpartner masses be less than about 1 TeV/c2.

A second solution to the problem of the enormous range of integration in (4)

is offered by theories of dynamical symmetry breaking such as Technicolor.5 In

200

the technicolor scenario, the Higgs boson is composite and new physics arises on

the scale of its binding. Arc - 0(1 TeV). Thus the effective range of integration

is cut off, and mass shifts are under control.

A third possibility, which is appealingly economical but entails the sacrifice

of perturbation theory for the electroweak interactions, is that of a strongly

interacting gauge sector.6 This would give rise to WW resonances, multiple

production of gauge bosons, and other new phenomena.

Nature may choose any (or none) of these human inventions, but we are

driven unavoidably to the conclusion that some new physics must occur on the

1 TeV scale.

3 REACHING THE 1 TEV SCALE

For the reasons we have just outlined, 1 TeV collisions among the elementary

constituents become an important landmark. Both general arguments and spe-

cific speculations all point to new phenomena and important clues at energies

of ~ 0.3-3 TeV. The accelerators now operating or soon to come into operation

will thoroughly explore the few hundred GeV regime. The properties of these

machines are summarized in Table 1.

To proceed to the 1 TeV scale with useful luminosity, we may contemplate

two possibilities:

• An e+e~ collider with 1 to 3 TeV per beam;

Table 1: Accelerator projects under way

Date

now

1986

1987

1989

1990

Collisions

PPpp

e+e-

e+e~

ep

Location

CERN SppS

Fermilab Tevatron

Stanford SLC

CERN LEP

DESY HERA

v/I (TeV)

0.63

2

0.1

- 0 . 2

- 0 . 3

Mass scale (TeV/c2)

- 0.15

- 0 . 4

0.1

~0.2

- 0 . 1

201

# A p±p collider with 10 to 20 TeV per beam.

With current technology, we know how to build a practical hadron supercollider.

An electron-positron collider to explore the 1 TeV scale awaits tests of the linear

collider concept at the SLC, and the development of efficient, high-gradient

acceleration methods. According to the experts, a serious proposal for such a

machine is a decade away.7

In this context, a number of machines are under discussion for construction

or operation in the mid-1990s:

e SSC: the Superconducting Super Collider in the United States, character-

ized as a 40 TeV proton-proton machine with an instantaneous luminosity

of 1033 cm~2sec~1. A conceptual design has recently been submitted to

the Department of Energy. Some aspects of it will be reported by Don

Stork in the following talk.8

• LHC: a Large Hadron Collider in the LEP tunnel could be a 10 to 18 TeV

p±p device with luminosity in the range of 1031"33, depending on the ap-

proach taken. The high energy option requires the development of 10 Tesla

magnets, which has obvious appeal for the future.

• CLIC: CERN is also discussing the option of CERN Linear Colliders, now

conceived as an e+e~ facility with ^/s = 2 TeV and a luminosity of 1034.

There is no doubt that the successful demonstration of linear collider principles

at SLC will be followed, after appropriate further development, by an Apres-SLC

proposal.

4 S S C PHYSICS: A FIRST LOOK

The discovery reach of a hadron supercollider is determined by hard scatter-

ing processes in which the constituents interact at high energies, as depicted in

Fig. 2. Cross sections may be calculated in the renonnalization group improved

parton model, provided we know the behavior of the quark and gluon distribu-

tions within the proton as functions of x and Q2. For the parton subprocesses

202

Figure 2: Parton-model representation of a hard-scattering event.

of interest, the range over which the structure functions must be known is

(10 GeV)2 £ Q2 £ (104 GeV)2, (8)

which may correspond to (i) as small as 10~4. With the parton distributionswritten as //°'(x, Q2) for the number density of partons of species t in hadrona, hadronic cross sections are given schematically by

da{a + b -H. c + X) = Y2Jdxadxb- (9)

where do represents the elementary cross section. Structure functions suitablefor the extrapolation to supercollider energies are available,9 and the parton-levelcross sections are known for a great many reactions of potential interest.

One indication that the parton-model procedure is sound, and that knowl-edge of the structure functions derived from experiments on deeply inelasticlepton scattering is adequate, is provided by SppS data on hadron jets. Fig-ure 3 shows representative data from the UA-1 Collaboration10 on the inclusivejet cross section da/dpydy \y-0, compared with the predictions of the QCD Bornterm. The agreement is quite satisfactory.11

Thus satisfied with the reasonableness of our procedure, we. may make the

extrapolation to supercollider energies. A useful way to display the results is to

203

Kfl

UAl HCIUSIVE

JET CROSS-SECTION

0 26 <.O 60 60 100 120 110 160

Figure 3: The inclusive jet cross section for the pseudorapidity interval |rj| < 0.7,

as a function of the jet transverse momentum, as measured by the UA-1 Collab-

oration. The open dots correspond to the data at y/s = 546 GeV and the solid

dots to those at yfl = 630 GeV.

examine the trigger rate for events with transverse energy ET greater than some

threshold E^*n. This is shown in Fig. 4 for the nominal operating conditions of

the SSC: yfi = 40 TeV and £ = 1033 cnr'sec"1, as well as at 10 and 100 TeV.

At 40 TeV, a "high-£7T" trigger with threshold set at 2 TeV will count at 1 Hz

from two-jet QCD events. This is of interest in planning triggers which will

efficiently select "interesting" events from the 2 • 108 interactions which will take

place each second in an SSC interaction region.

5 ELECTROWEAK PHYSICS

The principal standard model issues to be addressed with a multi-TeVhadroncollider are these:

204

2 0 . . • • •« • • • - , . » .

16

16

i- 10bJ

66

4

2

\

\

\

-

.d610 10

"ET-Trigger" Role (Mi) ot 3 ? ' 1O53 cni2 ne"1

Figure 4: Counting rate for an ET-trigger in pp collisions at an instantaneous

luminosity of £ = 1033 cm~2sec~1 (after EHLQ). The threshold is defined for

transverse energy deposited in the central region of rapidity, defined by |y,| < 2.5

for jets 1 and 2.

• Ti rate of W± and Z° production. This is chiefly of interest for investiga-

tions of the production mechanism itself and for the study of rare decays

of the intermediate bosons. We expect that by the time a supercollider

comes into operation the more basic measurements such as precise deter-

minations of the masses and widths of the intermediate bosons will have

been accomplished.

• The cross section for pair production of gauge bosons. These are sensitive

to the structure of the trilinear couplings among gauge bosons, and must

be understood as potential backgrounds to the observation of heavy Higgs

bosons, composite scalars, and other novel phenomena.

• The Higgs boson itself. In the minimal electroweak model, this is the lone

boson remaining to be found. Elucidating the structure of the Higgs sector

(and mot merely finding a single Higgs scalar) is one of the primary goals

of experimentation in the TeV regime.

Let us take a moment to look briefly at each of these points.

205

Figure 5: Cross sections for W* production in pp collisions in the Drell-Yan

picture, integrated over all rapidities, and restricted to the interval \y\ < 1.5

(after EHLQ).

The integrated cross sections for W+ and W~ production in pp collisions are

shown in Fig. 5 as functions of the cm. energy y/s. Also phown are the cross

sections for production of W± in the rapidity interval —1.5 < y < 1.5. The

number of intermediate bosons produced at a high-luminosity supercollider is

impressively large. At' 40 TeV, for example, a run with an integrated luminosity

of 1040 cm"2 would yield approximately 6 • 108 Z°a and 2 • 109 W±B. For com-

parison, at a high-luminosity Z° factory such as LEP (£ ~ 2 • 1031 cm~2sec~1)

the number of Z°s expected in a year of running is approximately 107. There is

no competitive source of charged intermediate bosons.

The angular distribution of the produced intermediate bosons is of great

importance for the design of experiments. At supercollider energies, many in-

termediate bosons will be produced within a narrow cone about the beam di-

rection. In a 40 TeV machine with an average luminosity of 1033, there will be

a flux of about 10 W+/second emitted within 2° of the beam direction, in each

hemisphere. Special purpose detectors deployed near the forward direction may

thus have significant advantages for the study of rare decays.

There are many reasons to be open to the possibility of new gauge bosons:

206

• High energy parity restoration in an SU(2)L®SU(2)R®U(1)Y electroweakgauge theory;

• The occurrence of extra U(l) gauge symmetries, implying additional Z°s,for example in unification groups larger than 517(5);

• The low-energy gauge groups emerging from superstring modeis.12

In a specific theory, the style of c&lculation just described leads to an estimateof the cross section for the production of new gauge bcons. As an example, Ishow in Fig. 6 the cross section for production of a new R -boson with standardgauge couplings to the light quarks. For the 40 TeV energy projected for theSSC, we may anticipate sensitive searches out to a mass of about 6 TeV/c2.

Incisive tests of the structure of the electroweak interactions may be achievedin detailed measurements of the cross sections for the production of W+W~,

M(W') [TeV/c ]

Figure 6: Cross section for the production of & heavy W-boson with rapidity\y\ < 1.5 in pp collisions at 2, 10, 20, and 40 TeV (after EHLQ).

207

W±Z°, Z°Z°, W±r), and Z°i pairs. The rate for W±^ production is sensitive to

the magnetic moment of the intermediate boson. In the standard model there

axe important cancellations in the amplitudes for W+W~ and W±Z° production

which rely on the gauge structure of the WWZ trilinear coupling. The Z°Z°

and Z°7 reactions do not probe trilhvsar gauge couplings in the standard model,

but are sensitive to nonstandard interactions such as might arise if the gauge

bosons were composite. In addition, the W+W~ and Z°Z° final states may be

significant backgrounds to the detection of heavy Higgs bosons and. possible new

degrees of freedom.

The intrinsic interest in the process $<?,• —• \V+W~, which accounts in part

for plans to study e"1"e~ annihilations at cm. energies around 180 GeV at LEP,

is owed to the sensitivity of the cross section to the interplay among the 7-,

Z0-, and quark-exchange contributions. As is well known, in the absence of the

Z°-exchange term, the cross section for production of a pair of longitudinally

polarized intermediate bosons is proportional to s, in gross violation of unitarity.

It is important to verify that the amplitude is damped as expected. The mass

spectrum of W+W~ pairs is of interest both for the verificaiion of gauge cancel-

lations and for the assessment of backgrounds to heavy Higgs boson decays.

At this puuu, it is worth recalling why there must be a physical Higgs boson,

or something very similar, in any satisfactory electroweak theory. To do so,

let us consider the role of the Higgs boson in the cancellation of high-energy

divergences. An illuminating example is provided by the reaction

e + c - -+W+W~, (10)

which is described in lowest order in the Weinberg-Salam theory by the four

Feynman graphs in Fig. 7. The leading divergence in the J = 1 amplitude of

the neutrino-exchange diagram in Fig. 7 (a) is cancelled by the contributions of

the direct-channel 7- and Z°-exchange diagrams. However, the J = 0 scattering

amplitude, which exists in this case because the electrons are massive and may

therefore be found in the "wrong" helicity state, grows as s1/2 for the production

of longitudinally polarized gauge bosons. The resulting divergence is precisely

cancelled by the Higgs b&aon graph of Fig. 7(d). If the Higgs boson did not exist,

we should have to invent something very much like it. From the point of view of

5-matrix theory, the Higgs-electron-electron coupling must be proportional to

208

(a)

Figure 7: Lowest-order contributions to the reaction e+e"

standard model.

W+W~ in the

the electron mass, because "wrong helicity" amplitudes are always proportionalto the fermion mass.

Without spontaneous symmetry breaking in the standard model, there wouldbe no Higgs boson, no longitudinal gauge bosons, and no extreme divergencedifficulties. (Nor would there be a viable low-energy phenomenology of the \. sakinteractions.) The most severe divergences are eliminated by the gauge structureof the couplings among gauge bosons and leptons. A lesser, but still potentiallyfatal, divergence arises because the electron has acquired mass - because of theHiggs mechanism. Spontaneous symmetry breaking provides its own cure bysupplying a Higgs boson to remove the last divergence. A similar interplay andcompensation must exist in any satisfactory theory.

6 SUPERSYMMETRY AT THE S S C

As an illustration of the capability of the SSC to search for phenomena be-yond the standard model, let us consider one example from supersymmetry. In asupersymmetric theory, particles fall into multiplets which are representations of

209

the supersyminetry algebra. Superpartners share all quantum numbers except

spin; if the supersymmetry is unbroken, they are degenerate in mass. The num-

ber of fermion states (counted as degrees of freedom) is identical with the number

of boson states. By examining the quantum numbers of the known particles,

we readily see that there are no candidates for supersymmetric pairs among

them. Supersymmetry therefore means doubling the particle spectrum, com-

pared with the standard model. In fact, we must expand the spectrum slightly

further, because the minimal supersymmetric extension of the standard model

require? \t least two doublets of Higgs bosons. The interactions among old and

new particles are prescribed by the supersymmetric extension of the usual inter-

action Lagrangian, which we shall take to be the SU(3)coiOT ® SU(2)i ® U(l)y

theory. If supersymmetry is an invariance of the Lagrangian, it is evidently a

broken symmetry, because observationally boson masses are not equal to the

masses of their fermion counterparts. For supersyminetry to resolve the hierar-

chy problem, we have seen in §2 that it must be effectively unbroken above the

electroweak scale of O(l TeV). This suggests that the superpartner masses will

themselves be £ 1 TeV/c2.

The outlines of the search for supersymmetry at the SSC are given in EHLQ.2

Progress since Snowmass '84 was summarized recently at the Oregon workshop

by Dawson.13 Cross sections for the production of superpartners will be quite

ample for a luminosity of 1032 cm"2sec"1 or more, and a cm. energy of 40 TeV.

As an example, I show in Fig. 8 the integrated cross section for the production

of gluinos with rapidities |y,-| < 1.5, in the reaction

PP —> 99 + anything. (11)

On the basis of these and other cross sections and a rudimentary assessment

of the requirements for detection, we have estimated the discovery limits for

various energies and luminosities. The estimates for gluinos are shown in Fig. 9.

Consideration of similar curves for the whole range of conjectured superpartners

leads to the judgment that a supercollider like the SSC will be adequate to

establish the presence or absence of the superpartners predicted by models of

low-energy supersymmetry.

210

A •> 290 MeV

1

100

40

0.25i-L.

0.7S \2&

Gluino Mow175

Figure 8: Cross sections for the reaction pp —* gg + anything as a. function of

gluino mass, for collider energies y/s — 2,10,20,40, and 100 TeV. Both gluinos

are restricted to the interval jj/jj < 1.5. For this illustration, the squark mass is

set equal to the gluino mass. [From EHLQ, Ref. 2.}

21 f . 1 -

>

tninO

OC

10H events

_L J_! L.

0 20 40 60 80

(TeV)100

Figure 9: "Discovery limits" for gluinoa in pp and pp collisions. Contours show

the largest mass for which 104 gluino pairs are produced with |y,| < 1.5, for

specified energy and luminosity.

211

7 CONCLUDING REMARKS

In this brief survey, it has been possible only to scratch the surface of the

physics opportunities presented by a high-energy, high-luminosity hadron col-

lider. The examples we have considered here do begin to indicate the scope of

physics issues to be addressed, ranging from detailed study of known particles,

such as the intermediate bosons, to the search for high-mass exotica. The com-

prehensive studies of physics possibilities carried out over the past three years

have shown convincingly that

A 40 TeV collider which permits experimentation at integrated

luminosities of at least 1039 cm"2 will make possible detailed explo-

ration of the 1 TeV scale.

This conclusion is based on detailed consideration of the canonical inventions

intended to improve the standard model, technicolor and supersymmetry, and

of the standard model itself. In addition, there are many opportunities for

exploring constituent interactions at subenergies up to about 10 TeV in the

study of jets, the search for additional gauge bosons, etc. "Fixed-target style"

colliding beams experiments may be well suited to address rare W decays and

heavy flavor physics, for example. The SSC is not by any means a one-issue

facility, and it is important that we mount a diversity of experimental initiatives,

to realize its full scientific potential.

With respect to experimentation at the SSC, there are a few detector issues

which I like to raise at every opportunity.

• The utility of high-efficiency W and Z detectors. The discovery physics

we have considered in assessing the physics prospects of the SSC can all

be done by relying upon the leptonic decays of the gauge bosons, but

we can move to a deeper level of experimentation by learning to use the

nonleptonic decays as well.

• The UA-1 experiment has already indicated the value of "hermetic" de-

tectors, which can capture and measure all the visible energy emitted in

the central region. For a general-purpose SSC detector, it is of interest to

require henneticity for rapidities \y\ < 3.

212

• Examples from technicolor and the Higgs sector of the standard model

indicate that good-efficiency r, b,. . . tags will be of considerable value in

enhancing signals over background. Full utilization of the heavy flavor tag

requires measuring the four-momenta of the short-lived particles as well.

• How to reduc° the interaction rate of ~ 108 Hz to the 0(1 Hz) rate at

which complex events can be written on storage media (magnetic tapes,

optical discs)? There are many opportunities for creativity here!

• Bringing remote local intelligence into the detector components themselves

requires the implementation of radiation-hardened electronics, especially

near the beam directions.

We are faced with great opportunities!114

• • * • * • * * • * * • *

It is a pleasure to thank our hosts Bob Panvini and Tom Weiler and their

colleagues for assembling a stimulating scientific program, and for seeing to it

that our stay in Nashville was again a pleasant and interesting one. Fermilab

is operated by Universities Research Association, Inc., under contract with the

United States Department of Energy.

213

FOOTNOTES AND REFERENCES

1 P. Ramond, These Proceedings, p. .

2 For a summary of the standard shortcomings, see E. Eichten, I. Hinchliffe,

K. Lane, and C. Quigg, Rev. Mod. Phys. 56, 579 (1984).

3 M. Veltman, Ada Phys. Polon. B12, 437 (1981); C. H. Llewellyn Smith,

Phys. Rep. 105, 53 (1984).

4 Some recent reviews of the experimental implications of supersymmetry on

the scale of electroweak symmetry breaking appear in D. V. Nanopoulos and

A. Savoy-Navarro (Editors), Phys. Rep. 105, 1 (1984); H. E. Haber and

G. L. Kane, ibid. 117, 75 (1985); S. Dawson, E. Eichten, and C. Quigg,

Phys. Rev. I>31, 1581 (1985); R. M. Barnett, H. E. Haber, and G. L. Kane,

Nucl. Phys. B267, 625 (1986).

5 For reviews of the technicolor idea, see E. Farhi and L. Susskind, Phys. Rep.

74, 277 (1981); R. Kaul, Rev. Mod. Phys. 55, 449 (1983). A recent study

for the current generation of accelerators appears in E. Eichten, I. Hinchliffe,

K. D. Lane, and C. Quigg, Fermilab-Pub-85/145-T, Phys. Rev. D, (to be

published).

6 The idea of a strongly interacting gauge sector is an evergreen in particle

theory. In the context of the standard model, an early discussion appears in

B. W. Lee, C. Quigg, and H. B. Thacker, Phys. Rev. D16, 1519 (1977);

see also M. Veltman, Acta Phys. Polon. B8, 475 (1977). Recent investi-

gations appropriate to the supercollider scale are reported in M. Chanowitz

and M. K. Gaillard, Nucl. Phys. B261, 379 (1985); Phys. Lett. 142B, 85

(1984).

7 Report of the HEPAP Subpanel on Advanced Accelerator R&D and the SSC,

U. S. Department of Energy Report DOE/ER-0255 (December, 1985).

8 D. Stork, Thtse Proceedings, p. .

9 Structure functions for supercollider physics are given by Eichten, et al.,

Ref. 2, and by D. W. Duke and J. F. Owens, Phya. Rev, D30, 49 (1934).

214

10 G. Arnison, tt al. (UA-1 Collaboration), CERN-EP/86-29.

11 The curves shown are 1.5 x the lowest-order QCD predictions, evaluated with

Q2 = p\. The systematic errors on the data are ±70%. Theoretical uncer-

tainties are of a similar magnitude, but tend to increase the predicted cross

section. These are discussed by Eichten, et al., Ref. 2, and by R. K. Ellis and

J. C. Sexton, Fermilab-Pub-85/152-T.

12 See, for example, V. Barger, These Proceedings, p.

13 S. Dawson, in Supercollider Physics, edited by D. E. Soper (World Scientific,

Singapore, 1986), p. 171.

14 Basic references on supercollider physics include the following: EHLQ, Ref. 2;

Proceedings of the 1984 Summer Study on Design and Utilization of the Su-

perconducting Super Collider, edited by R. Donaldson and J. G. Morfin (Fer-

milab, Batavia, Illinois, 1984); Large Hadron Collider in the LEP Tunnel,

edited by G. Brianti, et al., CERN 84-10; Proceedings of the Workshop on

Blectroweak Symmetry Breaking, edited by T. Appelquist, M. K. Gaillard,

and I. Hinchliffe, LBL-18571; pp Options for the Supercollider, edited by

J. E. Pilcher and A. R. White (University of Chicago, 1984); Physics at

the Superconducting Super Collider Summary Report, edited by P. Hale and

B. Winstein (Fermilab, 1984); Supercollider Physics, edited by D. E. Soper

(World Scientific, Singapore, 1986).

215

SSC DEVELOPMENTS

Donald H. Stork

I. Introduction.In less than four years the Superconducting Super Collider (SSC) project has

gone from the initial realization that 40 TeV collisions were feasible to the presentserious consideration for multibill ion dollar funding by the Department of Energy(DOE). We here trace this remarkable history and project it to its central placein high energy physics in the 1990's. We describe the Conceptual Design Reportwhich defines the SSC as it is presently envisioned. Finally we review recenttask force studies of SSC detector development and summarize recent workshopconclusions on the physics capabilities of the SSC.

II. History and proposed scenario.

By the time of the 1982 Snowmass workshop it was realized that the physicsof the TeV mass scale was the key to the development of an understanding beyondthe Standard Model and was now within reach by U.S. technology. A radicalreexamination of the long range priorities of high energy physics was begun.The Lawrence Berkeley Laboratory high-rate detector workshop confirmed thefeasibility of operating at high luminosity with a hadron-hadron collider; theCornell high-energy accelerator workshop confirmed that a 20 TeV on 20 TeVhadron collider was technically possible with present technology. In mid-1983 theFermilab Tevatron came on the air demonstrating that operation of nearly 1000superconducting magnets was now reality.

In that climate, HEPAP was led to the proposal4 that construction of thedelayed CBA facility for proton-proton collisions at 800 GeV center-of-mass en-ergy be bypassed and that the U.S. proceed directly to a 40 TeV proton-protoncollider with luminosity 10^3cm~2sec~I. The spectacular discovery of the inter-mediate gauge bosons at the CERN SPPS 540 GeV collider and the fact that the1 TeV Tevatron pp collider would soon be in operation were important factors.A strong consensus of support within the high energy community helped to per-suade the DOE to support SSC research and development (R&D) starting in thefall of 1983.

This was followed by the formulation of a program of R&D for the SSC anda reference designs study was initiated by the high energy laboratory directors.The University Research Association (URA) was accepted as manager of thisprogram; the Chicago pp workshop confirmed that there was little physics

216

advantage to pp collisions and that the higher luminosity of pp had priority; theAnn Arbor accelerator workshop addressed a broad spectrum of acceleratorquestions. In May, 1984, the Reference Designs Study, a first detailed defini-tion of the technical requirements and comprehensive cost analysis ($3B in 1984dollars for construction of the SSC), was submitted to the DOE. The DOE thenapproved the proposal for a three-year R&D program to be directed by MauryTigner, who was appointed by tne URA Board of Overseers.

In parallel with that year of development and definition of the SSC acceleratorprogram an intensive study of the SSC physics prospects was carried out in aseries of workshops known as Physics at the SSC (PSSC). Meetings were held atFermilab (FNAL), Brookhaven National Laboratory (BNL), Woodlands, Texas,and Stanford Linear Accelerator Laboratory. In addition a Lawrence BerkeleyLaboratory (LBL) workshop was held on the physics of the Standard Modelat SSC and a cross section document, EHLQ, was prepared. This processculminated in the June, 1984, Snowmass workshop on physics at the SSC.

October 1. 1984, marked the formal beginning of a three-year SSC R&Dproject designed to produce a realistic proposal for construction of the machine.Major work was to be carried out by BNL, FNAL, LBL and the Texas AcceleratorCenter (TAC) as well as by universities and private industry. The activitieswere to be coordinated by a Central Design Group stationed at LBL. Majormilestones have been successfully met on schedule. Principal have been the Siting

12

Parameters Document in April, 1985, the magnet type selection on September

13, 1985, and the Conceptual Design Report13 in March, 1986.The workshops have continued with emphasis on detector issues (Madison

muon detector workshop," Fermilab SSC trigger workshop, IEEE radiationdamage conference, LBL workshop on silicon detectors, and LBL workshopon wire-chamber radiation damage ) as well as those in which an increasinglyrefined treatment of the Standard-Model and new SSC physics is being confrontedby the constraints of realistic SSC detector facilities (Eugene, UCLA, andMadison ). Notable among recent task force charges have been the discussion

22 23

of SSC detector development and cost, and the detailed examination of the

cost and physics limitation of a pp alternative.At the present time, a recommendation to fund SSC construction is under

serious consideration by DOE and we may consider the proposed scenario for itsconstruction and first operation as envisioned in the Conceptual Design Report.If forwarded to President Reagan by Secretary Herrington, the project could beincluded in the FY8G budget presented in January, 1987. If Congress does notreject it outright, initiation of a site search could begin that Spring. The siteselection process is expected to take 18 months with proposal review by a jointcommittee of the National Academies of Science and of Engineering which will

217

forward a small number of outstanding possibilities to the Secretary of the DOE.Given FY88 authorization, beneficial occupancy of one cluster of experimentalareas would take place in Winter, 1993, and of the second in Summer, 1994.

We could hear those magical words "SSC beam on!" in Fall, 1994. I havebeen told that the following are too fancifully optimistic, but in my scenario thehorizontal gauge boson is discovered in Winter, 1995, an unexpected new kindof event is found to be flooding the detectors in Winter, 1996, and not too longafter that two Higgs, the fourth generation, and SUSY aro discovered. But wenow return to present realities.

m. Conceptual Design Report.13

The Conceptual Design Report is a bulky report, with even bulkier appen-dices, which was delivered to DOE on March 31, 1986. It is not an engineeringdesign from which the accelerator could be constructed, but it is a design suffi-ciently thorough to insure that the SSC is well within the capability of presenttechnology and to provide the basis for a detailed and accurate cost estimate.

Of the 37-page parameter list, w« cite just a few that summarize the essentialcharacter of the machine. It is a 20 TeV on 20 TeV proton-proton collider 82.944km around as shown in Figure 1. It has two clustered interaction regions (IRs).

Futufabiteracton < ^ ^Regions *~

Interaction „-----Regions

A \ East" \ \ OusterH9

.6 knr

• * | i 2.4 km•fcj 1 106 mr

J, (Typical)

Figure 1. Layout of the 83 km SSC collider ring and West cluster detail showing the 1182 meterexperimental (X) and utility (U) straights, the 576 meter three-cell dispersion suppressors (D)and 96 meter half cells (C/2).

218

One cluster contains the injector/abort complex and two experimental facilityIRs. The other cluster contains four IRs, of which two are for future devel-opment. Of the four initially instrumented IRs two will have maximum lumi-nosity 1033cm~2sec~1 with ±20 meters space for experimental equipment be-tween beam quadrupoles and the other two will have maximum luminosity 5.6 x1031cm~2sec~1 and a ±100 meter space.

Beam intensities correspond to 405 megajoules of stored energy per beamand fast abort is required to protect the superconducting magnets. For a crosssection of 90 mb there will be a 90 MHz interaction rate in the high luminosityIRs. With a 4.8 m bunch spacing there will be 1.4 interactions per bunch crossingwith a rms beam size of 5 jum at a crossing angle of 75 /irad.

Adjacent IRs will be separated by 2.4 1 n with 106 mrad of horizontal bendin between. Injection is accomplished with a sequence that tracts the remarkableaccelerator development of the past few decades: a 50 KeV H~ source, 2.5 MeVRFQ, 0.6 GeV Linac, 8 GeV low energy booster, 100 GeV medium energybooster, and a 1 TeV high energy booster. In the final 20 TeV rings there are7680 horizontal dipole superconducting magnets of length 16.54 m and with fullfield of 6.6 T.

The SSC parameters are the result of many man-years of detailed study, sim-ulation, experimental tests, research and development, together with essentialexperience with the Tevatron I and other accelerators and colliders. They de-scribe a machine which is technically well understood and which can be built withthe confidence that it will provide through the 1990s and into the next centurya source for new understanding of the fundamental forces of nature.

The cost, in 1986 dollars, for the construction of the SSC, exclusive of ex-perimental detectors and with the assumption that the site is provided by thehost, is summarized in the table below. It is based upon some 2000 technicalitems entered into the Work Breakdown Structure tables found in the ConceptualDesign Report and perhaps as many more items for the conventional facilities.

SSC Cost Summary, FY 86

Technical components

Conventional facilities

Systems engineering and design

Management and support

Contingency

Superconducting Super Collider

M$

1

3

.424

576

288

192

530

.010

219

By far the largest cost item is found within the technical components cate-gory: $1,OO1M for the magnets. Of this sum S746M is for the 7680 horizontaldipoles; and the latter cost is dominated by a 78% materials cost! It is not sur-prising that a great deal of effort has gone into R&D on superconducting wirewith the result that very impressive progress has been made. As shown in Fig-ure 2 the critical current density achievable in production-size NbTi billets hasincreased dramatically from the 1800-2000 A/mm2 to the 2750 A/mm2 in theConceptual Design Report. Present indications are that values well "hove 3000A/mm2 may prove to be feasible for improved performance at less cost.

EE

E-~

4000

3500

~T 1 T 1 T 1 T 1 T -1—i—T—i—I—i—r—i-

Supercon' • Supercon (Fine Filaments)| n I C CI • 1 G C (Fine Filaments)[ O 0 S T

0 S T (Fine Filaments)

3000 -

2500 —

2000

1500

- SSC Conceptual Design Report- March. 1986

~SSC Reference Design Studj£. May, 1984 D

Tevatron Wire

i i < i 1 i i i i 1 i i i i 1

r?

ao

RU o U 8

4D D

I 1 I I

• •

• •

•

i i 1 i i i i

1981 1982 1983 1984 1985 1986 1987

Figure 2. Critical current density for NbTi superconductor from U.S. vendors.

It also is not surprising that great effort has gone into superconducting mag-net R&D. The ;hief competition was between the "collared, cold-iron," 6.6 Teslatype and the "auperferric" 3.0 Tesla type which was developed by the TexasAccelerator Center. The unanimous recommendation was for the former, andTigner's choice of the 6.6 Tesla magnet fixed the length around the acceleratorto be some 52 miles. The validity of the choice was reaffirmed by a HEPAPsubpanel during the week before this Vanderbilt Conference.

220

23 STRAND KEYSTONED CABLE

30 STRAND KEYSTONED CABLE

Figure 3. Cross sections of inner/outer 23/SO-strand keystoned superconducting cable.

Figure 3 shows the configuration of the superconducting wire packages. Eachstrand contains thousands of copper-clad NbTi filaments with diameter 5 micronsor smaller. Their arrangement in the ucos0" winding in the stainless steel collarfor a magnet dipole is shown in Figure 4. The collared coils are mounted in a 27-cm diameter flux-return iron yoke to form a cold mass assembly shown installedin the cryostat in Figure 5. Great design care and test experience has madepossible the very low cryostat heat budget of 25 Watts to 80° K, 2.5 Watts to20° K, and 0.3 Watts to 4.5° K for each dipole.

Figure 4. Coils and collar. Figure 5. Magnet in cryostat.

221

The first full-length prototype dipole magnet, Figure 6, has been shippedfrom BNL where it was produced to Fermilab where it has been installed in itscryostat. The Fermilab magnet test facility is now coming into operation with amagnet string test scheduled for the coming fall.

Figure 6. First full length prototype dipole ready for shipment from BNL to Fermilab.

The dipole magnets will be placed in the SSC tunnel, Figure 7, so that thetwo counter-rotating proton beams will be separated vertically by 70 cm. Figure8 shows the first of two vertical steps to bring the beams into collision at thehigh-luminosity interaction point.

222

r - r I I tV F M « 'A'

z< •-' ti-" air -uir- y///y^

Figure 7. Tunnel cross section showing 70 cm vertical beam separation and magnet transport scheme.

Horizontal and vertical collimators

1 m long leadshielding sections

QV QV

Neutral beam dumpand ionlzation chamber'

100 200 300

(meters)

Figure 8. Arrangement of qu&drupoles and vertical bends near the high luminosity interaction point, IF

223

IV. Workshops and Other Activity.

The SSC presents new detector challenges because of the increased complex-ity of interactions, the higher particle energies, and the much higher event rates.A fine review of current detector development which is pertinent to the SSC has

22

been made by the task force on Detector R&D for the SSC. It concludes thatsubstantial R&D is required in (l) radiation resistance, (2) faster time response,(3) improved granularity, (4) improved performance of electronics systems, (5)improvements in ct xnputing, and (6) improved performance for measurement ofmomentum and energy in the TeV range. In addition, a continued developmentof Monte Carlo simulation programs is needed. Within the context of thosebroad requirements the task force made specific recommendations for vigorousprograms of basic R&D related to SSC detector needs. These include the inves-tigation of wire chambers, silicon detectors, and scintillating fibers as trackingdevices, and the testing of major calorimetric systems based on liquid argon,warm liquids, silicon sampling and heavy scintillating glasses. Particle identifi-cation considerations first require Monte Carlo studies for optimization of themuon spectrometer configuration and for the evaluation of the need for the de-velopment of fast RICH (ring imaging Cerenkov counter) detectors for hadronidentification. Very-large-scale integrated circuit (VLSI) design centers are rec-ommended to develop improvement in the performance and reduction in the costof electronics. Advanced triggering and computing developments for major newand upgraded collider experiments will provide valuable experience for the SSC.Finally, there is an urgent need for increased manpower in the development ofMonte Carlo programs to simulate high energy pp collisions and to parameterizedetector response reliably in the TeV region. Many of these topics have receivedrecent attention at workshops and conferences and an intensified attack is indeedneeded. The LBL workshops on new solid state detectors and on radiation

18

damage in wire chamber detectors examined recent work in critical areas.

A first attempt to estimate the cost of the experimental facilities has been23

done by the Detector Cost Model Advisary Panel (G. Trilling, chair), theDetector Cost Evaluation Panel (R. Schwitters, chair), and the Off-line ComputerAdvisory Panel (S. Loken, chair). As an example, one of the generic 47r magneticdetector which they considered in their modelling is shown in Figure 9. It coversup to 6 units of rapidity with a 20% charged track momentum resolution 1 TeV,electromagnetic and hadronic energy resolution of 15 and 50 % at 1 GeV, andmuon momentum resolution 20% at 1 TeV. While the task force models cannotin any way be taken as proposals, they represent a natural evolution of theinstrumentation in use today and can be used for estimates of the total costs asis shown in the table below.

224

ELECTROMAGNETICCALORIMETER, 29 X .

SUPERCONDUCTINGMAGNET, I.S T

FORWARD TRACKING

ELECTROMAGNETICCALORIMETER

PRECISION HADRONCALORIMETER

CATCHER HADRONCALORIMETERMUON TOROIDS

CENTRALTRACKINGCHAMBERS

END CAP TRACKING

PRECISION HAORONCALORIMETER. 8.2 X.

ELECTROMAGNETICCALORIMETER. 23 X .

IR OUAD-

Figure 9. One of the SSC 4JT magnetic detector facility models.

Detector Costs

47r Magnetic Detector

Spectrometer for High Energy /x's

Upgraded Existing Detector

Additional Forward/Intermediate Detector

Specialized Detectors

Total after ± 15% inclusion

Off-line Computer Costs

Hardware Costs

Software

Total

$290M

159M

90M

95M

less

$558M

- $334M

- 174M

- 125H

- 102M

than 20M

- $865M

$64.6M

5.0M

$69.6M

225

Since the 1984 Snowmass workshop, several physics simulation programs haveundergone increasing sophistication and improvement by incorporating new the-oretical input and by matching new results from the CERN SPPS collider. Theyagree on the QCD processes and all include initial and final state gluon radiation,but differ in the treatment of the fragmentation process. Two popular MonteCarlo programs are ISAJET with independent fragmentation, and PYTHIA,a Lund-based Monte Carlo with color-string fragmentation. These and similarprograms are being used to evaluate prospects for the study of interesting physicsprocesses at the SSC. Three examples will serve as illustrations: the search foran intermediate mass Higgs particle, the search for supersymmetric gluino pairs,and the search for horizontal gauge bosons.

Above about 200 GeV mass the decay H —> W*W~ dominates. Productionand decay rates are known from the Standard Model for given Higgs mass andthe issue becomes one of the generation of QCD background and of direct W pairproduction, together with an evaluation of the detector trigger and event-analysis

15 19 20 21

capability. The process has been studied extensively. ' ' ' For example, a28

trigger strategy has been developed which successfully reduces the event ratefrom the raw 100 MHz to 1 Hz of recorded data and retains 1/3 of the Higgsevents for a mass of about 200 GeV:

Summary of Trigger Strategy

Trigger Selections

First Trigger Level:

a) Electron candidate. Ex > 25 GeV

b) Event Px.miss > 40 GeV

Second Trigger Level:

a) Electron candidate isolation

b) Ex > 80 GeV jet requirement

Third Trigger Level:

Charged particle px > 10 GeV

pointing to electron calorimeter cell

and ISAJET Results for H -> W + W

Rejection

Factor

10,000

4

1.5

20

220

Remaining

Cross Section (nb)

30,000

7,500

5000

250

1.1

H -, W+W~

Efficiency

0.86

0.43

0.37

0.32

0.32

Note that the 1.1 nb cross section corresponds to a 1 Hz data rate at maxirr;amluminosity. For an integral luminosity of 1040cm~z the number of events survivingall final analysis cuts is as follows:

226

mH(GeV)

300

800

Higgs Signal

1400

340

Background

1800

560

These results suggest that the Higgs can be detected if its mass is betweenabout 200 and 1000 GeV. However, at the highest mass it is very broad andappears as no more than a shoulder in the W pair mass distribution so that thebackground will require detailed understanding. Furthermore, the study is onlynow beginning to address realistic detectors with their proper resolution, plau-sible segmentations, cracks, and pileup problems. On the other hand, the onlysure way to identify the Higgs may be through its ZZ decay where each Z decays

31

into a lepton pair. The Higgs example provides an interesting challenge for thedevelopment of SSC detector facilities and for SSC physics analysis. It shouldprovide plenty of food for thought and discussion at the upcoming Snowmass1986 workshop in June.

A second physics example that has received considerable attention is oneof new physics rather than of the Standard Model, that is, the SUSY processof gluino pair production. When the gluinos decay each into a quark pair anda photino which escapes detection, the event is characterized by large missing

29

transverse energy and several jets. Background comes primarily from hardgluon scattering in which one gluon goes to a b-quark pair with one b quarkdecaying leptonically with large transverse missing energy going into a neutrino.These processes have been modelled in detail and trigger strategies have beenfound to give 1 Hz rates at signal to background ratios of 1 to 0.03 for gluinomasses between 100 and 1000 GeV. The analysis requires excellent QCD jetreconstruction, which is a further challenge to SSC detector design. Gluino pairproduction provides yet another stimulating topic for Snowmass 1986.

The third SSC physics example is the horizontal gauge boson which is pos-tulated to connect quark and lepton families. Its production and decay leads tovery massive and unmistakable lepton pairs such as e/i or \IT. Triggering on highPT leptons gives an acceptable data rate with little loss of signal. The dominantbackground comes from W+W~ pairs, but there is good separation of the sig-nal from background (Figure 10). If the mass were 5 TeV, hundreds of cleanevents would be collected per year, justifying in itself the construction of theSSC. New physics processes of this type do not suffer from pileup and so provide

33

motivation for preserving in the the design of the SSC and its experimentalfacilities the possiblity of running at luminosities greater than 1033 cm~2sec""1.

227

As the SSC proceeds towards construction, the issues of detector R&D andof the design of the experimental facilities are now beginning to receive greaterattention. An effort commensurate with the design of the machine itself is ur-gently needed to provide the best possible exploitation of its physics potential.The upcoming Snowmass workshop on the Physics of the SSC (June 23-July 11)will provide a lively and useful forum to help focus the energies of the high energycommunity in this direction.

tOTeV

Figure 10. Cross section for production and decay of the horizontal gauge boson into e/i lepton

pairs for masses of 1, 5, and 10 TeV. Reconstruction smearing is illustrated at 5 TeV by the

dashed curve. Background from WW decay to e/i is Bhown as the solid curves with and without

200 GeV PT cuts and from Drell-Yan production II as the dashed curve.

V. Conclusion.

We have said little of the physics motivation for SSC. Chris Quigg's talk atthis conference gives a sharply defined prospectus of the exciting physics expecta-tions. The Snowmass proceedings ' and both the Reference Design Study and

13

the Conceptual Design Report contain excellent summaries of the physics po-

tential. A number of recent articles address the subject for a broader audience.

228

In briefest summary, there is an increasing belief that the basic questions posedby the extraordinary success of the Standard Model will be answered by newphysics in the 1 TeV mass region which is accessible only to the SSC in theforeseeable future.

The broad consensus that the SSC ib of highest priority continues in theU.S. high energy community and is persuasive for strong federal support. Thecooperation of the national laboratories and universities has been an outstandingachievement of the program. While sharp technical debate over choices such asthe magnet type has occurred, the choices are accepted and a strong collaborativeeffort continues. The Conceptual Design Report is receiving high marks in itsreviews and the DOE has said that the information needed for the SSC decisionis in hand.

The broad debate over the high cost of the SSC has continued with concernamong the other sciences that funding will detract from their programs. Further-more, in a Gramm-Rudman-Hollings year the argument for SSC must be madewith special clarity. The debate has highlighted, however, the gradual dete-rioration of support for basic science during a time when the R&D program fornational defense is rapidly growing. A dramatic turn around of this imbalance iscalled for and it is increasingly clear that every effort must be made to increasegreatly the support for basic science in general. While the SSC funding ratewill not greatly exceed, in proportion to national income, the rate during theconstruction of Fermilab and other parallel high energy projects, it is proposedin a different fiscal climate and attitude toward basic science.

Nevertheless, the time for the SSC has come. We hope that the favorabledecision to proceed will soon be made.

229

REFERENCES

1. Proceedings of the 19S2 DPF Summer Study on Elementary Particle Phys-ics and Future Facilities, Snowmass, June, 1982, edited by Rene Donaldson,R. Gustafson, and F. Paige.

2. Prodeedings of the 1983 DPF Workshop on Collider Detectors, LawrenceBerkeley Laboratory (LBL), February, 1983, S.C. Loken and P. Nemethy,editors.

3. Report of the 20 TeV Hadron Collider Technical Workshop, Cornell Uni-versity, March, 1983.

4. Recommendation of the High Energy Physics Advisory Panel (HEPAP) tothe DOE, July, 1983.

5. Proceedings of the PP Options for the Supercollider, Chicago, February,1984.

6. Accelerator Physics Issues for a Superconducting Super Collider, Ann Ar-bor, December, 1983, workshop report edited by M. Tigner.

7. Report of the Reference Designs Study Group on the Superconducting Su-per Collider for the U.S. Department of Energy, May 8, 1984.

8. Physics at the Superconducting Super Collider Summary Report, Fermilab,edited by P. Hale and B. Winstein, June, 1984. Proceedings of the SSCFixed Target Workshop, Woodlands, Texas, January, 1984.

9. LBL Standard Model Workshop, Spring, 1984.

10. E Eichten, I. Hinchliffe, K. Lane, and C. Quigg, Supercollider Physics,Rev. Mod. Phys. 56, 579 (1984).

11. Proceedings of the 1984 Summer Study on the Design and Utilization ofthe Superconducting Super Collider, Snowmass, June, 1984, edited by R.Donaldson and J. G. Morfin.

12. Superconducting Super Collider Siting Parameters Document, SSC CentralDesign Group, June, 1985.

13. Conceptual Design of the Superconducting Super Collider, SSC CentralDesign Group, editor J. D. Jackson, SSC-SR-2020, March, 1984.

14. SSC/LHC Muon Detection Workshop, Madison, April, 1985.

15. Proceedings of the Workshop on Triggering, Data Acquisition and Comput-ing for High Energy /High Luminosity Hadron-Hadron Colliders, Fermilab,November, 1985, edited by B. Cox, R. Fenner, and P. Hale.

16. IEEE 1985 Annual Conference on Nuclear and Space Radiation Effects,IEEE Transactions on Nuclear Science 32, December, 1985.

17. Proceedings of the Workshop on New Solid State Devices, LBL, October,1985, edited by H. Spieler and D. Nygren.

230

18. Proceedings of the Workshop on Radiation Damage to Wire Chambers,LBL, January, 1986, edited by J. Kadyk, LBL-21170 (1986).

19. Supercollider Physics, Proceedings of the Oregon Workshop on Super HighEnergy Physics, Eugene, March-August, 1985, World Scientific PublishingCo.

20. Proceedings of the Workshop on Observable Standard Model Physics at theSSC: Monte Carlo Simulation and Detector Capabilities, UCLA, January,1986, edited by H.--U. Bengtsson, C. D. Buchanan, and A. Soni.

21. Workshop on Physics Simulations at High Energy, Madison, May, 1986.

22. Report of the Task Force on Detector Research and Development for theSuperconducting Super Collider, M. Gilchriese, Chairman, SSC CentralDesign Group, SSC-SR-1021, June, 1986.

23. Cost Estimate of Initial SSC Experimental Equipment, SSC Central DesignGroup, SSC-SR-1023, June, 1986.

24. An Assessment of the Antiproton-Proton Option for the SSC, B. C. Barish,study group chairman, SSC-SR-1022, May, 1986.

25. F. E. Paige and S. Protopopescu, BNL-37271 (1985).

26. H.-U. Bengtsson and G. Ingelman, Computer Phys. Comm. 34, 251 (1985);T. Sjostrand, Computer Phys. Comm. 39, 347 (1986).

27. M. Goodman, F. Paige, L. Price, A. Savoy-Navarro, and B. Wicklund, Fer-miiab Workshop on Triggering, Data Acquisition and Computing, Novem-ber, 1985, p. 4.

28. J. Gunion and M. Soldate, UCLA Workshop on Observable Standard ModelPhysics at the SSC, January, 1986

29. S. H. Aronson et al., 1982 Snowmass Prodeedings, p.505; S. Dawson andA. Savoy-Navarro, 1984 Snowmass Prodeedings, p. 263.

30. A, Savoy-Navarro and Y. Takaiwa, Fennilab Workshop on Triggering, DataAcquisition and Computing, November, 1985, p. 9.

31. R. Cahn, UCLA Workshop on Observable Standard Model Physics at theSSC, January, 1986.

32. H.-U. Bengtsson, W-S. Hou, A. Soni, and D. H. Stork, PRL 55, 2762, 1985.

33. R. Diebold and R. Wagner, 1984 Snowmass Proceedings, p. 575.

34. S. L. Glashow and L. M. Lederman, Physics Today, March, 1985, p. 28; J.D. Jackson, M. Tigner and S. Wojcicki, Scientific American, March, 1986, p.66; C. Quigg and R. Schwitters, Science, 1986; James W. Cronin, Bulletinof the Atomic Scientists, May, 1986, p. 8.

35. Letters exchanged in Science, Scientific American, Physics Today.

231

EXPERIMENTAL WINDOWS TO POST-COLLIDER ENERGIES

A. C. Melissinos

Department of Physics and Astronomy

Univers i ty of Rochester , Rochester , NY 14627

1. Introduction

2. Review of some current experiments

2.1 Nucleon decay

2.2 Monopole searches

2.3 The solar neutrino problem

2.4 The Fly's Eye experiment

2.5 The DUMAND project

3. The MACRO and ICARUS experiments

3.1 The MACRO experiment

3.2 Neutrino astronomy

3.3 The ICARUS experiment

4. Acknowledgements

Abstract

We discuss some of the experiments designed to probe the energy regime

beyond the reach of existing or proposed accelerators. We attempt to

classify the diverse efforts presently underway and give a brief update of

the results in the major areas of interest to particle physics. We then

describe two detectors presently under construction in the Gran Sasso

laboratory, as examples of the next generation of experiments.

1. Introduction

The era of particle accelerators, born with the invention of the

cyclotron, continues to dominate particle physics as large machines such as

LEP or the SSC are being built and being planned. Beyond the c.m. energies

that these large colliders will provide lies a vast uncharted territory,

which we show graphically in Fig. 1. What makes this "post-collider"

energy regime particularly interesting at this time is that there are spe-

cific theoretical predictions about phenomena occuring at these energies.

232

These phenomena and the particles they generate could be observed as

"relics" from the big-bong era when, for a brief interval, very high

energies prevailed in the universe. Alternately phenomena governed by

physics at very high energy could manifest themselves at low energies in

the realm of nuclear or atomic physics. Astrophysical and cosmological

considerations often set limits on the expected effects or can suggest the

specific experimental window. This has led to a close interconnection

between particle physics, the study of cosmic radiations and theories of

the early universe. We attempt to indicate this relationship by the

triangle of Fig. 2. Still, the major source of new information about the

universe comes from observational astronomy which has made rapid progress

at all wavelengths.

Fig. 1

10'

10°+

PLANCK MASS

M p ~ l/GN

- G.U.T.

P.O {AXIOM

a:UJo

10 ••

_E.W.

"QUARKS

— NUCLEI

Ou

O

-S.SC-TEVATRON

-L.E.P.-CESR

The energy scale of the

post-collider regime.

-10"

-• 10

Fig. 2

Particle physics and its connections

in the post-collider regime.

PARTICLE PHYSICS

EARLY UNIVERSE_COSMOLOGY—

COSMIC PARTICLES- o n d RADIATIONS

Current experiments that attempt to probe the post-collider energy

regime without the explicit use of particle accelerators could be loosely

classified into four groupings:

I. Particle properties and searches for proposed particles

a. Nucleon decay.

b. Search for magnetic monopoles.

233

c. Detection of neutrinos:

Low energy V from sun, stellar collapse

High energy V ,1/ from point sources

d. Searches for seculative particles such as axions, SUSY

partners, WIMPS.

A positive discovery by any of these experiments would have obvious

implications for physics at very high energies. It would also alter

our views of the very early universe and provide us with a snapshot of

the universe at the time that the corresponding particles decoupled.

II. Cosmic Rays and Their Properties1 R

a. Study of very high energy primaries: up to EeV = 10 eV energies.

b. Study of extensive air showers.

c. Search for point sources of very high energy f's. This is based

on the detection of the Cerer.kov light emitted during the

development of th- shower in the atmosphere.

d. Study of the spectrum, composition and interactions of primary

cosmic rays.

The relevance of these experiments is more toward the understanding of

the acceleration mechanisms that can impart such high energies to

single particles and how these particles propagate through the

interstellar medium.

III. Laboratory Experiments

a. Search for neutrino mass (almost exclusively from the endpoint of

the tritium /J-decay spectrum 3 H •• 3 He + e + 1/ ).

b. Search for neutrinoless double beta decay.

c. Reactor experiments such as neutron oscillations, e.d.m. of the

neutron.

These experiments are searching for manifestations at low energy of

phenomena that would crucially alter our views of the post-collider

energy regime.

IV. Classical and Other Astronomical Observations

a. Study of the 3°K microwave background radiation: spectrum,

anisotropy.

b. Space-based observations in the visible, infrared, X-ray and 7-ray

bands.

c. High resolution radio-astronomy with large arrays of telescopes.

234

d. Search for gravitational effects such as waves, lenses and their

manifestation on close binary systems.

e. Direct tests of general relativistic effects and deviations from

Newtonian gravity.

This last category is very broad and encompasses several communities

of researchers using very different tools and with different traditions.

However it is the collective information from such experiments that allows

us to form an image of the present and early universe; in turn this image

permits us to speculate about the physics that governed the universe at

those early times of exceptionally high energies.

I listed these groupings of experiments to give a feeling for the

broad and varied range of activities that are being pursued. In some

-espects this differs from collider experiments where all detectors are, at

least generically, identical. Particle physicists are mainly involved in

experiments in groups I, II. They have brought with them techniques and

analysis methods from research using accelerators and the new experiments

are becoming large, highly sophisticated and of appreciable cost. Further-

more the size of the experimental groups is reaching towards fifty or more

scientists which brings with it many of the organizational and sociological

problems of "big science".

It is worth noting that the experiments in group I have so far yielded

negative results and thus could only set upper limits. This was partic-

ularly valuable in the case of proton decay where theory had made explicit

predictions. In contract a positive result would have a momentus impact on

our understanding of nature, but the experiments are "high risk" In that

there is little other information to be obtained if the primary search is

negative. The technical spin-off can be substantial if the experiment is

carried out with "state of the art" technology.

The detectors in most cases, must be of large size since the «svent

rate is directly proportional to the area or volume. To address the

question of nucleon decay with detectors of very large volume the water

Cerenkov detector was introduced, wher_as for very high spatial resolution.,

fine-grained calorimeters of considerable size have been construe*fed. In

the search for magnetic monopoles and for rare cosmic ray events it becomes

essential to use very large planar arrays; a device combining many of these

properties is the recently proposed cryogenic liquid imaging detector. The

problems that can be addressed by various types of detectors are shown

235

schematically in Fig. 3; the heavy arrows are my own, rather subjective

view, of the experiment for which each detector is best suited. In many

cases the detectors are located deep underground to avoid the large flux of

low energy atmospheric muons and other backgrounds. One can say that in

order to explore the post-collider regime one has to be either undtir the

earth's surface or above its atmosphere.

FINE GRAINED |TRACKING CALORIMETERS!

SCLAR NEUTRINOS /

*- xCRYOGENIC LIQUIDIMAGING DETECTOR

VERY LARGE ~|ACCEPTANCE ARRAYS!

y-ASTRONOMY4

Fig. 3

Detector classes and

physics goals

In the following section I will briefly review some of the recent

major experiments. Results from these experiments have been published and

have been reported on several occasions. In the third section I discuss

two experiments that are being prepared for installation in the Gran Sasso

Laboratory in Italy. These are typical of the new large underground

detectors and their description should give the reader a general idea of

the techniques and aims of such efforts. I do not discuss the detection of

WIMPS (weakly interacting massive particles) which are covered in part

elsewhere in the proceedings. Similarly the current status of double

beta decay was reviewed by F. Avignone.(2) A discussion of the dark matter

in the universe and of neutrino oscillations in the sun can be found in the

presentations of M. Turner and A.

236

During the meeting I had time to describe the general features of the( *> )

Rochester-BNL-Fermi la:> cosmic axior. search experiment . Because of thelimited space this topic is not included in the proceedings.

2. Review of Some Current Experiments

In this section I give a brief update or. nuclear, decay, monopole

searches and the solar neutrino problem. 1 also mention the principal

characteristics of the Fly's Eye experiment and of the DUMAND project.

2.1 Nucleon Decay: The most significant results on nucleon decay have(6)

been published by the 1MB (Irvine-Michigan-Erookhaven) collaboration.

This group has operated a water Cerenkov detector since 1983. The

signature is a contained event with energy and momentum balance. Neutrino

interactions in the detector car. mimic this signature and are the primary

source oi baci^rounc.

The detector located in a salt ir.ine nesr Cleveland has a total volume

of 6,800 :r.3 of which the fiducial volulme is 3,300 m3 . The depth is 1,700

m.w.e. and the rate of tnuor.s traversing the detector is 200,000/day. The

present limits are obtained from 417 live days of data taking during which

401 contained events were observed. The total visible energy spectrum for

these events is shown in Fig. 4 and it is consistent with atmospheric

neutrino interactions. Eventhough one can identify candidate events the

limit on the proton lifetime as obtained from this sample is at the 90%

confidence level

T/3 (p + e^1T°) > 2.5 X 1032 years

T/B (other modes) ^ 1021 years

In conclusion, if proton decay takes place in the 1MB detector it must

be at the level of 1% of the neutrino interaction rate. We recall that the

prediction from SU(5) symmetry is that T ~ 1030 years with p -t e 1F° as

one of the dominant modes. It is expected that this experiment will continue

to run for another 2 to 3 years in order to improve on the above limits.

The other nucleon decay experiment in the U.S. is located at the

Soudan mine in Minnesota and is currently under construction. When

completed, in late 1988, it will consist of 1100 tons of fine grained

tracking calorimeter. The detector is fabricated in 5-ton modules so that

operating experience and preliminary results on muon angular distributions

can be obtained cr an earlier date.

237

Similar detectors are in operation around the world and some of them

are listed in Table 2.1. Many of these experiments have reported at one

time or another candidates for nucleon decay. These reports have not been

substantiated by the 1MB results.

Table 2.1 Some Nucleon Decay Experiments

Experiment Detector Fiducial Mass Operating Time

1MB Water Cerenkov 3,300 Tons 400 days

Kamioka(8) Water Cerenkov 900 Tons 300 days

Soudan II Track Calorimeter 1,100 Tons Late 1988

Frejus Track Calorimeter 800 Tons 200 days

Mont Blanc(9) Track Chambers 100 Tons >800 days

K. G. F . U ^ Track Chambers 140 Tons >3 years

2.2 Monopole Searches: The possibility of existence of magnetic

monopoles originated with Dirac's 1931 paper and is reexamined whenever

tentative observations are announced, or as new theories demand the

existence of monopoles. This is the case presently, when GUT theories

imply the existence of very massive monopoles with the usual Dirac charge

g=nc/2e. The search can proceed with ionization detectors akin to those

used for the detection of charged particles or with superconducting

induction detectors. Ionization detectors are somehow dependent on the

details of the interaction of monopoles with matter and are limited to

/J>10 ; but they can be made to cover large areas at a moderate cost.

Induction detectors on the other hand respond to monopoles of any velocity

and the observed signal must correspond to a change of flux through the

coil exactly equal to 2$0 = 27T(hc/e); however it is difficult and expensive

to construct induction detectors of large dimensions.

Another technique used to search for magnetic monopoles is by etching

plastic materials, such as "Lexan", CR39 or mica, which maintain the

defects (discolorations) produced by the passage of a monopole for a long

time (millions of years). When suitably etched these materials reveal pits

along the track which can then be easily recognized under a microscope.

This technique can be applied to geological samples which, of course, had a

very long time of exposure. The sensitivity does however depend crucially

on the velocity of the monopole.

238

100

SO

BO

70

60

SO

40

30

20

10

0

-\ 1 r-—-r~—r"

!MB DATA All E»=nu

D

0 2 0 4 06 OB 1 1.2 14 IB IBMinimum Energy [CeV]

Fig. 5

Present limits on the

flux of magnetic monopoles

including the sensitivity

level of future experiments.

Fig. 4

Minimum energy of 401 contained

events from the 1MB experiment

(ref. 6).

EARTH GALAXY

SUPERCLUSTER

|0-i0

10-"

io-|B

SUN SL

_LJ I I~ i i r

INDUCTION EXPTS. fto. /

TOKYO(He+CHa)

10"" IO"3 IO"E 10"'MONOPOLE VELOCITY, v/c

Ionization detectors have been operated by many groups: Texas A&M, UC

San Diego, Pennsylvania, Baksan in the USSR, etc. They have, typically,(13)areas of 10-100 m2 and no new data have been reported. Induction

detectors are operated by Stanford, IBM, Chicago-Fermilab-Michigan collab-(14)oration, Imperial College in the UK, and others. These detectors are

already multiloop, have typically an effective area of 1 m2 and rely on a

coincidence in two planes of the detector. In spite of an occasional

signal no events have been reported so far. At the present time, most of

these groups are upgrading their detectors to areas ~10 m2 .

The limits on monopole flux set by the various experiments are shown

in Fig. 5 as a function of velocity. The "yardstick" in such monopole

239

searches is the Parker bjund which is established by the existence of the

intergalactic magnetic fie

monopole flux higher than

-6 23intergalactic magnetic field of 3X10 Gauss over d, dances £.~10 cm. A

15 -2 -1 -1F_n = 10 cm sr sec

(15)would short out the intergalactic field. This result depends on the

velocity as shown in the figure. The results of the geological technique

mentioned earlier are included in the figure and are the only ones below

the bound. The limits expected by the new induction experiments

and by a new large area ionization detector * are also shown.

2.3 The Solar Neutrino Problem Neutrinos are copiously produced in

any star and for the sun one can make reasonably accurate predictions of

the neutrino flux from various nuclear reactions. Some of these reactions

produce neutrinos with a continuous spectrum while for others the neutrinos(19)

are monoenergetic. The expected solar neutrino flux at the earth is

shown in Fig. 6. The highest energy neutrinos come from

B B - * B e + e + f 1 A . 1 MeV e n d - p o i n t

whereas the most copious flux arises from+

p + p - » d + e + J / 0.42 MeV end-point

R. Davis and his collaborators have for many years studied solar

neutrinos by the capture reaction

1/ + J'ci •* J7Ar + e"e

where the a7Ar is detected by radiochemical methods. The Q-value (thres-

hold) for this reaction is 0.814 MeV and therefore it is sensitive almost

exclusively to the neutrinos from BB decay. These experimenters find a

flux

2.1 ± 0.3 SNU

to be compared with the flux predicted from theory

5.8 ± ? SNU.

[One SNU (solar neutrino unit) is defined as 10 captures/atom-sec].

The theoretical rate depends on the ninth power of the sun's interior

temperature and thus is quite sensitive to the models of the sun and to our

input assumptions. Another explanation of the discrepancy is the presence

of resonant neutrino oscillations which could transform the V to V ,

V , leading to reduced flux.

To address this problem a new experiment using gallium is being

prepared. In this case the capture reactionV + n G a •* " G e + e"e

240

has a Q-value of 0.236 MeV ar.d therefore it will proceed with the V frome

the pp reaction. The solar neutrino flux for this reaction is calculated

to be 107 SNU so that with a 30 Ton detector one expects 1000 events/yr

against a background of 70 events/yr. The experiment has been approved for

the Gran Sasso laboratory and the necessary tonnage of gallium could be

assembled in 2-3 years.An alternate approach to the radiochemical experiments is to attempt

to detect directly the elastic scattering of V from electrons.e

V ^ e -* v + e~e e

Since both Z° and W exchange contribute to this process, the cross section

is larger than for the purely neutral current reactions. Furthermore the

e ro.-ovs t.ie incident neutrino direction and the electron spectrum can be

-easurec. The recoil electron spectrum per detector atom is shown in Fig. 7

for neutrinos from the various solar reactions. Clearly the difficulty of

these measurements is the detection of such low energy electrons in the

presence of background.

en 105

101

NEUTRINO ENERGY (MeV) Te, ELECTRON KINETIC ENERGY (MeV)

rig. 6 The i.ux of solar neutrinos-2 -1

at the earth (-m -sec ); for

continuous spectra the differential

flux is per MeV.

Fig. 7 The recoil electron spectrum

from solar neutrinos interacting with

one electron V +e~ •+ 1/ +e~.e e

241

One proposal is to use the Kamioka detector ' , or its upgraded

version with a threshold of E ) 5 MeV and a concentrated effort is being

made to reduce the background In this energy region. Another proposal(23 )

involves the liquid argon imaging detector ICARUS which is discussed in

the next section. A third proposal is to use heavy water so as to exploit

the charged current reaction

V + d " * p + p + ee

which has a Q-value of \.Uk MeV. It may even be possible to detect the

neutrons from the neutral current reaction

followed by neutron capture on a deuteron with the emission of 6.25 MeV 7,

(n+d •+ aK-*"7). A large volume of D3 0 would be used as a Cerenkov detector to(2 A)

be installed in Sudbury in Canada.

2.4 The Fly's Eye Experiment: This experiment is designed to detect

very high energy primary cosmic rays by observing the fluoresc-'.r.r.e induced

in the atmosphere by the air shower. The path of the air shower is detected

by an array of sixty-seven 62-inch mirrors. The mirrors are housed in

motorized mounts, each mirror being viewed by a cluster of 14 photomulti-

pliers with appropriate light collectors. A schematic view of the experi-

ment including a second array which is currently being installed is shown in

Fig. 8. The mirrors are oriented so as to cover a large portion of the sky

- as a fly's eye - and since showers can be detected at large distance the

effective acceptance of the detector is 107 m s-sr for E~10 1 7 eV.

The detector can operate only on moonless and cloudless nights but has

logged in excess of 107 sec of data taking. Primaries with energy of 20 EeV

atmospheric air shower

Fig. 8

Schematic sketch of the

Fly's Eye experiment

(ref. 25).

242

(2XJ.019 eV) have beer, de tec ted . I t has been predicted t h a t pr imaries with

energ ies E ) 70 EeV w i l l be degraded because they are above the threshold

for pion production when s c a t t e r i n g from the 2.7°K background rad ia t ion

p + 7 -> p + t°

Thus a sharp cut-off may exist in the cosmic ray spectrum, consistent with

the data from Fly's Eye. However the rate of such high energy primaries is

so low that the data are not as yet conclusive.

Fly's Eye does also detect the direct Cerenkov light generated by

electron-rich showers, but with much reduced acceptance; such showers could

originate from very high energy 7-rays. Groups from the University of

Michigan and the University of Chicago plan to add an 1100 " muon and

charged particle detection system to the present setup. The purpose of

this instrumentation is to correlate the Cerenkov pulses with shower

activity and composition. It may even be possible to detect neutrino

interactions by observing an upward going electron shower.

2.5 The DUMAND Project: The acronym (Deep Underwater Muon And(27)

Neutrino Detector) correctly describes this project. The idea is to

locate an array of large photomultiplier tubes deep in the ocean off the

island of Hawaii. At a depth of. U.I km the water is clear and there is

little biological or other luminous activity. Thus the Cerenkov light from

high energy muons would reveal their direction, and with less precision -

through fi-rays - their energy. Down-going muons could originate from

atmospheric sources but upward (zenith angle >70°) muons come only from

neutrino interactions. Thus the basic goal of the detector is neutrino

astronomy.

The full complement of the proposed detector is shown in Fig. 9.

The 16" photomultipliers are mounted on strings; there are 21 tubes spaced

25 m apart for a 500 m long string. Six strings are moored to each cable

and are spaced at 50 m from one another. Finally six rows of cables are

deployed with a lateral separation of 50 m. Thus the total volume of the

array will be

V = 3.1 X 107 m3

The effective volume is considered to be about ten times larger.

At present the DUMAND group is developing instrumentation and is

studying the effects of the deep sea environment on the photomultipliers.

The main thrust is to operate a prototype of the string and gain experience

from its response. Following that step a triad of full strings will be

243

installed leading to the eventual deployment of the entire array.

ARRA1 30 KM OFF SHORE4 7 KM DEEP

A RETRIEVAL

Fig. 9

Schematic sketch of

the DUMAND project

(ref. 27).

3. The MACRO and ICARUS Experiments

These recently proposed experiments are good examples of large

detectors that would have the capability of exploring the post-collider

regime. The detectors will be installed in the Gran Sasso underground

laboratory which is now being completed in central Italy. The laboratory

is part of the construction of a new vehicular tunnel east of Rome; the

location and layout of the lab are shown in Fig. 10. There are three

experimental halls typically 100 m long by 20 m wide each. The overburden

is in excess of 4,000 m.w.e. The easy access - as compared to mine shafts

- and the logistic and support structure should make Gran Sasso one of the

best laboratories for large underground experiments.

At the G.S. depth, atmospheric muons loose about 1 TeV of enerpv; the

integral spectrum above this range is roughly given by

_24 ( ^ ^ ^ 1

The reduction in penetrating muons as compared to the flux at sea level is

244

of the order of 10 . This is essential for these experiments which have a

large area, and by necessity must have a loose trigger and long time gates.

For instance, a monopole with /?=10 takes 15 fisec to traverse 5 meters

which is a typical dimension of the apparatus; the drift time in 2 m of

liquid argon is of the order of 1 msec. Yet, evenat this depth the singles-2 -1

rate at the experimental location is 3 m sec indicating some of the

difficulties encountered by very low rate experiments.

3.1 The MACRO Experiment: The acronym for this experiment stands for

Monopole And Cosmic Ray Observatory; it is being carried out by a collab-

oration of some 40 Italian and 40 U.S. physicists. The basic features of

the experiment are:

a) large surface area

b) good spatial and energy resolution

c) very good timing resolution.

It consists of liquid scintillator counters which are sensitive to 1/10 of

minimum ionization and have a time resolution of 2 nsec. The scintillator

arrays are separated by ~ 6 m as can be seen in the schematic drawing of

the apparatus (Fig. 11). The space between the scintillators is filled

with concrete absorber to filter out strongly interacting particles. Sets

of limited streamer tubes are placed in layers between the concrete to

provide tracking information. It is expected to achieve Ax ~ 1 cm and

AS ~ 0.2. Finally sheets of Lexan and C39 will be interspersed in the

absorber; these detectors integrate the monopole flux and it is planned to

develop them after several years of operation.

The detector consists of nine 12 m wide by 5.7 m high and 12.4 m long

for a total length of 111.6 m. This yields a top and bottom surface of

" 1,400 m2. To evaluate the overall acceptance we note that a simply

connected surface of total area A has the same acceptance as a plane

surface A_ = (1/2) A . The acceptance for isotropic flux of a plane

surface A is,

= 4*^ Aj =e =

where we have defined an effective area A = (1/4) A . For the MACRO

detector

A_ = 4,100 a 4

= 47T ( 1 / 4 ) A_, - 13,000 m 2 - s r

245

Thus, 1 event in 1 year of operation corresponds to a flux F = 0.25 X io"15

cm sr sec , namely four events/year at the Parker bound. In contrast,

the rate of atmospheric muons crossing the detector is 1 Hz so that in one

year a sample in excess of 10 will be available. This could be useful i.i

studying the composition of showers with several muons. Of course, should

reports of muon clustering at particular celestial orientations persist

until MACRO becomes operational, it will be possible to check such effects

with great accuracy.

Fig. 10

Location of the Gran Sasso

laboratory in Italv

Fig. 11

Schematic of one module of

the MACRO experiment

(ref.18).

246

Another important goal of MACRO is to search for and identify point

sources of high energy neutrinos; it could also check for neutrino

oscillations by exploiting the difference in path length of atmospheric

neutrinos that traverse the earth when coming from below the horizon. The

experiment is also sensitive to exotic particles that are penetrating

enough to reach the detector.

3.2 Neutrino Astronomy: Since the detection of high energy neutrinos

in 1962 it became clear that it would be possible to detect neutrinos from

astronomical sources if a large enough detector were available. The

neutrinos interact in the rock under the detector

Va + P ~* " + ^

and the produced muons are observed in the detector. The difficulty is in

identifying the neutrino induced muons in the large flux of atmospheric

muons. However, muons observed below the horizon cannot be atmospheric and

thus must come from neutrino interactions; the directionality of the muons

reflects the neutrino direction and should be a sufficient constraint to

separate point-sources from the remaining isotropic background of

atmospheric neutrinos.

The rate of neutrino induced muons crossing the detector is almost

independent of the energy. We write

R = F .a.2..pr 0 -9 - 7 - 1 - 1

F^ ~ 10 [E^/GeV] m sr sec

a ~ 10"38[E /GeV[ cm2

23 "p ~ 6X10 nucleons/g

2. ~ 500 [E /GeV] g/cm2

Here £. is the maximal length of rock that a muon of energy E could

traverse, and therefore represents the effective target length. Combining

these expressions we find a muon rate of order

R - 3X10"10 m"2sr"1sec"1

Given the acceptance of MACRO one then expects ~100 events/year. This is

to be contrasted with the yield from certain astronomical sources which are

estimated to yield 10-30 counts/year.

The preferred candidates for intense neutrino point sources are X-tay

binaries; as already mentioned, they must be located in the sourthern

247

hemisphere in order to be below the horizon at Gran Sasso. The expected

neutrino flux is calculated on the basis of the observed high energy

7-rays from sources such as LMCX-4 (in the large Magelanic cloud),

VELA X-l, or CYG X-3. Yet the 7-ray flux from these sources is not known

with great certainty and this is reflected in the differing estimates on

the feasi-bility of neutrino astronomy.

3.3 The ICARUS Experiment: As the acronym Indicates "Imaging Cosmic

And Rare Underground Signals' the detector for this experiment will

have very high spatial resolution. It will consist of a liquid argon

volume in which the tracks of charged particles are established with

resolution of 2 mm or better. The primary ionization electrons along the

track are drifted in a 1 KV/cm field toward three readout planes. There is

readout along X, along U and along V to provide a point in the plane and

the Z coordinate is obtained from timing (TPC). The drifting electrons

pass through the wire planes and induce a charge on the wires. The FET

amplifiers are sensitive enough to detect the induced charge eventhough no

amplification has taken place in the argon.

A schematic of one readout unit is shown in Fig. 12b. The maximum

drift distance is 2.3 m requiring an anode potential of 250 KV. The

detector is continuously active, the contents of each wire being stored in

memory; if a trigger occurs then the contents of the memory are recorded

while otherwise the memory is overwritten. Since the.e is no amplification

in the argon the sense wires are relarivcly thick (100 /im) which is

necessary in order to support a 30 m span. There will be approximately

200,000 channels and the maximum drift time is 1.2 msec. To achieve such

long drift distances it is important to maintain very high purity In the

argon. It has also been proposed to use an argon-methane mixture in order

to increase the free proton content of the detector.

The layout of the detector in the gallery is sketched in Fig. 12a.

The liquid argon cylinder is 30 m long and 14 m in diameter; this provides

a volume of 4.600 m3 or 6,500 Tons of argon. The surface area is 1,600 m

and therefore the acceptance is 5,000 m!-sr. An important feature of the

detector is the presence of a magnetic field; this will be axial and of

strength 0.5T. An external muon detector using resistive plate counters

will surround the coil in order to provide timing and certain triggers.

The principal trigger is based on pattern recognition of the information

collected by the readout planes.

248

Fig. 12

Schematic of the ICARUS

experiment (ref. 23).

(a) Layout in the tunnel

(b) Details of the electron

TPC read out planes.

It I)

SQEEMC SOC WESam L£H

umc sis was HSEBWCm am

A detector such as ICARUS will have excellent calorimetric properties,

with energy resolution AE/E ~ 1.7%/v/E. It should also have a low energy

threshold and it has been proposed that the threshold could be lowered

below 10 MeV. This depends, among other factors, on natural and delayed

radioactivity and on electronics noise. It is however clear that ICARUS is

representative of a new generation of detectors with multiple capabilities;

these could be decisive for the detection of new phenomena of which we are

presently unaware.

In the more conventional arena ICARUS could search for nucleon decay

with complex topologies and, in view of its excellent resolution, the

background from neutrino interactions could be greatly reduced. On the

other hand its volume is not much larger than that of 1MB and even with a

methane-argon fill the number of free protons is limited. The detector

should be able to detect solar neutrinos from the 8B decay through their

scattering off electrons. If the recoil electron threshold is E ^ 4 MeV

then 9 events/day are expected while for E ^ 7 MeV there are 3 events/day.

249

ICARUS is well suited for the detection of low energy V ,U ; thee e

presence of significant fluxes of such neutrinos could be expected from

supernovae explosions and even from terrestrial reactors. Of course

atmospheric neutrinos and high energy neutrinos can be detected in the

usual way. If monopoles catalyze proton decay in the sun (Rubakov(29)effect) there should be a significant flux of 100 MeV neutrinos which

would be detectable providing indirect evidence for magnetic monopoles.

The large volume, the cryogenic load and the ambitious readout scheme

make the construction of ICARUS a real challenge. On the other hand such a

detector could address many of the current questions concerning cosmic

radiations, and one could reasonably hope that it would uncover new physics

as well.

Acknowledgements

This review dealt with experiments in which I have not personally

participated. I wish to apologize to the experimenters if I have misrepre-

sented their results by omission or mistake. I am particularly thankful to

the following colleagues who provided me with information about their

corresponding experiments: Dr. D. S. Ayres on Soudan 2, Dr. B. Cabrera on

the Stanford monopole experiment, Dr. S. Bermon on the IBM monopole

experiment, and Dr. H. H. Chen on the proposal for the Sudbury detector.

Dr. A. W. Mann was kind enough to inform me on the progress of the Kamioka

experiment, Dr. V. Peterson and Dr. C. Roos on the DUMAND project, Dr. P.

Sokolsky on Fly's Eye and Dr. J. VanderVelde on the 1MB nucleon decay

experiment. I also thank the participants of the MACRO and ICARUS

experiments for permission to quote from their proposals. Finally thanks

are due Bob Panvini, Tom Weiler and their colleagues for a very pleasant

and informative meeting.

Preparation of this manuscript was supported in part by DOE under

contract DE-AC02-76ER13065.

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1. See for instance, B. Cabrera, L. Krauss and F. Wilzcek, Fhys. Rev.

Lett. 55, 25 (1985); A. Drukier and L. Stodolsky, Phys. Rev. D30, 2295

(198A); M. W. Goodman and E. Witten, Pnys. Rev. D3_l» 3059 (1985).

Also see the talk by F. T. Avignone, these proceedings.

2. See for instance, F. T. Avignone, et al., Phys. Rev. Lett. 50, 721

(1983); D. 0. Caldwell et al., Phys. Rev. Lett. 54, 261 (1985). Also

250

see the talk by F. T. Avignone, these proceedings.

3. See the talk by M. S. Turner, these proceedings and references

therein.

4. See the talk by A. DeRujula, these proceedings and references therein.

See also H. A. Bethe, Phys. Rev. Lett. 56, 1305 (1986).

5. A. C. Melissinos, J. Rogers, W. Wuensch, H. Halama, A. Prodell,

W. B. Fowler and F. Nezrick, "A Search for Galactic Axions", proposal

for experiment E-805 at Brookhaven National Laboratory: University of

Rochester preprint (1986).

6. H. S. Park et al., Phys. Rev. Lett. 5_4, 22 (1985); J. C. Van der Velde,

"Experimental Status of Proton Decay" , University of Michigan preprint

(1985).

7. VJ. Allison et al., "The Soudan 2 Nucleon Decay Experiment: Description.

and Status Report", Argonne National Laboratory preprint ANL-HEP-PR-

84-30 (1984).

8. See talks by M. Koshiba in Proc. of XXII Int. Conf. High Energy

Physics, ed. by A. Meyer and W. Wieczorek, Leipzig, July 1984, p. 250.

9. See talk by E. Fiorini in Proc. of XXII Int. Conf. High Energy

Physics, op. cit. p. 246.

10. See talk by S. Miyake in Proc. of XXII Int. Conf. High Energy Physics,

op. cit. p. 244.

11. P. A. M. Dirac, Proc. Royal Soc. London, _133_, 60 (1931).

12. A. M. Polyakov JETP Lett. 20, 194 (1974); G. T'Hooft, Nuclear Phys.

B79, 276 (1974).

13. See for instance G. Giacomelli, "The Experimental Detection of

Magnetic Monopoles", University of Bologna preprint (1986).

14. See for instance B. Cabrera, "Cryogenic Particle Detectors for

Magnetic Monopoles and Neutrinos", Stanford University preprint

BC45-86 and to appear in proceedings Vlth Moriond Workshop, Tignes

France (1986).

15. E. N. Parker, Astrophys. Journal _160, 383, (1970).

16. P. B. Price and M. H. Salamon, Phys. Rev. Lett. 56, 1226 (1986).

17. S. Bermon et al., Phys. Rev. Lett. 5_5, 1850 (1985); also S. Bermon,

private communication.

18. Proposal for "A large area detector dedicated to monopole search,

astrophysics, and cosmic ray physics at the Gran Sasso laboratory",

B. Barish and E. Iarocci, spokesmen. See also CalTech preprint

251

CALT 68-1292 (1983} .

19. See for instance J. N. Bahcall et al., Astrophys. Journal 292 , L79

(1985) and references therein. See also A1P Conf. proc. 9JS, "Science

Underground", (1982).

20. R. Davis, in Proceedings Informal Conference or. Status and Future of

Solar Neutrino Research, G. Friedlander ed, ENL Report 40879, (1978),

Vol. 1, p. 1. See also Solar Neutrinos and Neutrino Astronomy

(Homestake 1984) AIP Conf. Proc. JJM3, 1, (1985).

21. L. Wolf er.stein, Phys . P.ev. D20, 2634 (1979); K. A. Bethe, Phys . Rev.

Lett. 5J>, 1305 (1986).

22. A. W. Mann, private communication.

23. ICAR'JS, A proposal for the Gran Sasso Laboratory, INFN-AE-85- 7

(September 1985) CERN, Harvard, Milano, Padova, Rome, Tokyo, Wisconsin

Collaboration; C. Rubbia, CERN Internal Report 77-78; W. A. Huffman,

J. M. Lo Secco, and C. Rubbia, IEEE Trans. Nucl. Sci. NS-26 (1979),

64; E. Aprile, K. Giboni, and C. Rubbia, Nucl. Instr. and Methods,

241, 62 (1985); M. Baldo-Ceolin, Symp. on Photon and Lepton

Interactions, Kyoto, 432 (1985).

24. H. H. Chen, Phys. Rev. Lett. 5_5, 1534 (1985); also Sudbury Neutrino

Observatory report SNO-85-3 (1985) available from U. of Cal. Irvine,

Dept. of Physics.

25. R. M. Baltrusaitis et al., Nucl. Inst. and Methods A24Q, 410 (1985),

Phys. Rev. Lett. 5_4, 1875 (1985), Phys. Rev. D3J_, 2192 (1985).

26. J. van der Veide, private communication.

27. See for instance V. J. Stenger Report HDC-9-85; also P. K. F. Grieder

Report HDC-10-85; Hawaii DUMAND Center, University of Hawaii (1985).

28. V. J. Stenger, Astrophys. Journal 28_4, 810 91984); also G. Cocconi,

CEPJM preprint (1985).

29. V. A. Rubakov, Pis'ma Zh. Eksp. Theor. Fiz. 3_3, 658 (1981); (JETP

Lett. 3J3, 644 (1981)) and Nucl. Phys. B203, 311 (1982); C. G. Callan

Jr., Phys. Rev. 32_5, 2141 ,1982) and phys. Rev. D26_, 2058 (1982).

Experimental Bounds on pp-Decay, Cold Dark Matter and

Solar Axions with an Ultralow Background Ge Detector

253

Presented by F.T. Avignone, III1

w i t h

S.P. A h l e n ? , R. L. B r o d z i n s k i 3 , S. D imopo lous 4 , A.K. D r u k i e r 5 ,

G. G e l m i n i 6 , B.W. Lynn 7 , H.S. Mi l e y 1 , J .H . Reeves3 ,

D.N. S p e r g e l 5 and G.D. Starkman 4

ABSTRACT

The PNL/USC ultralow background prototype Ge detector in the Homestake

goldmine is being applied to searches for Ov pp-decay, dark matter candidates

and solar axions. An upper bound of 2.2 eV has been placed on the Majorana

mass of the electron neutrino. The low energy data exclude particles with spin

independent Z° exchange interactions having masses between 20 GeV and 5 TeV,

as significant contributors to the cold dark matter of the halo of our galaxy.

The existence of stable Dirac neutrinos more massive than 20 GeV is also excluded

except for a narrow region around the Z° resonance. Finally, Dine-Fischier-

Srednicki (DFS) axion models with F/2x' < 0.5 X107 GeV are ruled out by the

maximum count rate attributable to solar axions.

1. Department of Physics, University of South Carolina, Columbia, SC 292082. Department of Physics, Boston University, Boston, MA 022153. Pacific Northwest Laboratory, Richland WA 993524. Department of Physics, Stanford University, Stanford, CA 943055. Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 021386. Department of Physics, Harvard University, Cambridge, MA 02138

On leave of absence from Department of Physics, Univ. of Rome II, ViaOrazio Raimondo, Rome, Italy 00173

7. Stanford Linear Accelerator Center, Stanford, CA 94305

254

I. INTRODUCTION

It is not uncommon that new technology attracts unanticipated applications.

Ultralow background Ge detectors, developed specifically for sensitive searches

for the Ov pp-decay of 7 6Ge (see Figure 1 ) , represent a technology applicable

to a number of other fundamental experiments. High resolution Ge detectors

revolutionized •) ray spectroscopy in the mid 1960s; they continue to play a

major role in nuclear spectroscopy today. Germanium detector technology has

been developing in the directon of large intrinsic, very high resolution

crystals. The sensitivity required in searches for very weak \ ray lines was

first enhanced using the concept of Compton-suppression and anticoincidence

shielding However, a limitation in sensitivity was found due to the

radioactive background in the Ge crystal, cryostat and electronic parts, the

construction materials of the live shield (including photomultiplier tubes)

and in the bulk shield itself. A detailed study was made of the materials

used in commercial low background detectors, and a discussion of the improve-

ments achieved by material selection was given in an earlier article.

The Ge crystals themselves are virtually free from primordial or manmade

radioactivity because of extensive zone refinement; however, cosmogenically

produced radioisotopes have been observed. In addition, cosmogenic activity in

the shielding materials, and materials selected for low background cryostat

construction, are also observable. This background is greatly reduced by

going deep underground with a detector built from selected materials. Figure 2

depicts the results of background reduction over the past four years in

different shielding configurations.

While the program of background reduction continues, the present low

levels represent a new technology which has been applied to a number of

interesting searches for rare decay modes and exotic particles. They include

255

searches for Ov and 2v pp-decay of 7 6Ge, electron decay to y and v, dark

matter candidates for the hidden mass of the galactic halo, and DFS solar

axions. The electron decay and 2v pp-decay are not discussed in this paper.

II. pp-Decay of 70Ge

When pairing forces in even-even nuclei increase their binding energies

significantly over those of odd-odd neighbors, single p-decay can be energeti-

cally forbidden -He in some cases pp-decay is energetically favorable. In

such cases several modes have been proposed, t-.'c of which are:

(Z.A) - (Z+2.A) + 2B + 2v , (1)

and (Z,A) - (Z+2.A) + 2p . (2)2

These processes have been reviewed extensively. Equation (i) is an ordinary

.<econd order weak process and, while not yet measured in laboratory experiments,

it has been observed in geochemical experiments. The process represented

by equation (2) violates lepton number conservation, however, and requires non-

zero Majorana-v-mass (see Figure 1). It has recently been shown that explicit

right handed couplings also require Majorana-v-mass in the context of certain

gauge theories (see Doi et al. Ref. 2). The importance of Ov fip-decay to Grand

Unification Theories (GUTs), as well as to cosmology, centers around the sensi-

tivity of this decay mode to these properties of the electron-v.

The semi-leptonic interaction for the p-decay of a d-quark is written

as follows:

-GF cos eH = ,,2 , jP L v n L p V + jjj[nRL ^ + nRR V j , (3)

where j^ (j~) are the components of left (right)-handed leptonic currents,

J. (Jn ) are the components of the left (right)-handed hadronic currents,

and Tin, HDI and IDD are their relative weightings. The Cabibbo angle is 6 ,

256

Figure 1. Diagram depicting neutrinoless pp-decay

• " - v ^

r-'."?"! L

IKE 2*00 3000 4800

Figure 2. Background spectra ofthe PNL/USC, 135cm3 prototypeGe spectrometer.

0 20 40 60 80 100

Figure 3. Ten weeks of datafrom the low energy portionof the Ge detector spectrum.

257

-5and the Fermi coupling coefficient, Gp, is 1.023 x 10 /M2 where M is the

proton mass.

The pp-decay rate for the Ov mode can be expressed in the following

general form:

wCyr"1) = u-^yr"1) {x +«2y +c<3z +a4xy+a5xz+a6yz}, (4)

where x, y and z are proportional to -m >, H D D ancl IDI respectively. The

quantities {a-} depend on the nuclear and atomic wave functions and relevant

matrix elements. There are a number of theoretical calculations, using different

models, and they give surprisingly similar values for the limits on the Majorana

mass of v from experimental half-life limits. All of the published and

otherwise available data through mid 1986 have been examined in various

combinations to obtain a "world limit". The combined spectrum was subjected

to a maximum likelihood analysis with the result T° v (76Ge) > 4.9 x 10 2 3 yr.

The calculations of Grotz and Klapdor, which do not include interferences from

right handed couplings, imply <m -> <0.92 eV. It is remarkable how similar the

results are for the different models used in the calculations . They are 2.2,

1.5 and 1.9 eV respectively to a confidence level of la.

TABLE I Limits on <m >, x, y and z with all interference terms included in

eq. 4. Values for T, v - 1023yr. Scale values by the ratios of

the square roots of T? v."5

Ref. (5) Ref. (7) Ref. (6)

<m >maxx(max)y(min)y(max)z(min)z(min)

4.9.

-9.1.

-1.1.

953146

eVXXXXX

1010101010

— o

— D

- J-C,0

3.46.6-5.65.6-6.87.7

eVXXXXX

1010101010

-6-6-6-7-7

4.2 eV8.3 X 10-8.2 X 108.4 X 10-7.4 X 108.1 X 10

258

Continuous progress is being made in background reduction, and the Ge

diodes have been procured and a first generation cryostat has been built

which will allow us to utilize 1440 cm 3 of Ge. This should provide a

sensitivity on the order of ';m >~ 0.5 eV in a few years. If data from other

groups with the same level of background and detector size are available, the

future "world limit" could be significantly lower.

III. Limits on Cold Dark Matter Candidates

Observations of the galactic rotation curves suggest that most of theQ

matter in the universe is non-luminous. A number of arguments suggest thatg

this matter is non-baryonic. Since only 7.8% of the natural isotopic mixture

of Ge has a nonzero spin (the isotope 7;iGeJ, our best bounds apply to spin

independent (s.i.) interactions. Bounds on dark matter candidates that couple

to baryons through Z° exchange, like stable massive Dirac neutrinos and

scalar neutrinos , are presented. Our results exclude a halo dominated by

particles with scattering cross section o • = a , with 20 GeV <m £5TeV

and apply to s.i. reactions in the range of o • = 10 o , to o - 10 cm2

S.I Wed K 5.1

for which the dark matter particles would be stopped in the earth's crust

before arriving at the detector. Here, a , is the scattering cross section

for a heavy standard neutrino from a Ge nucleus. This range also includes12

neutral technibaryons, recently proposed as dark matter candidates , having

a cross-section ? 10a ' , . They are excluded for masses larger than 20 GeV.

The presence in the detector of 73Ge with j=9/2, allows us to obtain some bounds

on particles with spin dependent (s.d.) interactions, in which case our bounds4 s d ^ 28apply to particles in the range a ~ 10 a ' , to o ^ 10 cm2.

The measurement of the nuclear recoil due to the scattering of weakly

interacting massive particles (WIMPs) requires a detector with a low energy

threshold and excellent background rejection. Because of its low band

259

gap (0.69 eV at 77" K) and high efficiency for converting electronic energy

loss to electron-hole (e-h) pairs (2.96 eV per electron-bcê at 77" K ) ,

germanium is probably the best suited material for a semi conduct, ing WIMP

detector. In late 1985, the threshold on the detector was reduced to an

equivalent incident electron energy of 4 keV which permitted detection of Ge

nuclei-WIMP scatterings with recoil energies greater than 15 keV. Ten weeks

of low energy data a"e shown in Figure 3. Interpretation of the data require^

knowledge of the relative efficiency factor (REF), which is the ratio of e-h

pairs produced by an electron, to the number produced by a recoiling Ge

nucleus. The calculated REF, with some experimental points, is shown in

Figure 4.

The particles that comprise the halo are assumed to have a velocity

distribution function, f(v), with an r.m.s. of 250 km/s and a maximum of

14550 Km/s while the halo, like the galactic spheroid, slowly rotates with

a velocity of 80 km/s. The maximum halo velocity may be higher in which

case our quoted limits extend to lower masses. The predicted detection rate

of recoils having energy T, R (T), was calculated according to,

R (T) = nxAT/^(v,T)f(v)vd3v , (5)

where AT is the range of recoil energies detected in a given channel and n

is the local density of dark matter. The integral was evaluated over all

velocity phase space. The cross section as a function of recoil energy, da/dT,

for an incident WIMP depends upon its mass, m , and velocity, v, according to,

da GF mN c 2 mN T + mx

2 \b)

x exp(-m..TR /3).

In equation (6), m,. is the mass of the nucleus, Z and N are the number of

protons and neutrons respectively, T is the recoil energy, Gc is the weak

HAIO DENSITY -_ 0 0 ! y±. p,

Figure 4. Energy dependence ul relative efficienty (actor (REF)The threhold of the dashed curve is 0.27 keV, the data are fromChasman et al. Phys. Rev. Lett. 15, 245 (1965)

Figure 5 Maximum halo density consistent with theobserved count, rate.

K

s• • •

nln

n i n

»v hmiis

IGlOflUill |

Figure 6. Maximum ratio of total Dirac neutrino mass tototal baryonic mass in our galaxy.

Figure 7. Excluded regions of the coupling constant-mass plane lie above the curves.

281

coupling constant, 8 W is the Weinberg angle and E = m (c2 + v 2/2). When the

de Broglie wavelength, corresponding to the momentum transferred in the recoil,

is smaller than the nucleus, the assunption of a coherent interaction with a

point-like mass is no longer valid, and the finite size of the nucleus must be

included in the calculation. The exponential factor in equation (6) is a nuclear

form factor derived with the assumption of a gaussian density distribution of

nucleons inside a nucleus of radius R = 1.2A , where A is the number of

nucleons. Since detailed models of nuclear structure predict less nucleon

density at small radii, a more accurate form factor would decrease less rapidly

with increasing T than that used in equation (6). Note that for small energy

transfers, E<15 keV, the WIMP does interact with a point-like nucleus, and there

is no loss of coherence.

The halo model used in the calculation is conservative. If the maximum

18halo velocity is chosen closer to the local escape velocity of ^ 750 km/s ,

the lower limit of the excluded mass range decreases. Figure 5 shows the

limits obtained for standard as well as a "perverse" halo model in which all

of the dark matter particles were assumed to lie on purely circular orbits.

This model, which yields a lower limit of 35 GeV for the excluded mass range,

is in contradiction with all existing galaxy formation theories, which predict

isotropic or radial velocity distributions. This minimal model would be

difficult to reconcile with observations of the isothermal velocity distri-

bution of spheroid start, which in the cold dark matter scenario has the same

history as the dark matter in the halo.

Since the predicted count rate also depends upon WIMP density, limits on

the density of interacting dark matter particles in the halo can be obtained.

Figure 5 also shows these limits for particles with s.i. Z° exchange inter-

actions for the standard isotropic halo model and for the model that assumes

262

that all of the particles are on purely circular orbits. Both models include

the sun's motion relative to the galactic halo. Figure 5 can be used for other

s.i. vectorial interactions by multiplying the vertical axis by the ratio

(a Via • ) . For example, for neutral technibaryons this ratio is approxi-W & Q K S.I

mately 0.1.

Under the assumption that the ratio of total mass of dark matter to the

total mass of baryonic matter in our galaxy, F , = M /M, does not

differ from the cosmological ratio, the bounds on the local density of massive

stable Oirac neutrinos can be translated into bounds on their cosmological

density. Figure 6 shows the upper limits on F , under two sets of assump-

tions: first, all the halo mass is baryonic, and second, M,. includes

only the observed baryons (stars, gas, dust, etc.). The cosmological ratio

of stable Dirac neutrinos to baryons, F . was calculated using an

analytic solution to the Boltzmann equation a to find pu and the largest

value for p " consistent with bounds from big-bang nucleosynthesis.

The existence of these particles is, therefore, excluded for masses larger

than 20 GeV except • a narrow mass range near the 2° resonance at m = m o / 2 .

The detector oackground has a smooth continuum as well as the narrow-line

components. The low energy peaks are primarily due to the presence of 2 1 0Pb in

a solder connection. The solder was just removed, and the radioactive shield he

been upgraded by the use of 448 year old lead in place of the copper which

has measurable amounts of cosmogenic radioactivity. Thus, the background in

some areas of the spectrum has been reduced more than a factor of ten. The

energy threshold was set at 4 keV because of noise at lower energies. The

shapes of the low energy x-ray lines suggest that AE(FWHM; ^ 500 eV in this

energy region. The strong increase of noise below E , = 4 keV is believed to

be largely due to microphonics engendered by mining operations. Hardware and

software are being developed to reduce this noise and permit lowering the

263

energy threshold to about 1 keV. By the end of 1986 rejection or detection

of the existence of coherently interacting particles cf mass .> 8 GeV should

be possible.

Our main results are shown ' Figure. 7, where the range of mass and

cross-section of particles excluded as main components of the halo are

presented. The ratio g/g is defined as (a/a . ) ^ where a is the cross

section for standard heavy Dirac (s.i.) or Majorana (s.d) neutrinos. The

validity of our experimental bound extends to cross-sections on the order

_ 90

of 10 cm2. The halo cannot be composed of particles that interact with

nuclei thougn spin independent interactions whose coupling constant (normalized

to the coupling of massive D^'rac neutrinos to baryons) lies above the solid

line. Nor can the halo be composed of particles that interact with nuclei

through spin dependent interactions whose coupling constant (normalized to

the coupling of massive Majorana neutrino to baryons) lies above the dashed

line.

IV. Laboratory Limits on Solar Axions

It is well know thai the strong CP problem can be solved by the intro-

duction of a light pseudoscaiar axion. Its mass and couplings are inversely

proportional to the vacuum expectation value (VEV) which breaks the Peccei-

Quinn U(l) symmetry. ~ The CP problem is not sensitive to the magnitude of

the particular VEV. but the detectabi1ity of the axion is sensitive, through

its mass and coupling constants. With few exc_ptions, the standard axion

has been ruled out by a large number of experiments. c It was, however,

recently pointed out that if they are short lived ( T "- 10 s) they have not

been ruled out and have been proposed as a possible explanation for the anomalous

positron and electron peaks in heavy-ion collisions. Laboratory limits, coupled

with those deduced from effects on stellar evolution, have ltd to the VEV being

264

restricted to values large enough ( 10 GeV) to make the axion "invisible".

The detection of invisible axions from the iun, via their electromagnetic

24interactions, has already been considered.

Atomic enhancements can be exploited when axions interact with bound

25electrons in a process analogous to the photoelectric effect, which is enhanced

by factors of ^10 when the photon energy is near the electron binding energy.

This process, called the axioelectric effect, is shown in Figure 8. Such effects

are expected to be large for solar axions since their energy should be comparably

to atomic energies; the average sclar temperature is near 1 keV. In the dipole

approximation with axion energies w <••• m (in natural units h = c = 1) we have

- axion , UJ -.- ,-,,.°axioelectric ~ a ^2nT °photoelectric' (

em eand

"axion = (2*eV'F)2 Tn • (8)

— 1 7 ft

where a = (137) and x' is a constant of order unity, and which Srednicki

argues is greater than one in the DFS model. F is defined by the axion-electron

interaction Lagrangianm

L - 2xe f- aeh5e , (9)

where a is the axion field. Equation (7) includes all Coulomb effects

26for the nonrelativistic electron. The axion mass can be related to F by

m • 5 7.2 eV [ F 1 . (10)axion L F J v '

The most reliable theoretical lower bound may be placed on F by requiring

that the solar bremsstrahlung axion luminosity not exceed the photon luminosity.

Such a large axion luminosity would imply that the sun is significantly younger

9 +

than ^ 4.5 x 10 years, the age of the oldest known meteorites. This gives

F/2xe > 1.08 x 107 GeV . (11)

Motivated by this bound, the axionization cross sections per kg for C, Si, Ge

and Pb were calculated with Eq. (7) for F/2x' = 107 GeV and are plotted in

265

Figure 9. It is clear that the detector should have the lowest possible

background and an energy resolution of the order of 1 keV; this is possible

with semiconducting detectors. Because of their low threshold energy, Ge

detectors can make use of the huge enthancement in the axioelectric cross

25section. It has been shown that the axioelectric event rate for solar

DFS axions could exceed by 4 to 5 orders of magnitude the published design

capabilities of bolometric detectors. Because of its low band gap and high

efficiency for converting electronic energy loss to electron-hole (e-h) pairs

germanium detectors are probably the best suited particle detectors for DFS

axions.

In the following, a solar model1" c is used wherein the solar axion flux

is calculated with solar temperature T = 1 keV. The expected flux is shown in

Figure 10. Only the bremsstrahlung emission process is used as a source of

29axions. For F/2x' = 10 7 GeV, the axionization event rates in Ge can be

obtained by multiplying o . , f . (see Figure 9) by the solar axion flux

shown in Figure 10. In Figure 11, the number of events per kg per day for

germanium are plotted against the incoming axion energy for F/2x' = 0.5 x 10 7

GeV (solid line) and F/2x' = 10' GeV (dashed line). The major contribution

to the event rate comes from a narrow band between 1 keV and 10 keV. This

is because both the solar axion flux and the axioelectric cross section peak

Speculative astrophysical arguments have been made which place more severelower bounds on F/?x'e: F/2X^ •> 4 x 10

7 GeV (red giant cooling) 2 7, F/2X' > 4xl09

GeV (He ignition in red giants) 3 0, F/2X' can be as large as 3X109 GeV (x-ray

pulsar cooling) 3 1, and F > 10 9 GeV (white dwarf cooling)32. All of the abovearguments rely on the details of models of stars which are very different thanthe sun; the strongest bounds rely on a proper understanding of stellar evolution.Cosmological arguments suggest an upper bound on F/2X' of 10 1 2 GeV. 3 3

266

'F.eeElectron

\ Anon\

ion Bound

u

P

r 'r i

r /,-

Tf

5 10i KeV)

Figure 8. The axioelectriceffect.

Figure 9. Axioelectric cross sectionsfor C (dots), Si (dot-dash), Ge (dash)and Pb (solid).

AXIUI. Hate for GermaniumI O O O •

I'SC 'PNL Dola set 2 j

-> iON ENEWGi2 3 4 5

*X1ON ENERCY(KeV)

Figure 10. The flux of solar axionson earth for a solar temperatureT = 1 keV and bremsstrahlung produc-tion and F/2x' = 0.5 x 107 GeV.

Figure 11. Solar axion events perkg per day for Ge, F/2x' =0.5X107 GeV (solid), l.DxlO7 GeV(dashed). The crosses are datapoints.

267

in this region. In the following, the expected rates are compared with the

count rates observed ^ n tê uH''al'Jw bacty ounc; qermar " urn spectromete1 described

earlier. Three months of data were accumulated, of which six weeks were low in

microphonic noise. Also plotted in Figure 11 are some of the experimental points

(crosses) for ui ~ 4 keV. The statistical error- on these data is estimated at

± 25%. From this, the experimental bound

F/2xe ; O.b x 1 07 GeV (12)

may be deduced. For 2x' = 1 the laboratory bound on the DFS a>ion mass is

m g < 15 eV . (13)

If 2x' • 1, as argued by S r e d n i c k i / stronger laboratory bounds on the axion

mass result.

The coupling of axions to photons is irrelevant for the above consider-

ations; only the coupling of axions to electrons is important""". Therefore,

bounds similar to (13) are obtained for any light pseudoscalars or light scalars

34 tH-'

that couple directly to electrons. Familons and singlet-Majorons" (associated

with right-handed neutrinos) have couplings similar to (9) where 2x' is

replaced by a model dependent coupling constant and F is the large global

horizontal symmetry breaking scale. Tr"iplet-Majorons (associated with left-

handed neutrinos), appear if lepton numoer is a global symmetry spontaneously

broken (up to this point the same applies to single-Maiorons) at a scale v-j-

(the vacuum expectation value of a triplet Higgs field) small with respect to

the electro-weak scale. From the coupling of Majorons, M, to a pseudoscalar

electron current we hav'e,

L = 2-v 2 GpV Tm Meii 5e . (14)

By comparison with (9), the bound analogous to (12) becomes

vT •' 6.9 Mev . (15)

0

a

268

For- the interaction of a light (m •• 1 k e V ) scalar a> with a scalar electron

c u r r e n t , the interact :•

L = \eeu . (16)

The crass section for the scalar ionization for nonrelativistic electrons is

°scal arelectric 4nu °photoe ! ectric

including Coulomb effects This does not suffer- the suppression factor

(u)/2m ) 2 so that bounds on

o , = A2,-In (18)scalar •

from the sealarelectric effect could be "- 10 6 times stronger than those on

;. fr-om the a> ioe'ectric effect for energy depositions of 1 keV. This

o+ r-j^rse * - apples 'or theoretical astrophys i ca i Pounds on a , , analogous

to those in Refs. 26-32 from the theoretical limits on light scalar emission

f"om stars and overciosure of tne universe.

There is a problem of conceptual self-consistency which must now be faced.

We have given a laboratory bound i w ax ions F/2X1 ^ 0.5 x 10' GeV. SupposeF/2X1 were indeec 0.5 x 10 7 GeV. Then the solar axion luminosity, £ , would be

e J a

approximately four times the solar photon luminosity, £ .. To calculate the axion

f lux, a mode1 of the sun was used which was dominated by QED, weak and nuclear

processes; axior physics were assumed unimportant for solar dynamics. This might

not be the case ;f i\ ~ 4 il , and therefore the laboratory bound might be

conceptually self-inconsistent. However, a laboratory bound stronger by a factor

of 2 to 3 would be conceptually self-consistent. Thus, future improvements in

our laboratory bounds are crucial.

As stated eaHier, the rapid increase of noise below £... . -, , = 4 keV is

attiibuted to microphonics engendered by mining operations, and steps are being

taken to eliminate or tag such correlated events which will permit lowering of

the energy thresno'd to about I K.ev. Steps, discussed above, that are being

26S

taken to increase the sensitivity of the fjp-decay search, should result in a

background reduction between 1 and 2 orders of magnitude. According to Figure 11,

the axioelectric absorption peak in germanium occurs at lower incoming axion

momentum. For example the axionization rate for u = 1.4 keV is ^ 16 times that

f c w = 4.7 keV, Thus an improvement in the limit may also come from examination

of the Ge data for w near the peak.

Our DFS bound F/2x' ^ 0.5 x 10" GeV is a laboratory bound relying on a

realistic model of the sun, the closest and best understood star. Linrts on

Majorons have also been displayed (v, ^ 6 . 9 MeV for triplet Majorons) and for

most familons which couple directly to electrons. (For models in which familons

couple dominantly to quarks, our bound does not apply ) Our laboratory bound

does "ot rely on a detailed understanding of the dynamics and evolutions of

red giants, white dwarfs, neutron stars or other stars as do the more

sophisticated theoretical bounds.

Using the axioelectric effect, semiconducting Ge detectors could eventually

set limits F/Zx > 10s GeV (v, < 0.3 MeV) or, more exciting, see solar axions

or other light bosons. The discovery of these particles would allow us to study

physics at energies beyond the reach of accelerators and provide us with a new

laboratory tool to study the interior of stars.

ACKNOWLEDGEMENTS

SD is supported by NSF grant PHY83-10654 and is an A. P. Sloan Foundation

Fellow, BWL is supported by DOE contract DE-AC03-75F00515, GDS is an NSERC

(Canada) Postgraduate Scholar, DNS is supported by NSF grant ^ 'V-83-06693

and GG by NSF grant PHY-82-15249. RLB is supported under DOE Contract

DE-AC06-76RL0 1830, and FTA is supported by NSF Grant PHY-8405654.

270

2.

4.

5.

6.

10.

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J. Bagger, S. Dimopoulus, E. Masso and J. Reno, Phys. Rev. Lett. 54, 2199(1985); E. Kolb and K. Olive, FERMILAB preprint Pub-85/116-A (19857.

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271

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26. D.B. Kaplan, Nucl. Phys. B260, 215 (1985). M. Srednicki, Nucl. Phys.B45, 689 (1985) argues that 2x' > 1 for DFS axions. Combined with ourresults this would give an even stronger bound on the axion mass. Thereare, of course, many invisible axion models in which 2x' can be anything,and therefore our axion mass bounds must be considered Conservative.

27. D.S. Dicus, E.w. Kolb, V.L. Teplitz, and R.V. Wagoner, Phys. Rev. D18, 1829(1978) and Phys. Rev. D_22. 829 (1980). M. Fukujita, S. Watamura, andM. Yoshimura, Phys. Rev. 48, 1522 (1982).

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29. G.G. Raffelt, Phys. Rev. D3_3, 97 (1986).

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31. N. Iwamoto, Phys. Rev. Lett. 53, 1198 (1984) and D.E. Morris, LBL Report18690 me (1984). However, these calculations neglect possible internaland external heat sources arid assume that the observed x-ray spectra arethermal and neglect the possibilities of non-thermal magnetosphericemission and internal heat sources: this result must therefore be

272

considered speculative. Furthermore, note that the upper bound on theluminosities of the well-known x-ray sources SN 1006, Tycho and Cast isbelow the predictions of the standard cooling model, K. Nomoto, S. Tsurute,App. J. 2_50, 19 (1981). This suggests additional cooling mechanisms forx-ray sources including, possibly, axion emission.

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273

STRINGS IN SPRING ( 8 6 ) !

P. Ramond

Phys i c s Department. U n i v e r s i t y of F l o r i d a . G a i n e s v i l l e . FL 32611

ABSTRACT

We present an overview of recent progress in string theory. We treat in

detail the mechanics of some of the Calabi-Yau compactification and summarize

some of its experimental consequences.

Invited Lecture at the 7th Vanderbilt High Energy Physics Conference.

Vanderbilt University. Nashville, Tennessee, May 15-17. 1986.

John Simon Guggenheim Fellow.

Supported in part by DOE Contract No. FG05-86-ER40272.

274

The recent past'- ^ has witnessed the emergence of closed string theories as

the best candidates for describing a totally unified view of all known

interactions. There are essentially two reasons for this - one is that, unlike

local field theories, closed string theories seem to allow for an amicable

coexistence between gravity and Quantum Mechanics, albeit in a higher number of

dimensions than presently observed: the second is that this union can only be

consumated for certain gauge groups, and it happens, remarkably enough, that

[21there is one closed string field theory1- J which is capable of depicting the

chiral quantum numbers of elementary particles observed in the laboratory. It

leads to a gauge unification via exceptional groups, as long advocated by Gursey

and collaborators.'- ^

Thus it is believed by many theorists that the equations of motion which

rule our observed universe have been found: there remains to find solutions for

them. Using well known data from the low energy world, certain stabs at the

vacuum structure of this theory have been presented. One of them leads to

compactifying from ten to four dimensions via Calabi-Yau manifolds; the other

does not use manifolds but orbifolds as coset structure.'- -" The Calabi-Yau

approach relies heaviiy on local field theory analysis, and does not clearly

represent solutions of the full itring theory; the orbifold, on the other hand,

deals explicitely with solutions of the full string equations - it has not yet

been explored fully. Neither approach provides an answer to the cosmological

constant puzzle, but transfers it to a yet-to-be understood mechanism of

supersymmetry breaking.

The exciting feature of these "solutions" is that they teach us that the

phenomenological Higgs structure needed to parametrize the low energy world has

its origin in the nature of the compact ification, thus providing us with a

275

unified picture of symmetry breaking linking space-time (from ter. to four) to

gauge symmetries (from E_xEg to the standard model).

There have been many exciting developments in string theory. The most

formal has been the beginning of an understanding of string field theory. The

open string field theory has been formulated classically by Witten as a

realization of a non-commuta<.ive geometry. There is no such crisp picture

for closed strings. In another direction, there has been much activity in

developing the Polyakov approach, stressing the two-dimensional nature of the

theory. Although this has led to much pretty mathematics, it has not yet

proven to be very fruitful, although many believe that it will be the key for

providing a geometrical understanding of closed string theories as theories of

space-time. Eventually, one would like to formulate string theories in such a

way as to make explicit the emergence of a (modified?) equivalence principle in

the local limit. At the moment, the relation between closed strings and gravity

relies solely on perturbation theory: there is a massless spin 2 particle in

both theories.

Thus, there are many developments to describe and the reviewer has to choose

among many. For this experimentally oriented audience, it seems appropriate to

describe in some detail the original attempt to link the heterotic string in ten

dimensions to the real world in four. This we do after a brief description of

the known string theories.

I. List of String Theories

Even though we are only using pertubation theory, there are few string

theories. It is hoped that non-pertubative methods will further reduce this

list. We have

276

A) The original non-supersymmetric theory.1 J

- il describes open strings (Veneziano) and closed strings (Virasoro-

Shapiro) evolving in 26 space-time dimensions.

- it contains a tachyon in its purely bosonic spectrum.

B) The original (type I) superstring.1- J

- it describes open said closed strings (Ramond, Neveu-Schwarz) evolving in

10 space-time dimensions.

- its supersymmetric version (Gliozzi-Olive-Scherk) contains no tachyon.

- only the gauge group SO{32) can be added to it without causing anomalies

(Green-Schwarz).

C) Type II Superstrings (Green-Schwarz). •"

- they have two supersymmetries..

- they describe closed strings evolving in 10 space-time dimensions.

- they come in two types, type a) which contains vector-like fermiens, and

type b) which has chiral Fermions - it has no anonsaly.

D) The Keterotic Superstring (Gross, Harvey, Martinec, Rohm)'- J

- it has one supersymmetry and describes closed strings in 10 dimensions.

- it has the gauge symmetry Eg*Eg or SO(32) and has (10 diirensional) chiral

ferraions, and no anomaly.

E) The Ncn Supersyir.T^tric Heterostring. (DHAGMV)'-9j

- it describes closed string in 10 dimensions

- it has the gauge group O(16)xO(15), a chiral fermion content and no

anomaly.

- it lias no supersymmetry and thus a naturally large cosmological

cons tan t.

In this list *e have not Included several other string theories, ruch as string

theories with tachyon. of which there ire many, and string theories rh

277

correspond to different vacua of the afore-mentioned strings; of this type are

the ingenious Narain strings. J j We warn the reader ihat it may be unwise not

to describe in detail string t'eones with tarhyon such theories, although

unstable in their allocated dimensions, might recover their health by

conspactifying to lower dimensions.

II. Compac t i f i ca i i on

r-? 121

In the following we describe the earliest attempt1- ' J at the

compact ification of the E oxE c heterotic string. It relies heavily on the localft o

field theory limit of the string, and in that sense may not lead to a true

solution of the full theory. •* Still we feel tiiat it is sufficiently

interesting to devote the rest of this review to ii.

The aim of the approach is to find a solution of the equations of motion of

the heterotic string which has built into it all the desiderata of the low

energy world. Then the known low energy particles will be identified with the

solutions of the equations of motion in this background.

The heterotic string contains massless and massive panicles. The massive

particles have masses of order of the Planck mass, and are presumably irrelevant

to the low energy world. The massless particles arrange themselves into a N=l

supergravity multiplet and a N=l Yang-Mills supermultiplet transforming as th?

adjoint of E_xE_., all in ten dimensions. In other words, the massless modes are

Gravi ton h ^ (35)

fi=l supergravity I Gravi tino */*„ (56)

in 10 di-^nsions ^ Kalb-Ramond field B ™ (28) ; all singlets of

Spin 1/2 field X (8)

Scalar field $ (1)

278

N=l Yang-Mills i" Vang-Mills Field AM (S) (1,248)+(248,1)

in 10 dimensions j Gaugino x. (S) of E^xEg

The numbers in parentheses refer to the number of degrees of freedom carried by

tho Fields. The local field theory action describing th•; interaction of those

two multiplets has been investigated on its own. - Howtv?"-. the action for

these particles extracted from the siring theory must be modified, at least. by

adding terms involving four derivatives which are necessary for anomaly

cancellation. These extra terms alter the form of the transformation of borne

of the fields under, among others, supersymmetry.

Trie authors of Ref. [4] look for a background solution to the local field

theory which satisi'es certain criteria. These criteria are

- N=l unbroken supersymmetry in four dimensions. (Needed to explain the great

disparity between our scale and that of gravity.)

- Ten-dimensional space-time breaks down in a maximally symmetric

four-dimensional space-time and an unknown 6-dimensional compact space, K. The

requirement that the four-dimensional space be maximally symmetric just means

that it is one of three types: flat (Minkowski). like the surface of a sphere

of constant cruvature (De Sitter) or like the surface of a hyperboleid of

constant curvature (Anti-De Sitter). Presumably the coset space K is compact

(like a circle) with radius of curvature of the order of 10 cm.

Having set up these desiderata, they proceed to derive a set of necessary

conditions for such a background solution to exist. Their first observation is

that the maximally symmetric background values of M requires the fermion fields

to have no background values. Recall that a fermion with respect to the

ten-dimensional manifold is necessarily a fermion with respect to

four—dimensions as well. Thus

D

279

= 0 for all fermions. (1)

•where b stands for background.

The next remark is that for N=l supersymmetry to survive, it must be that

the variation of any background fermion under supersynunetry be zero as well

6 4 = 0 for all fermions, (2)Q D

while the supersyrametrie change of all background boson values is automatically

zero since *k = 0. Now the background values of the boson fields is determined

by solving the set of equation (2). The exact form of 6 + is known for the

local field theory case, improved for the anomaly cancellation, but not for the

whole string theory. However it is assumed that it is sufficient to deal with

the mass less modes only. Equation (2) have several consequences:

- firstly the foui—dimensional world must be flat.

- secondly if the field strength of the KR field improved by the Chern-Simmons

ri4i

form vanishes,1 J there must exist a real spinor in the internal manifold K

which is covariantly constant. From these it follows that

the Ricci tensor of K must vanish

the manifold K is Kahler.

there exists a crucial relation between the gauge fields and the Riemann

tensor over K.

Let us describe a bit the coset space K. It is six-dimensional, and thus

has at most 0(6) transformations over it. It can have spinors as well, which

transform as 4 and 4^ [Recall that 0(6) ~ SU(4).] A real spinor will thus

transform as 4 + 1 In equations, a covariantly constant spinor satisfies

(m=l 6)

280

(a 4 « npT )n = 0, (3)v m 2 m np' v '

where w is the connection and T are the 0(6} generators. It is easy tom np

build a non-zero solution of this equation, by taking n = r) to be constant

along one direction, zero in the other, corresponding lo the breakdown

SU(4) D SU(3)

= 1 + 3 with T|

Then (3) will be satisfied if u has zero values whenever n and p correspond

to generators not in the SU(3) subgroup, because then T r/ = 0. This means that

the connection has only SU(3) values. The manifold K is said to have SU(3)

holonomy. Thus K is Kahler. Ricci flat and has SU(3) holonomy. Such spaces are

hard to find. Only a finite number are known - they are called Calabi-Yau

spaces. The holonomy group is very familiar from General Relativity where it is

(in 3+1 dimensions) S0(3.1). If one travels in a closed loop in the space, the

naive transport of a vector will change the direction of the vector, and when it

comes back to the same point, it will have changed direction! To put it right

one needs the holonomy group which then rotates the vector to its original

direct ion.

In addition, there is a crucial relation between the gauge fields (E_xEg)

over K and the Riemann tensor of K'

f F* , = Rr rS R , . (4)

[mn pq] [mn pqjrs l '

281

Let us now consider the mass less modes which can exist in this

compactification. We first consider a generic equation like

(D4 + O,-) <J>(x,y) = 0, (5)

where x denotes four-dimensional space-time and y labels K. The niassless modes

in 4-dimensions must obey

= 0;

they are 'riarm*.:n i c functions over the internal manifold K We can expand <£(>:. y)

in terms of such harmonic forms ever K

*(x.y) = 2 *.{x)

Then we *.=e that to each mssslest mode in four dimensions if. (x), there

corresponds a mrssiess (harmonic) mode over K. There will be as many rnassless

physical particles "±s ha:monic mode? over K.

The nuinber of solutior.s 'o tht- equatio;i

2S2

depends, on the t ransf ormai ion properties of 4'[v) under the holonotny group.

Thus, in crder to know how muiv massless modes can exist in our background

solution, we just have to first decompose the field conten; of the N=l

supergravily and Yang-Mills supermu]tiplets in terms of the holonomy group of K.

We first do this for tht supergravity multiplet. Its physical content in

verms of the SO(S) liRht cunt little group is

(2000)

-

(0100)

2S

(0000)

1 r>C

In order to arrive at four dimensions, we decompose Sr'(S) as

SO(S) D SO(f.) x SO(2).

where SC>(2) is the helicity. and S0(6) is the largest ho', •

Given the decompositions for the vector and spinor represe

•-.: •••: group K can have.

h 0 1 - 1

; 8 = 4 + i-s -

h 1/2 -1/2

where h is the h e l i c i t y . we have the whole N=l supergravity multiplet sp l i t t ing

as

283

he 1i c i t v

2

3/2

1

1/2

0

-1/2

- 1

-3/2

- 2

S0(6) rep

1

4

2(6)

2(f) + 20

3(1) + 15

2(1) + 20

2(6)

4

1

20'

2(1) + 3 ( 3 ) * ^ + 6 + S

2(3j - 2(3)

I + 3

1

In the last coiumri we have indicated the actual breakdown under The actual

holonomy group S'J . This index will be carried solely by the +.(>'). Since we

have N=l supersymir.e'.ry , we caxi read off the expected supermu 1 t i pi c-1 b and their

transformation under the holonomy:

supermult iplet

(2,3/2) [supergravity]

(3/2.1)

(1.1/2) [gauge]

(1/2.0) [Wess-Zumino]

SU(3) holonoinv transformation

I

3

2{3) + 3

6 + 8 + 2(1) + 3

As It happens, the multiplicity of harmonic functions which transform as

antisymmetric tensors under the holonomy is known from purely topological

considerat ions!

284

[4 141As a toy model, suppose we had S0(6) ho)ononr> ' [and no i SU(3)]. Then

the possible antisymntetric tensors (forms) iruns form as

1 6 1L> 1 ^ + 1 0 10 6 1

8 indices: 0 1 2 3 2 1 0

The number of harmonic tensors with these transformation properties is given by

the Betti numbers. b n(=b_). b (=br), b (=b } arid b. and they are a

characteristic of the manifold. For instance, one can relate them to well-known

topological invariants such as the Euler number \^~.

6K = 2 (-if b (9)

p=0 p

In the case of a manifold with SU(3) Violonomy. we express the vector index into

two complex numbers [6 = 3 + 3 ] and are chus led to forms with covariant

(contravariaiit) indices, each transforming as 3 (3). The forms transform as

(0.0) - 1; (1.0) '" 3: (0.1) ~ 3; (1.1) " 3x3 = 8 + 1 ; (2.0) ~ (3x3) = 3; (0.2)3.

~ 3; (1,2) "" 3x3 = 6 + 3, (2,1) " 6 + 3; (2.2) ~ 8 + I; (3.0) ~ 1; (0,3) ~ 1.

Here the notation is: (p.q) denotes a form with p(q) antisymmetrized

co-(contra-)variant indices. Let b be their Betti numbers. The Euler

characteristic is

3

p.q

We obtain the following content of massless modes coming from the N=l

supergravity multiplets

285

mu)tiolicitv

bo.ob o , i

:bi o + b o . ^

helicitv

: (2.3/2)

: (3/2.1)

: (1.1/2)

1 + b2 J : (1/2.0)

It is fortunate that for Ricci flat manifolds with SU(3) holonomy. there are no

harmonic forms which transform as 3 or 3 of the holonomy. Hence the survivors

are just

b o o ( 2 . 3 / 2 ) • [ b Q 0 + b l l + b 2 1 ] ( 1 / 2 . 0 ) .

and b~ is made up entirely of forms transforming as 6. while b1 .. is made up

of forms transforming as 8 + 1_. Another mathematical fact: as long as K is

simply connected, there is only one scalar harmonic form, hence b_ _ = 1 which

means only one graviton! There is of course another scalar harmonic form coming

from taking the trace of the (1.1) form, and it can also be shown to be unique.

With those facts in mind, we can set b_ = b(6) and b = b(8) + 1. Thus we

are left with the following massless modes:

(2.3/2) + [2 + b(6) + b(8)]-(l/2.0).

For a given Calabi-Yau space there will be definite values for b(6) and b(8).

We now proceed to a similar analysis for the N=l Yang-Mills supermultiplet.

This multiplet. for the EoxEc, heterotic string, has the quantum numbers of the

adjoint representation. The relation (4) for the background configuration

implies a relation between the Yang-Mills field strength over K, F^ and the

mn

286

Riemann tensor or between the gauge potential A and the connection u . Wem m

already know that u n p transforms as SU(3) of holonomy. Thus this relation will

not break a linear combination of SU(3) coming from Egx£g and the original

manifold SU(3). One can choose any SU(3) from EgXE^ as long as the relation (4)

is satisfied. One choice which works is to extract the SU(3) from one E_,

leaving the other untouched. This step leads us to the decomposition

E 6 x SU3

with the adjoint decomposing as

248 = (78.1) + (27.3) + (27.3) + (J.8) . (11)

Thus the left-over "low energy" group is E-xE . The group E,. is well known as a

possible candidate for a chiral grand unficiation of the low energy

interactions.

Now, the N=l Yang-Mills multiplet in ten dimensions breaks down in four

dimension to a self-conjugate N=4 supermul tiplet "•

helicity S0(6) SU(3)

1 I I

i/2 4 1+3

0 6 3 + 3

-1/2 4 1+3

Following the previous analysis, it means that we will have one N=l Yang-Mills

287

supermultiplet transforming as the (1.248) of EgXEg Now for the other

iiiultiplet originally transforming as the adjoint of the cannibalized Eg. 'sing

(11), we see that

(Z8-I) yields a holonomy singlet YM multiplei.

(27,3) yields Wess-Zumino multiplets corresponding to the compound

holonomy 3x3 = 6 + 3 i.e the (2,1) form

(27,3) yields Wess-Zumino muitiplets transforming corresponding to the

(1.1) form or 3x3 = 8+1..

(l.S) yields YM multiplets corresponding to the 8 of compound holonomy;

yields WZ multiplets corresponding to compound holonomy 0x3 =

1 5 + 6 + 3 .

Thus we are left with:

(1.1/2) ~ 78 of Eg-, b(6)(l/2,0) ~ 27 of Eg:

[1 + b ( 8 ) ] ( l / 2 . 0 ) ~ 27 of Eg; b ( 8 ) ( l , l / 2 ) ~ I of Egi

[b(6J + n ( 1 5 ) ] ( 1 / 2 . 0 ) ~ I of Eg.

ue recognize the adjoint Yang-Mills supermultiplet for E,.. We also see that

b

chirality in the fermion is broken: we do not have as many 27's as 27! In

fact, we have

«(27) - *(27) = b(6) - 1 - b(8).

Using (10), we note that the number of chiral families is exactly half the Euler

characteristic! Thus we have [1 + b(8J] vector-like families of 27 + 27 and an

288

excess of p- |<F I of chiral 27's. Recall that each 27 contains one family of the

known particles. In addition to these nice particles, we also have b(8) E_

singlet of Abelian U(l)"s. They cannot possibly enter the low energy spectrum

since they have anomalies. Fortunately, we also have b(6) + n(.15) Wess-Zumino

fields which are E_ singlets! It can be shown"- ^ in fact that b(8) of the WZ

multiplets coming from the N=l supergravity muitiplet in ten dimensions

actually "eats up" the b(8) U(l) gauge multiplets coming from the

ten-dimensional N=l Yang-Mills muitiplet. this is possible because a massless

antisymmetric Kalb-Ramond tensor can actually eat a massless vector field and

thus gain a mass. Hence the b(8) [(1,1/2) + (1/2,0)] disappear from the

massless spectrum. They presumably acquire a Planck mass.

Now the IS representation of SU(3) does not appear in antisymmetrized forms,

and the number of harmonic forms transforming as the 15 cannot be determined by

topoiogical considerations. Thus the following summary of massless survivors

mul tiplici tv helicitv; E-xE,.1>—o

1 [(2,3/2); l.V]

1 [(1,1/2); 1,248]

1 [(1.1/2): 78,1]

b(6) [(1/2,0); 27.1]

(1 + b(8)) [(1/2.0); 27.1]

( 2 + 2b(6) + nQ§)) [(1/2.0); I.J.] (12)

The first column refers to the multiplicity, and the first two labels inside

the square brackets refer to the helicities. the last two to the E_xED

transformation properties. Thus all we need to know from K are the three

289

numbers b(6). b(8) and n(!5). The first two are topologically determined - the

last is more complicated.

We now list for completeness the content of the chiral multiplets under the

standard model. It Is convenient to just give the decomposition of Eg with

respect to the color quantum numbers.

E c 3 SU-jXSLLxSU^ .b J J J

with

I§ = (1.1.8C) + (1.8.IC) + (8.1.IC) + (3.3.3C) + (3.3.3°)

22 = (3.3.1°) + (3.1.3°) • (1.3.3°);

Thus each Efi family of 27 contains, besides the usual particles, a charge -1/3

quark, a vector-like doublet of leptons. and two neutral leptons.

At this point we just have to choose the right manifold, but there are some

difficulties: l) Most Calabi-Yau spaces have enormous Euler characteristics

(i.e. number of chiral families), thus making them unsuitable for phenomenology:

too many families lead to a violation of asymptotic freedom for QCD. as well as,

among other things, a contradiction with nucleosynthesis.

2) The only fields in the model which could serve as Higgs fields transform as

27 or 27, and it is well known that it is not possible to break E_ down r.o the

standard model by using only these representations.

A miracle happens: there are Calabi-Yau spaces with 3 or 4 chiral families

(as requested by Nucleosynthesis), but they are in general not simply connected!

(one knows of only one'- * simply connected Ct manifold with Euler number ~6)

This fact allows for an additional topological mechanism,'- * introduced earlier

290

by Hosotani^ in the context of Kaluza-Klein theories, which actually breaks

E_ 'urther. thus allowing for the possibility of reproducing the standard model.6

Thus. we concentrate on Calabi-Yau manifolds which liave E'-uor characteristic

of at most 8. and are multiply connected. Fortunately only a few are known

They are built by starting from a sircpjy connected marifold rn which some

discrete gro-jp G or order ;i(C) acts freely, the word "freely" only me.-ms that

there are noi poin!'i of the manifold which are mapped mio themselves by the

action of G. One then fo;ms the quotient space K/C which is itself a manifold

as lung as C aci? freely. Or; it, TWO points y and y' of K which a)e images

unr'ei the action of G. j e.

c y -• >' - g(y)

arc taken o be the same. As long as there are no fixed points, there are no

singularities. This is to be contrasted with an orbifold ' where the group G

does have fixed points, leading to singularities in K/G The nice thing is that

this reduces the Euier number according to

) = x{K)/fi{C).

In addiTi^n to this, there may be yet other left-over discrete symmetries in

K/G. If two points of K are now to be identified in K/G. what happens to the

values of the fields at these points? We could of course choose fields which

have the same value at the two points

- \Hg(y)).

291

which would correspond to a given choice of the vacuum configuration.

Alternatively one could look for zero modes which satisfy a more general

condition, namely

where U is an element of G. This is an priori possibility since the zero modesB

do form representations of G. The trouble with this choice is that the fields

would not be single-valued. But in our case, the fields have extra transfor-

mation properties under EpXE^. Thus it is possible to undo the U transfor-

mation by borrowing a similar transformation from EgXEg. designed so as to

recover single-valuedness. This choice corresponds to a particular vacuum

configuration. We remark that the situation here is not any worse than in the

usual case, where one cannot offer dynamical reasons for the particular

direction spontaneous symmetry breaking takes- after all we do not even know why

Nature does not break color, nor Lorentz invariance. or seems to break only

chiral symmetries at low energies.

Call G the discrete group extracted from E-xEg . The physical states will

correspond to singlets under G+G . Of course. G must be chosen in such a way

that it is contained in the gauge group.

Let us give a very simple example of the procedure we have just outlined.

Suppose that G is Z-. Then it is like a parity, and the zero modes of K will

break up into two classes, corresponding to even and odd parities. Similarly,

under G (Zg) extracted from the gauge group, the zero modes will split up into

two classes. The vacuum configuration will contain only the modes which are

even under the combined parity P-P. We see that the number of such zero modes

will be half of what it was before. This is a general result, which indicates

292

that the number of "survivors" will be given by the number of original modes

divided by the order of G- In general, if G is made up of product of discrete

groups, one can extract G from either of E g or Eg . In the simplest examples. G

is extracted from Efi. leaving Efi unbroken. Some of the zero modes obtained for

K are necessarily singlets over G. This is the case for the Supergravity

multiplet (2.3/2). and the Yang-Hills supermultiplets of EgXEg It follows

that, having no gauge quantum numbers, the supergravity duo survives. Further-

more, if G is extracted purely from E_. the Yang-Mills supermultiplet for the Eg

will survive as well. Any representation cf Eg will split into a sum of

irreducible representations of G. This is the case for the adjoint zero mode as

well. Hence the surviving zero modes coming from the gauge multiplet of E_. will

have no G-charge. The surviving massless zero modes will transform according to

the surviving low energy group Eg/G . This is the most direct way of obtaining

the low energy gauge group. The determination of the other surviving zero modes

is a bit more complicated, because one has to determine how the b(6), b(8), and

transform under G. as well as the breakdown of the 27 and 27 under G.

At this point we note that all the surviving zero modes in the adjoint of

the gauge group cone from the sane place, all related by symmetries; it means

that the renorraalization group analysis of the gauge couplings is not altered,

and one can analyse the gauge couplings in a straightforward way. The same is

not true for the Yukawa couplings among the chiral multiplets. because the

survivors come from different zero modes, no longer related to one another by E_

group relations. Hence the Yukawa couplings do not obey E_-like relations,

while the gauge couplings do.

The choice of the discrete group G is motivated by phenomenology, although

it is hoped that some day it will be determined by dynamics. The discrete group

G can be Abelian or Non-Abelian. If it is Abelian, all the charges of Eg will

293

be neutral with respect to it [all the elements of an Abelian discrete groups

are represented by diagonal matrices, since all of its representations are

one-dimensional. Thus they commute with the members of the Cartan subalgebra],

which means that the unbroken subgroup of E_ will have rank 6. Thus,

phenomenologically. down to the TeV range there will be, in addition to the

standard model (which has four neutral currents), two other neutral currents.

These will have definite signatures. On the other hand, if G is non-Abelian. it

can be shown that there will be at least one more neutral current over the

standard model. Hence there will be either one or two "low mass" neutral

currents.

The zero modes over K can be decomposed into representations of G. If G has

n representations, we set

b _ R O ) + n(2) + + g(n)

where P.. represents the number of zero modes transforming as the S* '

representation of G. t=l is taken to be the singlet representation. In fact

the Betti numbei s of K/G. Thus, from the N=l supergravity remnants we- j

are left with

multiplicity helicitv

1 (2.3/2)

[2 + pî] (1/2.0)

In order to identify the generators from the gauge multiplet, we have to

decompose the 78 and 27 and 27 in terms of representations of

294

27 - " f.S*1). 7% -- 1— ~j —

where s' ' label the representations of G and £.. a. are representations of the

unbroken subgroup ER/G, for instance a. is the adjoint. We now look for

singlets under G + G. We can then list the survivors coming from the gauge

multiplets"-

[(1.1/2); 28. I] -» [(1.1/2): a^l]

b(6)[(l/2.0): 27.1] - 2 fa* > [(1/2.0); £ _.Y] .

e=\ -l e(l+b(8))[(l/2.0): 27.1] - 2 (5 [(1/2.0); £ _ . ! ] .

e=i - e

.0): I.I] -• 4!l C(1/2'°); -f.rI]-

_ tfiIn the above, the 6 representation is defined to be the one for which Sv ' x

Sv ' contains the singlet. What happens to the n(15) WZ multiplets which are

gauge singlets? Presumably, the n(15) zero modes transform as a sum of UIR of

G; only the singlets under G will survive to "low energies".

From the index theorem, the number of chiral survivors will be given by the

Euler characteristic of K/G, and thus be greatly diminished.

At this stage, we are left with a greatly reduced number of massless

supermultiplets. transforming under ER/G. We note two examples in the

literature — in the first. •• ' -" there are lour chiral families and G = Z^xZg

with E6/Z5xZ5 = SU ScSUgjXSUggXlLxUj; the second'-17"19^ has three families with

G = Z 3 and E ^ = S^xSUgXSl^.

Neither of these groups is, in the absence of extra breaking mechanisms, a

good candidate for the standard model. However, if there exist "flat

directions" in the potential, the degeneracy can be lifted by radiative

295

14corrections, allowing for large intermediate scales "" 10 GeV.

In addition we have not yet considered the particular mechanism of

supersynunetry breaking nor the vector-like E~. Tne actual mechanism of

supersymmetry breaking is as of this writing a complete mystery. Whatever its

nature, it must be clever enough to enter our sector only at the TeV scale and

still forbid any regeneration cf the cosmo.ogical constant. It is hoped that

the vector-like E Q will, with its strong interactions, trigger such a breaking

mechanism by gluino condensates. •*

The picture is therefore far from complete. However, it shows how the

synmetry breaking mechanism can be specified within this framework. There is

hope that the processes we have just analyzed will prove to be more general.

The number of unsolved problems is still formidable. However some general

features emerge: the expectation of extra neutral currents of mass perhaps not

larger than TeV. But these are soft conclusions, depending very much on the

analysis of the flat directions.

Finally let me close with one remark. It is often said that, because of the

smallness of the Planck scale, it -ill not be possible to observe stringy

effects in the laboratory. One can imagine an optimistic scenario where this is

not the case: if proton decay is observed, it will be governed by interactions

just a few orders of magnitude away from the Planck scale, it becomes reasonable

to imagine stringy interference effects appearing in the detailed analyses of

the decay products.

ACKNOWLEDGEMENTS

I wish to thank Prof. G. G. Ross and M. Ruiz-Altaba for illuminating

discussions. I also thank Professors Panvini and Weiler for their kind

invitation to speak at this conference.

296

REFERENCES

[I] M. Green and J. H. Schwarz. Phys Lett. 148B (19S4J 117.

[2] D. J. Gross, J. A. Harvey, E. Martinec and R Rohm. Phys. Rev. Lett. 54

(1985) 502.

[3] F. Gursey. P. Ramond and P. Sikivie, Phys. Lett 60B (1976) 177;

F. Gursey and P. Sikivie. Phys. Rev. LtCt. 36 (1976) 775;

P. Ramond, Nucl. Phys. B110 (1976) 214.

[4] P. Candelas. G. Horowitz. A. Strominger and E. Kitten. Nuclear Phys. B258

(1985) 46.

[5] L. Dixon, J. A. Harvey. C. Vafa and E. Witten, Nucl. Phys. B261 (1985)

67S; Nucl. Phys. B274 (1986) 285.

[6] E. Witten. Nucl. Phys. B268 (1986) 253.

[7] See for instance P. Nelson. Lectures on Modular Spaces, Harvard Preprint

1986.

[8] See for instance. "Superstrings", J. H. Schwarz. ed.. World Scientific

(Singapore. 1985).

[9] L. Dixon and J. A. Harvey. Nuclear Phys. B274 (1986) 93;

L. A1varez-Gaume. P. Ginsparg. G. Moore and C. Vafa. Phys. Lett. 171B

(1986) 155.

[10] K. S. Narain. Phys. Lett. 169B (1986) 41.

[II] M. Crisaru, A. E. M. van de Wen, and D. Zanon, HUTP-86/A026-A027 (April

1986).

[12] E. Witten. Nucl. Phys. B258 (1985) 75.

[13] A. H. Chamseddine. Nucl. Phys. B185 (1981) 403.

E. Bergshoeff. M. de Roo. B. de Wit and P. van Nieuwenhuizen, Nucl. Phys.

B195 (1982) 97; G. F. Chapline and N. S. Manton. Phys. Lett. 120B (1983)

105.

297

[14] K. Pilch and A. N. Schellekens. Nucl. Phys. B259 (1985) 637.

[15] T. Hubsch. University of Maryland Preprint 86-149 (1986).

[16] E. Witten. Phys. Lett. 149B (1984) 351.

[17] S. T. Yau is the Proceedings of Symposium on Anomalies, Geometry and

Topology, eds. W. A. Bardeen and A. R. White (World Scientific, Singapore.

1985).

[18] Y. Hosotani. IThys. Lett. 126B. 309 (1983); 129B. 193 (1983).

[19] B. Greene. K. Kirklin. P. Miron and G. G. Ross. Oxford Preprint, March

1986.

[20] M. Dine. R. Rohm. N. Seiberg and E. Witten. Phys. Lett. 156B (1985) 55.

299

RECENT PROGRESS IN PARTICLE PHYSICS*}

A. De Rujula

CERN — Geneva

A B S T R A C T

I d i s c u s s v a r i o u s s u b j e c t s ofcur ren t i n t e r e s t , among them thecoinc ident e lec t ron and positronl i n e s o b s e r v e d in heavy ionr e a c t i o n s , masses and mixings oft e r r e s t r i a l and solar neutrinos,progress in the grand unified frontand in l a t t i c e gauge t h e o r i e s ,super s t r ings , and the dark, mass andbig voids of the Universe.

*' Conc lud ing t a l k a t the 1986Vanderbilt Conference, Nashville,Tennessee, May 1986.

300

FOREWORD

Not all current topics are sytematically coverrd in a pleasantly small

conference, such as Vanderbilt's. Whatever little hope there is of an

even-looking summary talk is thus completely lost. What follows is not a

thorough review of particle physics in 1986, but a cocktail of topics of the

different speaker's choice, further sieved through my own taste.

THE DARMSTADT MONSTER

As L. Krauss discussed in a lively report , an unexpected and so far

totally incomprehensible effect has been observed in the collisions of very2) 3)

heavy ions (U,Cm,Th) with targets of the same elements ' . The projectile

energies (~6 MeV/nucleon) are such that, in a head-on collision, the Coulomb

repulsion reverses the motion of the nuclei as they barely "kiss". An original

purpose of these experiments was to create for an instant a concentrated charge

Zj+Z2, so high as to permit "vacuum sparkling": the creation of e+e~ pair6

which becomes possible when the electron binding energy exceeds its rest

mass . The ion pairs in these experiments add up to a total charge (180 to

188), somewhat above the estimated threshold Z ~ 173 for vacuum sparkling by

extended nuclear charges. Two experiments have found the expected positron

peaks but, lo, their yield and energy are far from having the very steep

Z-dependencp predicted by theory. Moreover, lo and behold, one experiment

reports totally unexpected electron peaks, in coincidence with the positron

lines. Some of these results are reproduced in Figs. 1, 2 and 3. The

experiments can distinguish electrons from positrons and measure their

energies, but cannot measure the angles of emission and the (e+e~) pair

invariant mass. The kinetic energies of both e + and e~ lines are ~37O keV,

independent of the colliding species. The lines are some 70 keV wide,

compatible with resolution. The effect is said to be present only in

"quasi-elastic" collisions. (An event is "elastic" if the measured outgoing

nuclei have the same charges as projectile and target, and their recoil angles

obey billiard-ball kinematics.) To thicken the plot, rumour has it that the

very clean peak in the sum energy E[e+] + E[e~] is now clearly resolved into

two narrow lines. Even without this latest spice, it is my contention that the

Darmstadt effect is beyond comprehension, that is, it is either spurious or

extraordinarily tricky.

301

> - _•<• , Th • Ih (

— •--.:•': ;••••:••;;" V ^--.r.

| 3 / K ? " , . . .* . , ' i . r-n • U . Cm;

1 . . : J % : -: / • - • • '

-' '" - • - - L _ • ° ^ , , H

' " ' • "'" - ° • i.- • Ih » U i

.'. •:' : . . •; < ' , . K : '_ 1 • fl '••"'•: - rt •'"*•'••• -- ' r r l i

l; , ftJ L^ • |

" • • • • ' " " ! ' \ ' ' T1'

~ • • - ' ' • - • - ' - - ^ _ , u c s , l t , ^_ _ , : , ; . ^.,,_ ^ - & 0G SOQ 1000

• ' - Ee. [keV]

Fig. 1 Positron creation probability Fig.2 Positron energy spectra for fiveper unit energy interval in U—U col- different collision systems. Cowan etl isions. Cleraente et a l . . a l . •*

Fig.3 Electron andpositron energy, andenergy sum and diffe-rence spectra in U+Thc o l l i s i o n s at 5.83MeV/nucleon. (a) to(d) are experimental,(i) to (Z) are htonteCarlo distributionsin "coincident" ener-

31gy bands .

600 903 1300

[keVIEr. • E,.]

302

The natural candidate for an explanation of _oincident and equal energy

e* and e~ peaks is a parent neutral particle, decaying into the pair, and

sufficiently long lived to escape from the nuclear charge neighbourhood before

it decays. But to result in so narrow a peak, in laboratory e + and e~ energy,

the parent particle must be made practically "at rest" (less than 100 keV cms

momentum; the cms and lab systems have a relative velocity of only c/20). The

results shown in the third line of Fig. 3 are Monte Carlo calculations based on

the production and decay of an 1.8 MeV/c mass "darmstadton" made precisely at

rest in the cms, with aBCeê") ~ 200 ub. The fourth line is a simulation of

internal pair conversion.

In the cms the colliding nuclei move at v/c = 1/10 and may get as close as

d — 2 nuclear radii. The collision time, during which the nuclei are

significantly accelerated. is of the order T ~ d/v - 2*10~ 2 2 s. The

corresponding energy uncertainty is AE ~ t = 3 MeV, some 50 times the width

of the observed peaks. There is plenty of spare energy to produce an

m = 1.8 MeV/c 2 object, and its expected energy uncertainty is more than one

order of magnitude bigger than the maximum spread that could explain the narrow

peaks. [Naturally, this simple expectation is borne by explicit calculations

based on models wherein the darmstadton is radiated by the colliding nuclei or

their electronic clouds, and by models in which it couples in various ways to

the nuclear electric and magnetic fields]. It becomes necessary to invoke, not

only the production of a new particle, but also the existence of a long-lived

intermediate state " I " . The natural I-candidate would be a compound nucleon

state in an island of quasi-stabil ty, with very similar properties for every

pair of colliding nuclei. Seraiclassical orbiting systems and vague notions of

nuclear states incorporating a darastadr.on-condensat-" nave also been discussed.

Whatever the identity of " I " , its properties must be very contrived. It must

decay "quasi-elast ic al ly" into the origir.^l nuclei and one or more

darmstadtons. The Q-value for this reaction must coincide with the darmstadton

mass to better than two parts in a thousand in all explored (Zj,Z2) combina-

tions, for the particle to exit with less than 100 keV momentum. It is

abundantly clear that we are progressively entangled in an indefensible mess.

In spite of the unsurmounted difficulties facing an elementary particle7 ) H)

interpret?tion of the Darmstadt effect, axions have been resuscitated and9)

doctored in attempts to explain f.he data. To avoid contraints from the muon

g-2 and from t|> and T decays, the new axion "a" must predominantly couple only

to members of the first family. Under these circumstances if must still survive

303

c o n s t r a i n t s from beam damp e x p e r i m e n t s ' , i T = 0 t r a n s i t i o n s in B and

it* -* ae*y decays . It does n o t .

It i s unp leasan t to face a quar.dary so b e w i l d e r i n g tha t cine can do nothing

wiser than to conclude with a puzzled awe.

MASSES AMD MIXINGS OF TERRESTRIAL AND SOLAR NEUTRINOS

The inordinate length of this chapter reflects a recent flurry of activity

in this f ield, typical of a subject of which we know nothing for sure.

12)Avignone presented at this conference resul t s from various experiments

on the double @-decay of 76Ge to the ground state of 76Se. Neutrinoless

BfJ-decay takes place iff neutrinos are Majorana par t ic les , not different from

antineutrinos. The 0+ -* 0+ t ransi t ion to the ground state oc:urs iff neutrinos

are massive and/or endowed of both right- and left-handed couplings. A 0+ + 2+

transition to an excited s tate would only proceed in the ambidextrous case

(experiments sens i t ive to t h i s pos s ib i l i t y are in progress but were not12)discussed at the conference). The present world-total limit on the 0+ + 0+

lifetime is 4.4*1023 year6. The conversion of this limit into an upper limit on

m (assuming right-handed cur ren ts to be tota l ly absent) is not an entirely

t r iv ia l nuclear task, but the recent calculations of a variety of groups are in

good agreement: Avignone quoted m < 0.8, 1.6, 2.0, 2.3 eV from Haxton et

a l . and the Osaka, Tubingen and Heidelberg groups, respectively. These numbers

are well below the widely known low<?r limit, ~14 eV, advocated by the ITEP

group. The simplest way to defer a strategic clash is to believe that neutrinos

are Dirac par t ic les .

Magnetic spectrometer experiments on He f3-decay also begin to present a14)serious threat to the Russian resul t . The University of Zurich group quotes

m < 18 eV (95% cor.f.). The Tokyo group1 J' result is m < 31 eV (95% conf.) and,

as of very recen t , the Los Alamos group obtains m < 27.2 eV (95% conf.).

Whether massive neutrinos are or are not useful to cosmologists in explaining

the formation of galaxies, groups or clusters , i s a matter of opinion, and

could conceivably be correlated with the even or odd character of the Annus

Domini. This year massive neutrinos are in trouble in the lab, and at home in

the heavens.

304

Some time ago, Simpson ' announced the discovery of a 2 to 4% probability

admixture of a 17 keV/c^ massive component to the electron (anti-) neutrino.

This he did by analyzing the decay of 3H in a total absorption "calorimetric"

detector, and observing a kink at 1.6 keV energy deposition, 17 keV below the

spectral end-point, see Fig. 4. As of the round of conferences of last summer,

(keV)

T'lkev>

Fig .4 Simpson's old*7^ ( l e f t ) and tiew^' ( r igh t ) spectra of 3H decay.The lower right-hand plot, meant to oppose the criticism of Ref. 24),shows f i ts with a 17 keV neutrii.o admixture, and two different screeningpotentials.

the situation had clearly reverses, three experiments had been completed, al l

of them measuring the fi-decay of the "obvious" isotope: 35CJt, whose Q value to

transmute into 35Ci is 166.8 keV. The Princeton group quotes 0.4% probabi-

l i ty as the 992 confidence limit on a 17 keV admixture to v . The corresponding

limits for similar experiments in India , Russia and Japan are 0.6%,

0.3% and 0.15%, respectively, a l l of them with 90% confidence. Not discouraged22)by his adversaries the world over, John Simpson has argued that the analysis

of the last three of these experiments is flawed. The written versions of these

results certainly give the impression that Simpson's criticism is well taken.

The authors fix m = 0 and f i t to the experimental points the remaining

parameters (the Q-value, and the possible coefficients of linear and quadratic

energy dependences, reflecting the spectrometer's response and/or electron

b ac ks c a 11 e r i ng e f f e c t s ) . They proceed to add an m ? 0 component

305

[v = v(m=0) + ev(m=17 keV)] maintaining the remaining parameters fixed at

their optimal m = 0 value, and they ascertain the confidence level of a fit

with this skew parameter set, as a function of z7. The correct procedure is to

optimise all parameters simultaneously for every value of m , and to compare

the quality of the corresponding fits, airce there are strong anticorrelations

between the different parameters, the results of the incorrect analysis are

totally misleading. Simpson goes as far as to reanalyze these experiments and

to find evidence for his effect in all of them (see Fig. 5). It must be

admitted that an unbiased naked eye would agree with Simpson's conclusion as

far as the Russian and Japanese experiments are concerned, and remain doubtful23)

in the Indian case. Simpson has also found an alternative fit to the

Princeton spectrometer response function that seems compatible with a 2%

admixture of m =17 keV (see Fig. 5). To my naked eye this fit is clearly not

very good, and is visibly distorted by the 17 keV addition. At this point of

the saga, more than half of the experiments seem to favour a 17 keV component,

and one is tempted to give this possibility a break. But there is a theoretical

criticism and two extra experiments that appear to be (again! ) lethal to the

m — 17 keV/c2 neutrino. Lindhardt and Hansen point out that a correct

treatment of the decay energy and Coulomb screening effects would explain away

most of Simpson's excess of events at low -energies. Their expectations areHupp.rimposed on Simpson's data in Fig. 6. Even more convincing are the new

experimental results. The S experiment of Markey and Boehm , whose results

are reproduced in Fig. 7, correctly places a limit e2 < 0.3% (90% conf.) on a

17 keV component. The response function of this particular spectrometer is very

flat, and a creative massage of these data may not be an easy task. All of the

experiments we have discussed analyze the mass structure of the right-handed

"anti"-neutr ino, and all of them but Simpson's are magnetic spectrometer

studies of the p-spectrum of ^5g decay. There is a further and totally26)

different experiment analyzing the left-handed neutrino. The Isolde group of

Borge et al. studies the bremsstrahlung spectrum of the electron-capture decay

I •+ i2i5Te* + v + y. The maximum photon energy for the dominant decay into

Te* (34.46 keV) is a convenient 150 keV, see the insert in Fig. 8, where the

comparison of theory and raw data, spanning many decades, is also shown. The

conclusion of this experiment is that a 2% (4%) m = 17 keV admixture is

excluded at the 98% (99.9%) confidence level.

Ho doubt, the most intriguing recent development in neutrino physics is2 7 ^ 2 8 ) 29)

the discovery by Mikheyev and Smirnov that the Wolfenstein matter-

induced neutrino oscillations could have a resonant character in some internal

layer of the Sun. What this means in practice is that an elegant "particle-

306

6

4

2

T-2

x10'3

:vIf

(a)

i i i

sin'e =0.(

n

)2

148 152TD (keV?

140ENERGY

160

t O n

(46

K

0.5

(50 (52

(c)

\\

(50 155 ISO

T^tkeV)

0.8

- 0.7

0.6

165 (70

Fig .5 Simpson's r e a n a l y s i s / z ; of the data of Kefs. 21) ( a ) , 19) ( b ) , 20)(c) and 19) (d ) . The l ine superimposed on the Kurie plot (c) i s s t r a i g h t .In (d) the l ine A i s the authors ' f i t 1 9 \ B is Simpson's.

F ig .6 Simpson's da taanalyzed by Lindhardtund Hansen 2 4) with athorough treatment ofCoulomb and endpoint-energy effects.

E (keV)

307

Fig.7 35S p-decay spectrum ofRef. 25). The dashed curvesare the expected results for32 admixtures of a massiveneutrino.

/Nme.

Fig.8 (a) Raw data forthe brems8trahlung spec-trum in *25j electroncapture , with thedecay scheme in theinset.(b) x contour plots forfits with a c2~probabi-l i ty admixture of aneutrino of mass nij.There are 73 degrees offreedom and tne 902confidence area lies tothe left of the curvelabelled "70". The watchis Simpson's result.

( a )

50 100ENERGY (keV)

O O i -

0 03i- .

(b)

C02H

rr. (keV)

308

physics" solution has been found to the solar neutrino problem: the scarcity of

"high" energy solar neutrinos relative to "standard" theoretical expectations.

This solution ucrks, unlike most others, for a vast range of parameters. In

short, electron neutrinos born in the core of the Sun suffer on their way out a

process akin to K /K, regeneration, and exit as muon neutrinos, to whichS .u

existing detectors are insensitive. To proceed, please glance at the following

self-explanatory expressions, concerning a simplified two-family world:

= 1-s c/Vw

w^

It is convenient to write the mass squared matrix M2 in the non-diagonal "weak"

basis because, while travelling through matter, v (but not v , nor v or v )

would acquire an extra effective mass m •+• m (vacuum) + 6m , via the v -e^ ee ee ee eexchange interaction on the ambient atomic electrons. The neutrino-electron

"6 LI 6 "s c a t t e r i n g weak Hamiltonian can be Fierzed to read v y v . e . y e . The electronij Li Li \X L

current in matter reduces to eyg e and is a measure of the number of electrons

per unit volume N " (p/m )(Z/A). The neutrino current reduces to v yQ v , and

the effect of the ambient matter ban be described as a potential to which the

neutrinos are subject, V = /2G_N . The corrected energy-momentum relation

k2+m2 = (E-V)2 boils down to 6m2 ~ 2EV. Collecting all factors one notices

that 6m2 is proportional to energy and to ambient densicy. The time evolution

of a neutrino beam in matter is governed by the equation

JLEdb

= M'

And now for the hat trick. At the high densities characteristic of the Sun's

core, and for a certain range of energies, the "ee" entry of M may be bigger

than the "\i\i" entry. As the neutrinos travel towards the Sun's surface these

entries cross at a certain critical density, and the angle 0[pE] that

diagonalizes M goes through a regime of maximum mixing, sin229[p E] = 1. If

the resonant density layer is sufficiently thick (larger than one neutrino

309

oscillation length), the previously quoted evolution equation predicts that a

very large fraction of v 's exits the Sun as v ' s . Representative results

are shown in Fig. 9, worth a thousand words. Notice the large domain of mass

differences and mixing angles that would significantly affect Clorine and

Gallium solar neutrino experiments. The obvious question is whether or not this

tentative solution to the solar neutrino problem can be checked elsewhere. The

answer seems to be negative, since the solar column- and mass-densities are

hard to reproduce in the lab. But there is a yet unexplored range of neutrino

mass differences and vacuum mixing angles for which atmospheric neutrinos could

resonantly mix as they cross the Earth. The signal would be a zenith-angle

dependence of the ratio of electron to muon events. Representative results of31)E. Carlson are shown in Fig. 10, where "up" and "down" events are integrated

over incident neutrino directions within cones of 70° half aperture about the

vertical. Unfortunately the effect is not very big, and it only occurs in a

small island of parameter space.

The flux of solar neutrinos from B decay, as monitored for the past few

lustrums in the Homestake mine experiment, shows evidence for a correlation

with the Sun spot cycle of ~11 years period. There is also a hint of an extra

time dependence with a period of six months. It would net be easy to account

for this type of effect on grounds of neutrino oscillations. Sun spots are

correlated with the solar magnetic field, which is thought to run toroidally

through the convective layer, as in Fig. 11. This field would vanish and flip32)

direction at the equatorial plane. As early as 1971, Cisneros pointed out

that if neutrinos had a magnetic moment, the solar magnetic field could

flip-flop them into a steri le right-handed helicity state, thereby affecting

their measured flux. Voloshin, Visotski and Okun have recently revamped

these ideas. Let IL, be the magnetic field orthogonal to the flight direction of

neutrinos and y. their magnetic moment. The energy-independent reduction factor

affecting the fertile left-handed flux is

= i -

The estimated values of H are within an order of magnitude of one kiloGauss,

and the thickness of the convective layer is ~2.1010 cm. This means that for

the effect to be significant ( f^ l ) , u must be in excess of (3-10) 10"11

e*nY2m c. Unfortunately, t h i s is much l a rge r than the standard model

expectations and practically impossible to "predict" theoretically. But if for

310

10

1

10"1 »-'

10"2

10"3

io-4

- E 10"5

10"6

•9

10"8

ACCELERATORREACTORS ^

FLUX^REDUCTION

FACTOR

U

10,-W

10

1

10r1

ACCELERATORS^-...- REACTORS ^

10"2

,-310

10-*

'510

10"6 -

,-7 _

10"4 10'3 10"2 10~1 1

10

10"1

10"9

10-10

REDUCTIONFACTOR

1Q"4 10"3 10"2 10"1 1

ic.

I 0.6"5

io-" to-" io-« ID-' iu-> to-1

Am' [eV3](O-'< IO-" IO-« 10-7 10-' 10-'

(b)

Fig .9 Contour plots of counting reduction factors in * CSL anddetectors of solar neutrinos , in obvious notations.

311

1.00

0.50

0)

0.10

0.05 I I I I I I I I I I I I I l

0.05 0.1 0.15Sin8(20)

0.2 0.25 0.3

Fig .10 Contour p l o t s 3 1 ' for a f ixed r a t i o R = 1.3, 1.4, 1.5 of e to nevents , induced by upward and downward moving atmospheric neutrinos within70° from the v e r t i c a l .

312

(a)

SUNSPOTS

(b)

Fig.11 "Magnetic moment" explanation of the time dependence of the solarneutrino

313

soae unforeseen reason, n happens to be in the appropriate range, the neutrino

flux follows the 11 year cycle of H_. But there is more to come, as foreshown

in Fig. 11. If U flips sign at the equator, it is small at small latitudes.

The spin axis of the Sun is tilted some 7* relative to the plane of our

planet's orbit. The Sun's central region where the higher energy neutrinos are

produced is relatively small, and can be "seen" around June and December

through the equatorial slit of small 1L. Around March and September neutrinos

aimed at the Earth travel through larger helicity-flipping magnetic fields.

This would explain the half-year cycle of v -induced events. What a long shot!Li

34)MEWS FROM THE GRAND UNIFIED FRONT

The recent improvements on the various measurements of the weak mixing

angle s i n 2 6 = 1-M£/M 2 b r i n g the e x p e r i m e n t a l e r r o r bars down to the level

where new important conclusions are within hand's reach. What follows i s a

b r i e f paraphrase of B i l l Marziano's t a lk on the subjec t . The present world

ave rage va lue of s i n 2 9 u i s dominated by the more local CERN average va lue . The

results, after radiative corrections, are:

0.251510.003510.0050 V J f - ^ v j l U.X CMS, Charm

0.2"5U 1 0.00 S 5 (M = 80.3tO*t 13 QeV)>JA2 preliminary

0 2.32510.00^0 ( M _ = 1 l . 5 l O . ^ t 1.5 QgY) UA2 preliminary

£ 0.004 (1986)

( 1 9 8 5 )

Believe it or not, this year's fattening of sin28 is not without consequence.

It is instructive to compare results with and without radiative

corrections. Choosing a couple of measurements that drives tha point home:

314

o.ozy t O.OAA [no R-C J

o.oo-t 16.0-f-i L *i*s^These results almost constitute a test of the standard model at the one-loop

level. Knowledge of the fine structure constants of the standard gauge groups

has also recently improved:

= 0.0I6T +QOOQI

-vO.O

-v 0.40

= 0.634010.0004

+0.014

If one follows the evolution of the 1985 couplings towards shorter distances a

la minimal SU(5), they all meet at M ~ \Qlk GeV. In the 1986 exercise the

values of the couplings do not find a meeting point, they rather criss-cross

about M . What used to be the argument for proton decay is now a hint of

supersymmetry, multiple Higgs bosons, aborigines of the desert, you name it;

the optimism of theorists is unassailable. The comparison of the original and

the supersyiD~.';atrical versions of SU(5) is particularly intriguing. In an often

used notation,

=t>.l\U0-006

= 21 10 MS

206 MeV

The minimal prediction disagrees with experiment unless there exists a handful

of light Higgs doublets. The SSSU(5) value is within a dumbfounding standard

deviation of the 2% precision 1986 experimental result. Given the recent

tendency of sin 9 to move about a little, it may be wise to wait for the dust

to settle and the precise v e experiments to

the trumpeters.

completed, before we commission

315

THE LATTICE

Discreet progress in discrete physics was reviewed by three speakers at

the Conference. Bender discussed the attempts to solve the operator equations

of quantum field theory on a. la t t ice, via analytical methods not involving

Monte Carlos. In the present early stage of developmpnt of this field it is

difficult for me to judge i ts distance to success. Wolfram discussed, among

other things, cellular automata and their applications to the analysis of

turbulence in the motion of two-dimensional fluids. He expressed hope that

developments in this direction would eventually suffice to tackle problems as

hard as non-perturbative QCD. Developments on the more conventional lattice

approach to QCD were discussed by Kuti, some of whose conclusions I proceed to35)

reproduce

It is now agreed that calculations of the (3-function of pure-SU(3) have

reached the "scaling" limit. This achievement is considerable, and deserves a

translation into English for the very hypothetical non-expert reader. The

[3-function is a measure of the response of the coupling constant to a change in

scale, or "wavelength of the probe". "Pure" SU(3) is a simplified chromo-

dynamics with gluons but no quarks. QCD is asymptotically free: in perturbation

theory and for sufficiently small coupling, the coupling itself tends to vanish

at short distances (large momenta). That the scaling limit has been reached

means that the non-perturbatively calculated ^-function joins smoothly with its

limiting behaviour, as calculated perturbatively for small coupling constants.

This is an indication that for hadrons (glueballs) of fixed size, lattices have

been used that are fine enough to describe their coloured field distributions

with accuracy. Indeed, if the scaling limit has been reached for a certain

observable, its behaviour for finer lattice spacings can be predicted without

further ado via perturbative renormalization group techniques: the lattice has

reached enough resolution to give recults that consistently extrapolate into

the continuum theory. Progress in the understanding of the pure glue (3-function

presumably implies that predictions for the spectrum of glueballs should soon

become more reliable. Numerically significant results in a more realistic

theory with quarks and gluons will still necessitate time, ingenuity and bigger

or more specific computers.

316

SOME OTHER PAST AND FUTURE EXPERIMENTS

A great wealth of data on charm, charmonia, botton and bottonia were

discussed by Brown, Morrison, Wilson and Kaplan. Characteristically following

the trend of our times, experiments in these areas are converging towards

standard model expectations, wherever they temporarily dared to disagree with+

them. The F meson, tastelessly renamed D~ by the particle data group, is now

firmly established at 1970.5±2.5 MeV mass, not a single MeV off the theoretical

expectations of more than a decade ago. "Hie F* is found, and the F*-F mass

difference is 140+8 MeV (TPC) or 144+11 M- ,' (Argus). The latio R of D+ to D°

lifetimes is no longer surprisingly large. The Fermilab microvertex experiment

measures R = 2.5±O.2±O.1, while the Mark III collaboration estimates

R = 2. 3+0. 5(-0. 4) + 0. 1, from the D+>0 + e+.. . branching ratios.

Kernan and Barger discussed the present situation of the CERN pp collider

experiments, particularly UA1. With the improvements of the analysis and

statistics, these data are no longer indicative of a wealth of new physics. The

"missing energy" mono- and multi-jets can be described within the standard

model , mainly as 11+ tv and Z •* vv with conventional intermediate vector boson

transverse momentum distributions. The agreement with theory can be converted

into limits for the production of various new particles. Two examples: the mass

of a new sequential charged heavy lepton must be above some 42 GeV, and the

number of extra neutrino generations that would show up in large missing energy-

events involving Z -»• vv decay is 6N < 7. The unexpectedly large charm

constituency of jets is also gone and the top quark search was not discussed.

There is an excess of equal sign dimuon events in the UA1 data that could be

interpreted as a bs *• bs mixing, fluctuating beyond 100%. Kernan quoted a ratio

of like-to-unlike sign dimuons of R = 0.51+0.08 (statistical), with "Drell-Yan"

and T backgrounds subtracted; and theoretical predictions for no mixing

R = 0.13 (Isajet), 0.2 to 0.28 (Eurojet), 0.23 to 0.26 (Barger, Phillips) and

0.25 (Halzen, Martin). It was my impression that the statistical significance

of the effect and the accuracy of the expectations were at the moment insuffi-

cient to claim a significant discovery, but I should address the interested

reader to Kernan's contribution to these proceedings for a more detailed

account of the facts.

This must have been a bad year for summer conferences: a score of talks,

that I have not summarized, dealt with the future rather than the past. The

most imminent amongst these announced future developments are improved searches

for rare K decays (K++it+ti+e-, iC+»ie, K++n++?) and new measurements of CP

317

violation parameters (e , e 1 and r\ ) . They were discussed by Zeller and

Donoghue, respectively. By comparing theory and experiment all the way from the

strongly interacting resonances to superstrings, Donoghufe convincingly

demonstrated that the interest on a subject is inversely proportional to the

amount of non-null data relevant to it. It follows that rare K. decays and CP

violation are extremely interesting.

SUPERSTRING: INSPIRATION, SIGNATURES AND FORGERIES

Having already tried twice before , I am not going to attempt to

introduce, however superficially, the very many mathematical concepts handled

by superstring practitioners. All I try to do in this chapter is to

over-summarize last year's progress, as discussed and perceived during this

Conference .

*)Every well-meaning spiel on strings begins with a propaganda paragraph,

and here it goes. In the good old days one needed one field per particle type.

The amplitude for a given process, such as e*e~ + ji+^~ in Fig. 12a, used to be

computed by summing over all "topologies" with the external legs fixed and the

branches of the internal "histories" generated by vertices such as A ey e. In

this field-theoretical realm, gravitation was untractable. The sta.idard gauge

group, particle masses and families were of mysterious pedigree, and their

description required a bewildering number of cryptic parameters. Nowadays we

are monotheistically told that all particles share a single superstring as

their common ancestor. The amplitudes for all processes can be extracted from

the sum of all topologies describing the propagation of strings, as in Fig.

12b. Gravitation is no longer a problem, but a necessity. The gauge group is

severely constrained, and the hope can be exclaimed that the theory is unique,

and that the identity and properties of all particles arc computable in terms

of the Planck, mass, -ft and c; tararaa, tararee!

Every balanced review of superstrings should also include a'grumbling

paragraph; this is it. Last year's superstring progress is not of the kind

which is easy to review. No correct postdiction has been derived. If in a

physicist's mood one defines progress as the obtainment of specific and

"Propaganda": n.l Committee of cardinals in charge of foreign missions(Oxford English dictionary).

318

(a)

Fig.12 Past and future topological views of 2 + 2 scattering amplitudes.

convincing testable signatures, there is no reason yet to be proud of super-

strings. Superstring theories are formulated in ten dimensions and not even the

principle governing the descent to four flat and six compact dimensions has

been clearly individuated. One hopes that this "4+6" collapsed state of affairs

is fairly stable, since 10 = 5+5 looks temptingly more symmetric, and a sudden

flattening of the fifth dimension would have somewhat catastrophic consequen-

ces. The originally claimed uniqueness of compact ifications in six-dimensional

Calabi-Yau manifolds is no longer tenable: many new classical "orbifold solu-

tions" have been found [an orbifold is a manifold with singular fixed

points, such as a cone and its vertex]. Anomaly- and tachyon-free examples of

superstrings have been discovered40)

that are not even supersymmetric. The

question of whether the original Calabi-Yau compactifications are or are not

acceptable is s t i l l the subject of a lively debate . The "phenomenological"

avenues for a breakdown of the heterotic gauge group down to the standard model

319

one appear at the moment to be many ; the role of grand unifier could be

played by Efe , S0(10) or SU(5). The ugly beasts of the standard model, such as

scalar particles with vacuum expectation values and the ensuing non-vanishing

cosmological constant, have not been exorcized. A] 1 known explicit compactifi-

cation schemes predict that the proton decays in a matter of seconds and/or

that there exist cosmological ly unacceptable stable coloured scalars and/or

that neutrinos are very heavy and/or that there are observable flavour-changing

neutral currents. At the moment, and in a very strict sense, these are the only

true superstring signatures, the rest are forgeries. But beauty lies in the

hands of the string holder, and none of the above suffices to justify despair.

There have been interesting "superstring inspired" developments concerning

the ways that the well perused N = 1 supergravity models could fit into the low43)

energy limit if superstrings . On their closest point of approach to phenome-

nology, most ?f these developments can be regarded as classifications of

possible extensions of the low energy gauge group. An interesting counter—44.)

example is the thorough study by an Oxonian group ' of a particular compacti-

fication leading to a three-family world. Though the model may not be problem-

free, it shows that it is possible to obtain Yukawa couplings compatible with

the correct "texture" of the quark mass matrix and weak current mixing angles.

Superstrings are not understood to the point where they provide clear-cut

choices in the vast domain of parameters and possibilities characterizing

extensions of the standard model. The compactification barrier has not been

pierced, and phenomenological break-throughs are still lacking. Tax payers and

experimentalists should still be alloved to sport a healthy and total ignorance

of superstrings.

On the more formal level, we have witnessed during the past year several

developments of great aesthetic value and (at least to me) unfathomable physics

potential. One of them is Witten's very compact covariant formulation of a

Lagrangian of open bosonic superstrings, an attempt to deal with the non-

perturbative aspects of the theory, described in some detail by Pierre Bamond

at this Conference. Another ambitious programme, motivated by an increased

understanding of the pivotal role played by modular invariance in string46) 47)

theory , concerns the study of g = => Riemann surfaces (the genus, g, is

the number of handles of the surface spanned by the string in its motion). This

approach, which would treat space-time as a property of string solutions,

rather than an ugly input, is very reminiscent of the old bootstrap programme

of S-matrix theory [one sincerely hopes that the similarity does not extend to

320

the number of concrete r e s u l t s ] . In a sense, we continue to ignore

what superstrings r ea l ly are . They are not quite a theory, a model or a48)

scenario. A. Salam ca l l s them an a t t i t ude , and tha t , they definitely a re .

A PEEP INTO THE COSMOS

All of a sudden we are told r.hat the Universe is completely different from

what we thought, a fact dramatized by Mike Turner at this Conference. The point

i s that the f i r s t l a rge , unbiased, three-dimensional pictures of galact ic

d i s t r ibu t ions are beginning to emerge (see Fig. 13). These surveys reveal an

unexpected foamy s t ruc tu re , with galaxiss concentrated on the surface of large

bubbles some 50 megaparsecs across. (Cosmologists make fluid writing very

d i f f i c u l t by not knowing how large the Hubble constant i s . Double a l l distances

i f i t is 50 km/sec Mpc, and not 100.) Fig. 13a, the work of Lapparent, Geller49)and Huchra , p o r t r a y s the 1100 br ightes t galaxies in a s l i ce of the sky of

135°X6° solid angle coverage and 150 Mpc depth. The distances are painstakingly

measured as optical r ed - sh i f t s . Fig. 13b is the more recent 21-cm radio survey

of Hayness and G i o v a n e l l i of the 2700 b r i g h t e s t galaxies in a six times

b igger region of 5C°x90°*120 Mpc s i z e . I t shows evidence that the

Piscis-Perseus filament remains a filament when seen "sideways". The

i n t e r p r e t a t i o n of these figures is not t o t a l l y straightforward . They become

fain ter with distance for the obvious reason that they show galaxies above a

ce r ta in apparent br ightness threshold. The most prominent features of these

p ic tu res : the body of the crucifix in Fig. 13a, and the v e r t i c a l nai l in Fig.

13b, are in fact Martian canals. These "God-fingers" pointing at the observer

from a l l direct ions in the sky, simply ref lect the. v i r i a l velocity and

consequent red-shif t dispersion cha rac te r i s t i c of galaxies in rich c lu s t e r s .

The observational evidence for the cosmofoam is s t i l l being gathered, and so i s

the theory behind i t . One hopes elementary par t i c le cosmology will eventually

provide the i n i t i a l conditions out of which galaxies and c lus t e r s evolved, but

whether the bubbles are remnants of very early perturbations or formed in a

post -galac t ic era is not quite clear . A few years ago, Ostriker and Cowie, and

Ikeuchi speculated that very powerful f i r s t generation galaxies or even things

as small as supernovas could trigger the formation of voids. But. voids of the

observed size seem to necessi ta te enormous "ieed" explosions, delivering some

10r e rgs . Not prone to speculate, p a r t i c l e physicists have not yet developed

the phenomenology of the decays of s ingle par t ic les weighing ~10 Planck

masses. Maybe the bubbles are simply blown up by foss i l pockets of extra

uncompactified dimensions, belatedly curl ing up.

321

RIGHT ASCENSION (hours)

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2 1 0RIGHT ASCENSION (houis)

120

H

540 t

( b )

( c )

13 (a) Optical redshi f t survey of 1100 galaxies brighter thang gmagnitude 15.5. In the dimension orthogonal to the paper the slice is 6°wide, (b) Galaxies brighter than optical magnitude 15.7 in the Piscis-Perseus filament. (c) "Sideways" 21-cm redshift view of the samestructure " ^ .

322

We do not understand the masses of elementary part icles , nor the mass

density of the Universe. The natural average energy density, p, in a Universe

that - like ours - is much older than a Planck time (10~1'3 sec) is the

"closure" denBity, corresponding to an ever slowing expansion; in the

established notation QQ = p/p[c-_.are] = 1. In the inflationary and

neoinflationary models of the Univers" that solve many problems (flatness,

uniformity, monopoles) of the previous standard cosmology, QQ = 1, as well.

The riddle, as every non-<_reatonist school teacher knows, is that the matter

that can be accounted for in the form of stars and dust in galaxies only adds

up to Q - 0.01. The successful theoretical account of the abundances of

primordial elements limits the contribution of ordinary matter, luminous or

dark, to the range 0.014 to 0.15. Thus, more, than ~85% of the mass of the

Universe is thought to consist ~>i some mysterious and unusual form of matter.

The range of D's from 0.02 to -Q.Z is also accounted for by the non-luminous

halos of galaxies, which could deceivingly be made of Jupiters, black holes

and/or lukewarm stars , a l l of them utterly unt i t i l la t ing objects.

At our parking spot in the Milky Way, the average densities of ordinary

and "dark" matter are comparable, and a variety of experiments can be devised

to ascertain whether some unknown constituent "particles" of the halo of our

own galaxy are falling upon our heads. The distribution of velocities of these

particles in their galactically bound orbits can be fairly confidently

modelled. Avignone reviewed recent progress in the exclusion of certain

galactic dark mass candidates, gathered with a Ge detector originally conceived

to search for |3j3 decay. Halo particles with sufficiently low cross-sections to

cross the 4-km water-equivalent overburden could s t i l l interact with Ge nuclei

in the detector, kick them out of their place, and produce observable electron-52)

hole p a i r s . The present l imi ts from the non-observation of signals over

background are reproduced in Fig. 14. The continuous line labelled "spin-inde-

pendent" is for particles with interactions of the same form as those of Dirac

neutrinos. It shows the excluded region as a function of mass and coupling,

normalized to the conventional neutrino neutral current strength. Good old

Dirac neutrinos of 20 GeV to 10 TeV are excluded as sole constituents of the

dark mass of our galaxy. Also shown in Fig. 14 is the excluded region for

particles whose (spin-dependent) interactions would be rescaled upwards from

those of Majorana neutrinos. (Particles that at low energies couple to nuclear

spin can a1so be detected in this experiment, since natural Ge contains 7.8% of

the A = 73 isotope, whose spin is 9/2.) Sometime ago, Dimopoulos, Lynn and

Starkman made the very in teres t ing observation that the cross-section of

axions on atomic electrons would be enhanced, like the photoelectric cross-

323

EXCLUDED AS DOMINANT HALO COMPONENT

(5.D COUPLING)

en \

Fie.14 Limits Jzy onc o u p l i n g s andmasses of hypo-the t ica l sole cons-t i t u e n t s of ourgalaxy's dark halo.The lower (upper)curve is for Dirac-(Maj or ana-) l ikec o u p l i n g s to Genuclei .

— EXCLUDED AS DOMINANT HALO COMPONENT

COUPLING)

0 0 !:oooo

MAS? ICEV)

section, at incident energies comparable to atomic binding energies. Thanks to

54)this axioelectric enhancement, worthwhile bounds on the coupling of solar

axions to electrons can be obtained with the very same "gg-decay1' detector.

These bounds are at the moment comparable to those obtained by demanding the

"luminosity" of solar axions radiated by electrons not to be so large as to

• ake the age of the Sun shorter than that of the oldest meteorites. Tighter but

more speculative limits on the couplings of axions to electrons can be obtained

from the cooling or ignition characteristics of other stars (red giants ' ,

i 57) .. . , 58),X-ray pulsars , white dwarfs ).

CONCLUDING REMARKS

The past history of XXth century physics is one of antitheses leading to

synthesis. This is botanically symbolized in Fig. 15a, in a way that I learned

from Strominger. The inconsistency of electromagnetism and thermodynamics begat

quantum mechanics, and swiftly bore fruit in the form of explanations of the

photoelectric effect and the black-body spectrum. Similarly, relativity and

Newtonian gravity married into general relativity, and the advance of Mercury's

perihelion and the bending of light by the Sun were their early offspring. Some

324

(a)(b)

Fig.15 (a) Genealogical tree of XXth Century physics, (b) the Renaissancephysicist: branches and hidden roots.

other fruitful intercauses are also reflected in Fig. 15a. The most recently

announced match is that of quantum field theory with general relativity. The

progeny that this union is said to have borne are superstr ings, and the puta-

tive gory details of inflationary cosmology. But the conceivable experiments

relevant to these issues are not like the ones of olden days. The big bang is

presumably not reproducible and the accessible predictions of super6trings, if

any, may all refer to past experiments. That is why in the Figure these fresh

fruits are depicted as a species more citric than the earlier plums.

We are not at the moment faced with a great antithesis to be resolved.

There is, on the contrary, a considerable cross-talk between the different

branches of physics, a fact reflected in Fig. 15b. Nuclear- and astro-

physicists share thoughts on baryosynthesis, solid state and particle

325

p h y s i c i s t s exchange knowledge on spontaneous symmetry breakdown, et c o e t e r a , e t

c o e t e r a , e t i o e " r a . One would hope t h i s wide ranging un i ty t o r e s u l t in the

b i r t h of some new kind of r e n a i s s a n c e p h y s i c i s t . Alas , the p r e s e n t panorama i s

w i l d l y d i f f e r e n t , as one can see in the d ive rg ing r o o t s of F ig . 15b.

F a s h i o n a b l e p a r t i c l e t h e o r i s t s only t a l k to mathemat ic ians and fel low

d i v i n i t i e s . P a r t i c l e phenotnenologists a re hooked to compute r s . Acce le ra to r

people must deal with p o l i t i c i a n s , and many experintent a 1 p h y s i c i s t s have become

members of t ha t l a t t e r c l a s s .

ACKNOWLEDGEMENTS

I am i n d e b t e d t o L. A l v a r e z Gaumi5, S .L. Glashow, P.G. Hansen , L. I b a n e z ,

R. J o h n s o n , G. Kane, L. K r a u s s , J . P r e n t k i and J . Simpson fo r d i s c u s s i o n s .

326

REFERENCES

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3) T. Cowan e t a l . - Phys .Rev .Le t t . 56 (1986) 444.

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6) L.C.R. Wijewardhana and A. Chodos - P h y s . R e v . L e t t . 56 (1986) 302.

7) S. Weinberg - P h y s . R e v . L e t t . 40 (1978) 223;F. Wilczek - P h y s . R e v . L e t t . 40 (1978) 279.

8) A.B. Ba len tek in e t a l . - P h y s . R e v . L e t t . 55 (1985) 4 6 1 ;G. Mageras - M a x - P l a n c k - l n s t i t u t P r e p r i n t (October 1, 1985).

9) L.M. Krauss and F . Wilczek - Yale U n i v e r s i t y P r e p r i n t YTP 86-02 (1986) ;R.D. Pecce i , T.T. Wu and T. Yanagida - DESY P r e p r i n t 86-013 (1986) .

10) D. Kaplan - Talk a t t h i s Conference . See a l s o Krauss and Z e l l e r iiRef. 5 ) .

11) W.A. Bardeen, R.D. Peccei and T. Yanagida - DESY P r e p r i n t 86-054 (1986 ) .

12.) F.T. Avignone - Talk a t t h i s Conference .

13) F. Leccia e t a l . - Nuovo Cimento 78A (1983) 50.

14) M. F r i t s c h i e t a l . - P h y s . L e t t . 173 (1986) 485.

15) Resu l t s r e p o r t e d in the Proceedings oi the Vlth Moriond Workshop oMassive Neut r inos in P a r t i c l e Phys i c s and A s t r o p h y s i c s , Tignes (Januar1986) .

16) T . J . Bowles - CERN P a r t i c l e Physics Seminar, July 8 t h , 1985.

17) J . J . Simpson - P h y s . R e v . L e t t . 54 (1985) 1891.

18) T. A l t z i t z o g l o u e t a l . - P h y s . R e v . L e t t . 55 (1985) 799.

19) V.M. Datar e t a l . - Nature 318 (1985) 547.

20) A. Apalikov e t a l . - ITEP P rep r in t 114 (1985) .

21) T. Ohi e t a l . - P h y s . L e t t . 160B (1985) 322.

327

22) J . J . Simpson - in the Proceedings quoted in Ref. 5).

23) J . J . Simpson - d-unnent on "Experimental Search for a Heavy Neutrino in theBeta Spectrum of 3 5 S " , submitted to Phys. Rev. Letters Comments.

24) J . Lindhardt and P.G. Hansen - University of Aarhus Preprint (June 1986).

25) J. Markey and F. Boehm - Phys.Rev. C32 (1985) 2215.

26) M.J.G. Borge et a l . - Isolde-CERN Preprint (1986).

27) S.P. Mikheyev and A.Yu. Smirnov - Ins t .Nucl . Research, Moscow Preprint 1985and Proceedings quoted in Ref. 15). For a very clear exposit ion, that Ifollow, see: H.A. Bethe - Phys.Rev.Lett. 56 (1986) 1305.

28) S.P. Rosen and I . Gelb - Los Alamos Preprint LA-UR-86-804 (1986);V. Barger, R.J.N. Ph i l l ips and K. Wishnant - University of WisconsinPreprint MAD/PH/280 (1986);R.S. Raghavan, S. Pakvasa and B.A. Brown - University of Hawaii PreprintUH-511-590-86 (1986).

29) L. Wolfenstein - Phys.Rev. D20 (1979) 2634;V. Barger et a l . - Phys.Rev. D22 (1980) 2718;S. Pakvasa - Proceedings In ternat ional Duraand Symposium, Honolulu(Ed. V. Stenger), Vol. I I , P. 45 (1980).

30) Computations by M. Cr ib ier , W. Hampel, J. Rich and D. Vignaud of theGal lex Collaboration; reported in the Proceedings of Ref. 15).

31) E. Carlson - Harvard University Preprint HUTP 86/A034 (1986).

32) A. Cisneros - Astrophysics and Space 10 (1971) 87.

33) M.B. Voloshin and M.I. Visotski - ITEP-1 (1986);L.B. Okun - ITEF 86-14 (1986);L.B. Okun, M.B. Voloshin and M.I. Visotski - ITEF 86-20, 86-82 (1986).

34) Talk by W. Marziano at th i s Conference, and references the re in .

35) Talk by J. Kuti at t h i s Conference, and references the re in .

36) A. De Rujula, H. Georgi and S.L. Glashow - Phys.Rev. D21 (1975) 147. Theextraordinary precis ion of th is predict ion is in part due to pure chance.

37) A. De Rujula - in P r o c e e d i n g s of t he Vth T o p i c a l Workshop on ppCol l iders , St Vincent, Aosta (1985) (ed. M. Greco).

38) A. De Rujul.-1 - Talk at the High Energy Physics Conference of the EuropeanPhysical Society, Bari , I taly (July 1985), containing e a r l i e r referencesto superstr ings (eds . L. Ni t t i and G. Preparata, Laterza, Bar i ) ;A. De Rujula - "Superstrings Supersede Supersymmetry", Nature 320 (1986)678.

39) L. Dixon et a l . - Nucl.Phys. B261 (1985) 768.

40) L. Alvarez-Gaum^, P. Ginsparg G. Moore and C. Vafa - Harvard UniversityP r e p r i n t HUTP86/A013 (1986);L. Dixon and J. Harvey - Princeton Preprint (1986).

328

41) L. Alvarez-Gaum^, S. Coleman and P. Ginsparg - Harvard University PreprintHUTP85/A037 (1985);M.T. Grisaru, A.E.M. van der Ven and D. Z-inou - Harvard UniversityPreprint HUTP86/A020, A026, A027 (1986);D.J. Gross and E. Witten - Princeton University Preprint (1986).

42) For a recen t r ev iew, see : J. E l l i s , L. Ibanez and H.P. Ni l l e s - CERNPreprints TH. 4439, 4459, 4444 (1986), respect ively .

44) B.R. Green et a l . - Oxford University Preprints (1986).

45) E. Witten - "Noncommutative Geometry and String Field Theory", PrincetonPreprint (1985).

46) J. Shapiro - Phys.Rev. D5 (1972) 1945;D.J. Gross et a l . - Phys. Rev. Let t . 54 (1985) 502; Nucl.Phys. B256 (1985)253; ibid B267 (1986) 75.

47) D. Friedan and S. Shenker - Enrico Fermi In s t i t u t e Preprint EFI 86-18B(1986).

48) A. Salam - IAEA ICTP Preprint 86-35 (January 1986).

49) V. de Lapparent, M.J. Geller and J .P . Huchra - Astrophys . J .Le t t . 302(1986) LI.

50) M.P. Haynes and R. Giovanelli - submitted to Astrophys.J. Le t t . (1986).

51) For a clear in t roduct ion, see: B. Schwartzschild - Physics Today (May1986), p. 17.

52) S.P. Ahlen et a l . - Boston universi ty Preprint (January 1986).

53) S. Dimopoulos, B.W. Lynn and G.D. Starkman - SLAC Preprint 3850 (1985).

54) F.T. Avignone et a l . - SLAC-PUB-3872 (1986).

55) D.S. Dicus, E.W. Kblb, V.L. Tepll tz and R.V. Wagoner - Phys.Rev. D18(1978) 1829 and Phys.Rev. D22 (1980) 829;M. Fukujita, S. Watamura and M. Yoshimura - Phys.Rev. D48 (1982) 1522;L.M. Krauss, J .E. foody and F. Wilczek - Phys.Lett. B144 (1984) 391;G.G. Raffelt, Phys.Rev. D33 (1986) 97.

56) D.S.P. Dearborn, D.N. Schramm anc G. Steigman - Bartol Research FoundationPreprint BA-85-54 (1985).

57) N. Iwamoto - Phys. Rev.Lett. 53 (1984) 1198;D.E. Morris - LBL Report 18690 me (1984).

58) G.G. Raffelt - Max-Planck Ins t i tu t Preprint MPI-PAE/PTh-6 7/85 (1985).

329

"Quarks, Strings, Dark Matter, and all the rest"

Seventh VanderbiJt High Energy Physics Conference

May 15 - 17, 1986

Thurs., May 15, 1986, 9 am, Lecture Hall, Owen Management School

Bob Panvini and Greetings and Introduction 9:00 am

Tom Weiler

Hans Paar, Chair

F. Gilman (SLAC) Physics at the Z° 9:10 am

A. Kernan (UC Riverside) Collider results from CERN 10:00 am

Coffee Break, 10:45 - 11:00 am

Gabor Domokos, Chair

L. Krauss (Yale) e+e~ peaks at GS1: axions and other goodies 11:00 am

M. Zeller (Yale) Raxe kaon decays 11:45 am

LUNCH at Branscomb dining hall, 12:30 am - 1:30 pm

C-Y Chien, Chair

C. Quigg (FNAL) TeV Physics: present motivation, prospects 1:35 pm

D. Stork (UCLA/CDG) SSC Developments 2:20 pm

J. Brown (Illinois) c-quark physics in e+e~ collisions 3:05 pm

Coffee Break, 3:50 - 4:05 pm

Steve Csorna., Chair

R. Wilson (Harvard) fr-quark physics in e+e~ collisions 4:05 pm

J. Donoghue (U Mass) Models of CP violation 4:50 pm

Banquet at Cob-*n Building, Cocktails 6:15 pm and Dinner 7:00 pm,

followed by entertainment: Becky Hobbs, country honky-tonk piano and vocals.

Fri. May 16, 1986, 8:45 am, Lecture Hall, Owen Management School

Stese Gottlieb, Chair

J. Kuti (UC San Diego) Present status of lattice QCD 8:45 am

C. Bender (Washington U.) Finite-element approximation in quantum field theory 9:30 am

330


Bill Bugg, Chair

A. Melissinos (Rochester) Experimental windows to post-collider energies

S. Majewski (U. Fla.) Progress in detector development

LUNCH at Branscomb dining hall, 12:00 am - 1:00 pm

Ralph Roskies, Choir

Dark matter in the universe

An ultra low background Ge detector applied

to dark matter and solar axion searches

GUTS, Evidence for and against

M. Turner (Chicago/FNAL)

F. Avignone (So. Carolina)

W. Marciano (BNL)

Coffee Break, 3:25 - 3:40 pm

Mac JViestayer, Chair

D. Kaplan (Fla. State)

R. Morrison (Santa Barbara)

High mass pairs and search

for narrow resonances

New charm results using high

precision vertex detectors

10:30 am

11:15 am

1:10 pm

1:55 pm

2:40 pm

3:40 pm

4:25 pm

Sat., May 17, 1986, 8:45 am, Lecture Hall, Owen Management School

Lou Clavelli, Chair

V. Barger (Wisconsin)

P. Ramond (U. of Florida)


D. Lichtenberg, Chair

S. Wolfram (Inst. Adv. Study)

Collider physics

String Theory

Cellular Automata and Field Theory

A. DeRujula (CERN/Boston U.) Summary

8:45 am

9:30 am

10:30 am

11:15 am

331

P A R T I C I P A N T S

Name

G. Aubrecht

F. Avignone

V. Barger

A. Barnes

V. Barnes

C. Bender

I. Bloch

J. Brown

W. Bugg

R. Capps

H.Y. Cheng

C.Y. Chien

L. Clavelli

H. Crater

S. Csorna

C. Darden

A. DeRujula

G. Domokos

S. Domokos

J. Donoghue

G. Feldman

T. Ferbel

F. Gilman

S. Gottlieb

B. Harms

Institution

Maryland

South Carolina

Wisconsin

Vanderbilt

Purdue

Washington Univ.

Vanderbilt Univ.

Illinois

Tennessee

Purdue

Indiana

Johns Hopkins

Alabama

Tennessee, Space Center

Vanderuilt University

South Carolina

Boston Univ.

Johns Hopkins

Johns Hopkins

Massachusetts

Johns Hopkins

Rochester

SLAC

Indiana

Alabama

332

Name

A. Hendry

W. Holladay

R. Holmes

D. Kaplan

A. Kernan

L. Krauss

J. Kuti

D. Lichtenberg

Z.H. Lin

S. Majewski

J. Mandula

W. Marciano

A. Melissinos

M. Mestayer

R. Morri3on

B. Niczyporuk

V. Oberacker

S. Oh

H. Paar

R. Panvini

D. Prindle

C. Quigg

P. Ramond

T. Reeves

R. Roskies

Institution

Indiana

Vanderbilt

Syracuse

Florida State

UC Riverside

Yale

UC San Diego

Indiana

Alabama

U. Florida

Department of Energy

Brookhaven

Rochester

Vanderbilt

UC Santa Barbara

SLAC

Vanderbilt

Duke

NIKHEF

Vanderbilt

Vanderbilt

Fermilab

U. Florida

Vanderbilt

Pittsburgh

333

Name Institution

D. Scott Ohio State, Mansfield

A. Shapiro Department of Energy

D, Stork SSC - Central Design Group and UCLA

M. Turner Chicago/FNAL

T. Weiler Vanderbilt

R. Wilson Harvard

S. Wolfram Inst. for Advanced Study

G. Word Vanderbilt

D. Wong UCC San Diego

M. Zeller

Documents

Vllth Vanderbilt Conference on Elementary Particle Physics