Review of QCD results from LEP

I{I ,SKVIKR

UCLEAR PHYSICS

Nuclear Physics B (Proc. Suppl.) 39B, C (1995) 184-197

P R O C E E D I N G S S U P P L E M E N T S

R e v i e w of Q C D resul ts f rom LEP

Howard Stone

Princeton University, N J, U.S.A.

A b s t r a c t : All four experiments at LEP have used their data to test the predictions of QCD. The strong coupling constant a , has been measured to higher than dO(c~) in the perturbation expansion. The value of as has been shown to be flavor independent. The QCD color factors have been measured and found to be consistent with SU(3) as the underlying symmetry of the strong interaction. The existence of the triple gluon vertex has been demonstrated and the spin of the gluon definitively determined. In the realm of soft, non-perturbative QCD, the string effect and other inter-jet phenomena have been investigated. Intra-jet effects have also been examined.

1. I n t r o d u c t i o n

LEP is an ideal place to s tudy QCD, as the initial s ta te is well defined and the cross section for e+e - ---+ hadrons is large on the Z pole. and, in contras t to the si tuat ion at lower energy exper iments , the f ragmenta t ion effects are relatively small.

q

* : : :

Fig. 1. The conceptual development ofa hadronic final state in e+e - anhilation.

Another advantage of studying QCD at LEP is that initial s ta te radiation ceases to be a complicat ion on the pole.

The exper imenta l challenge in s tudying QCD, is connecting the observed final s tate, (Fig- ure 2), to the underlying quarks and gluons with which the theory is concerned. The use of Monte Carlo simulations therefore plays a crucial role in these studies.

Yet another advantage of s tudying QCD at LEP is tha t the reconst ructed jet directions are very close (typically a few tens of milli- radians) to the directions of the quarks and gluons from which they formed.

J

1 Fig. 2. A hadronic event observed in the ALEPH detector

0920-5632/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved. SSDI 0920-5632(95)00069-0

11. Stone~Nuclear Physics B (Proc. SuppL) 39B, C (1995) 184-197 185

The development of a hadronic event in an e+e - annihilationis illustrated in Figure 1. The process can be considered in 5 phases. In phase one, the e+e - annihilate and produce a Z. The physics of this process is well described by standard electroweak physics [1]. In the second phase, the Z couples to a quark- antiquark pair. Again, this process is well understood in the framework of standard electroweak physics. The initial quarks are very high Q2 objects and they readily radiate many gluons, the first of which is indicated in phase 3 of Figure 1; it is at this point that QCD [2] comes into play.

At high Q2s pertubation theory can be applied to QCD, and phase 3 of Figure 1 is in principle well understood. In fact, the cross section for e+e - ~ 3-jets is only fully calculated to O(a: ) [3].

• ','° ,.o . ¢ ~

- o . ~ . o . <

Fig. 3. Left) An example of a leading log parton shower contMning 8 partons. Right) The three basic building blocks from which an arbitrarily complex leading log parton shower can be constructed.

In phase 4 of the development, the Q2s of the partons get lower and the number of partons involved gets larger. Perturbation theory cannot calculate the processes occuring in this phase. Leading log and next to leading log calculations do exist for this phase of the development, but they do not take into account all the diagrams. In particular, loop diagrams are excluded since the system in question must be constructed from the 3 basic building blocks shown in Figure 3.

Eventually the Q2s of the partons reduce to

values near the hadronic mass spectrum. At this point the quarks and gluons form colorless clusters which will eventually decay into the observed particles. This is represented in Figure 1 as phase 5.

There are many models for the conversion of the multi-parton state into hadrons. The most popular models incorporate some kind of string fragmentation scheme, in which the partons from phase 4 are mapped onto strings which are subsequently evolved according to the equations of motion of the string [4]. The equivalent to proper time for a string is the area swept out by the string in space-time, and the strings are broken with a probability proportional to this area. 1

When the string is broken one, new end of string is associated with a quark and the other with an antiquark. In the Lund model, the JETSET [5] Monte Carlo, hadrons are broken directly off the strings.

In the cluster models, for example the HER- WIG [6] Monte Carlo, the strings are allowed to evolve to the hadronic mass scale. Gluons are then split into quark-antiquark pairs and colorless clusters constructed which then decay isotropically in their rest frames.

Another model for the transition from phase 4 to phase 5 is the independent jet model [7]. Here, the high Q2 partons pair-up with quark- antiquark pairs from the vacuum to form hadrons. A frequently used model that incorpo- rates this scheme is CO JETS [8].

1.1. The L E P Detectors

All four LEP detectors [9-12] have the same general configuration. The particles pass first

1 This is analogous to the law of radioactive decay, in which the invariant area is replaced by the proper time, and the probability of a disintegration is proportional to the proper time elapsed.

186 H. Stone~Nuclear Physics B (Proc. Suppl.) 39tl, C (1995) 184-197

Table 1 Some characteristics of the LEP detectors.

A L E P H D E L P H I L3 O P A L

C e n t r a l Tracking: Coverage I cos 01 0.96 0.96 0.98 0.98 tr(p±) at 3 GeV 0.4% 0.5% 8% 2%

E l e c t r o m a g n e t i c Calorimetry: Coverage [ cos 01 0.98 0.98 0.98 0.98 Granularity in degrees 0.8 × 0.8 0.1 × 1 2 × 2 2 x 2 ~(E) at 3 GeV ~r ° 7 10% 20% 1% 4%

Hadronic Calorimetry: Coverage I cos 0 I Granularity in degrees (r(E) for a 30 GeV jet

0.99 0.98 0.996 0.98 3.7 × 3.7 3.8 × 3 2.5 x 2.5 2 x 2

17% 25%

Muon Systems: Coverage I cos 0 I or(p) for a 10 GeV #

0.98 0.96 0.8 0.98 1% 2% 3% 2%

through a ver tex detector then a central tracking system, an electromagnetic calorimeter, a hadronic calorimeter, and finally a muon system.

Some characteristics of the detectors are summarized in Table 1. The general s t ructure of the ALEP H detector is apparent in Figure 2.

2. P e r t u r b a t i v e Q C D R e s u l t s

2.1. Measurement of as

LEP is an ideal place for measuring as. In addition to the points mentioned in the intro- duction, hadronic events are especially easy to identify, the detectors all have close to 4~r acceptance for such events, the backgrounds (2-% T, etc.) are low and the energies and directions of the jets are well reconstructed.

There are several methods employed by the LEP experiments to measure as. Firstly, fits to the Z lineshape yield model- independent

values for as. Secondly, event shape variables are sensitive to the value of the coupling between the gluon and the quark that occurs in phase 3 of Figure 1. Values of as can also be ext rac ted from examining the hadronic branch- ing ratio in 1- decays.

The first two of these methods are presented here, the third being the subject of a separate contribution in these proceedings [13]. Val- ues of as have also been obtained by studying scaling violations at LEP [14].

2.1.1. as f r o m the Z L i n e s h a p e

Experimental ly the ratio

F(Z ~ hadrons)

F(Z -4 leptons)

The quant i ty Rz is given by the s tandard model, and can be writ ten as

Rz = R~(1 + 5QCD)

H. Stone~Nuclear Physics B (Proc. Suppl.) 39B, C (1995) 184-197 187

where ~QCD is the QCD correction to the lineshape [15] and depends on a~.

tfQCD = 1.05(-~) + 0.9(a" ) 2~_ -- 13( a~)3:r

The Electroweak Working Group at CERN has combined all the lineshape data from the LEP experiments and performed a combined fit [16] with a~ as one of the free parameters. The result [17] is:

0.120 =t= 0.006 =k 0.002 1

The value of a~ and the mass of the top quark are correlated variables in the lineshape fit.

g

0.18

0.14

O.IZ

125 lfi0 175 g00 225

MTop

Fig. 4. The 68% and 95% contours relating a, to the top quark mass as obtained by fitting to the L3 lineshape data

This correlation with the 68% and 95% confidence contours obtained by a fit [16] to the L3 data (assuming a Higgs mass of 300 GeV) is shown in Figure 4.

2.1.2. Event Shapes and Jet Rates

There are several event shape variables that can be constructed from the data that are sensitive to the value of a~, and it is clear that the various jet rates are dependent on (x~.

Each of the variables used have slightly different sensitivities to fragmentation and higher order perturbative effects. By studying all the variables the systematic error due to hadronization and higher order effects can be estimated. The variables studied are now defined.

T h r u s t The sum of the projected momenta of the particles in the event onto some vector ff is calculated and ~ is varied until T is maximum; the sum of the projected momenta onto this axis normalized to the sum of all the momenta is then the thrust.

T = m a x

E [f,[

H e a v y j e t mass The event is divided into two hemispheres by a plane perpendicular to the thrust axis. The invariant masses of all the particles in each hemisphere are then calculated and the larger of the two is the heavy jet mass, MH.

MI~ = max[M+( ~T ), M-(ffT)]

Jet broadening variables Again, the event is divided into two hemispheres by the plane normal to the thrust axis, but now the effective transverse momenta of the particles with respect to the thrust axis are summed in each hemisphere. After an ap- propriate normalization the total jet broadening, BT, and the wide jet broadening, Bw, are calculated as follows: Compute:

2 E,

and then define:

BT = B+ + B _ and Bw = max(B+,B_)

E n e r g y - e n e r g y cor re la t ion The product of the energies of all pairs of particles in the event weighted by cos 0 of the angle between the pair is calculated and his- togrammed as a function of O. After appropri-

188 11. Stone~Nuclear Physics B (Proc. SuppL) 39B, C (1995) 184-197

ate normahzation the bin entries, EEC(xBin), are given by

1 N El" Ej Ab~n N ~-" ~ ~b,n(Xb,,~--Xij).

• events i , j S

J e t m u l t i p l i c i t y As previously stated, the central problem in studying QCD from the experimental point of view is the association of the observed jets with the partons from which they developed. Several jet-finding algorithims have been developed that a t tempt to reconstruct jets such that the jet energy and direction most closely resembles that of the parent parton. The most popular of these algorithims, until recently, was the so-called JADE algorithim [26].

Jets are defined in terms of a parameter called ye~,t. For all pairs, i j , of particles in the event the scaled invariant mass squared (also known as the metric):

yij = 2E~Ej/E2,s " (1 - cos Oij) (1)

is calculated. The pair for which yij is mini- mum are combined to form a cluster, k, with

Pk = p¢ + pj .

These clusters are now subject to the same algorithim as the original particles and combined to form pseudoclusters. The algorithim is i terated until all the yij are larger than the parameter ye~,t. The remaining pseudoclusters are then defined as the jets.

Fig. 5. A four patton configuration with two soft gluons.

One problem with the JADE algorithim is that it occasionally reconstructs 3-jet events out of what should be considered 2-patton configurations. Consider the configuration in Figure 5. The JADE algorithim might corn-

bine the two soft gluons into a pseudocluster and thus classify this as a 3-jet event, whereas the gluons should be combined with their ad- jacent quarks and the event classified as a two jet event.

To overcome these problems a different metric has been proposed [28]

y~j = 2Min(E~, El)(1 - cos O~j)/s (2)

The jet finding algorithim remains the same. When the new metric is used, it is referred to as the Durham or k± method. In the small angle limit, the Durham method picks up the transverse momentum squared of the lower energy particle with respect to the direction of the higher energy particle. Other jet finding algorithims that avoid the deficiencies in the JADE method have also been used [29].

The jet multiplicity variables that are of rein- vance for a , determinations are: Average jet rates:

1 N

i=1

and the differential two jet rate, D2(ycut)

Fixed (9(a 2) calculations exist for many event shape variables. For any variable, X, the cumulative cross section, R ( X ) is given by

Y

in R(X) = f 1 do" ~r dX

0

= a ,A (X)

[B(X) + oG

where/3o is

33 - 2N I f lo-

127r

The A(X) and B ( X ) are obtained from inte- gration of the ERT matr ix elements•

14. Stone~Nuclear Physics B (Proc. Suppl.) 39B, C (1995) 186197

Table 2 The form of the perturbative expansion for jet cross-sections in QCD

LL NLL[ Subleading

O(a~) ~=L ~ ~=L

a~L %L - - 3 r) 1

189

Fixed order matrix element calculations give a reasonable description of the data in the three jet region, but give a poor description of the two-jet region. The conclusion is that higher-order terms need to be incorporated.

Since fixed order calculations beyond O(a~), don't seem feasible in the near future, these higher-order terms are partially incorporated by adding contributions from the leading logs of the perturbation expansion. Such calculations are called resummed O(a~) calculations.

For any variable X the full 2 =d order prediction for the cumulative distribution is

1 R(y, ~,) = ~r(X < y) .

O'To t

This can also be expressed as

In R ( y , . . ) : . . A ( y )

+ + .

In terms of the logarithims L = - in y we can also express In R as

In/~(y, a~) = L.fLL(a~L) + fNLL(asL)

O0

E n-~-I

The relationship between the two expressions can be seen in Table. 2.

Recent theoretical advances have allowed the fixed order calculations to be merged with the

leading log and the next to leading log terms and provide predictions for the shape variables above [20,21,23-25]. The issue is how to avoid double counting of terms.

The first two rows of Table 2 comprise the full O(a~) calculation, while the first column is the leading log result and the second column is the next to leading log result. Many schemes for adding the first two rows and the first two columns have been proposed, and the differences in the final result for the value of as, depending on which scheme is used, are included in the theoretical error that is quoted for the value of as quoted.

Experimentally, for each variable used, the data is corrected for detector resolution, acceptance and initial state radiation through the use of detector simulation (mostly based on GEANT [19]), and various event level generators (JETSET,HERWIG etc.). The theoretical predictions are then fitted to the corrected experimental data, with as as a free parameter, in regions where the fragmentation effects are small.

Systematic errors are estimated by varying the event selection criteria, performing independent analyses with tracking and calori- metric derived data and by varying the data correction methods within the allowable ran- ges of the parameters that enter the Monte Carlos. At LEP the systematic errors are of the order of a few per cent, and the statistical errors are < 0.001. The results for a, obtained by the four experiments [33,32,31,34] and the average is summarized in Figure 6.

190 H. Stone~Nuclear Physics B (Proc. Suppl.) 39B, C (1995) 184-197

T . ~ ALEPH i

t . - I I ,DELPHI I - 31. • L . ~

A

_ _ _ _ _ ~ _ _

V

_ _ _ _ _ _ _ _ _ _ _ ~ _ _ _

-~ Bw

EEC

D 2 ( y )

< niet ]>

ALEPH DELPHI L3 OPAL

- - ' k - - - -

,

~ ,-- 0.125+0.005 0.1234-0.006 0.1244-0.008 0.120±0.006 0.12314-0.006

0.14 015 Avergge , =

0.1 011 0,12 013

Fig. 6. Summary of the a, values obtained by each experiment using resummed (9 (a,2) calculations for the event shape variables indicated.

The overall average from all four experiments obtained with the variables shown in Figure 6 is:

0 .123 ± 0 .006

As can be seen from Figure 6 the wide jet broadening shape variable yields values for a~ that are systematically low. This is probably because this variable is especially sensitive to higher order terms.

The values for a , obtained with fixed O(a~) calculati'ons are sensitive to the multi-jet (e.g. low thrust) s t ruc ture of the events and the fits are performed in these regions of the various shape variables. Using these calculations, the average LEP value for a~ is:

0 .119 ± 0 .006 ]

Pure next to leading logarithim calculations can also be used to extract values for a , . In this case the fit is performed in the two jet (e.g. high thrus t ) region of the shape variables. The LEP average for a~ obtained using these calculations is:

0.117 i 0.008 ] 2.2. The Energy Dependence of a,

c 0.18 o u

,.: 0 . 17 3D 0 ..C

0.16 Q.

o.~5 G] L ~, 0.14

E 2 0.13

0 .12 LO

0.11

0.1

' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I '

• TPC/27 & TOPAZ

~: ' t : o ALEPH

error ~ y -- statistTcal ~ ......... experimental sys. ..... hodronlzotlon

matching and scale e r r o r s n o t i n c l u d e d

i i I , , , I , , , I , , , [ , , q I i

20 40 60 8 0 100

E,~ (GeV)

Fig. 7. Values of a, obtained at different cen- ter-of-mass energies with similar analysis methods. The total error bars are the quadratic sum of statistical, systematic and hadronization errors.

Recently the T P C / T w o - G a m m a , TOPAZ and A LEP H collaborations have measured as using, as far as possible, identical analysis methods [46]. The T P C / T G data was collected at Ecru= 29 GeV with the P E P ring at SLAC and the TOPAZ data was collected at KEK with Ecru= 58 GeV. The A LEP H data was collected on the Z pole.

These three analyses used a shape variable called y3, which is obtained by following the jet-counting me thod described above (Section 2.1.2), but stopping the combination of pseudoclusters when there are only three "jets" remaining. The smallest value of yij in this 3-jet configuration is defined to be y3-

The as measurements were made using the resummed O(a~) calculation, and the same matching scheme was used in ,-ach analysis. Each experiment used various models to correct for hadronizat ion effects and the varia-

I-L Stone~Nuclear Physics B (Proc. Suppl.) 39B, C (1995) 186197 191

tion in the as values obtained with each model is included in the systematic errors quoted. All the measurements were made with charged particles tracked in t ime projection chambers. For the final analysis each experiment used the J E T S E T Monte Carlo to correct for fragmenta t ion and they all used the same model parameters .

The results of these analyses are shown in Figure 7. The best fit to the QCD prediction for the "running" of as is also shown, and is clearly compatible with the data. The data shown indicate tha t a constant value for as is ruled-out and , indeed, as "runs".

2.3. Flavor Independence of the Strong Interaction

Table 3 Results from LEP on the ratio of the strong coupling to b quarks to that of the coupling to the lighter quarks.

b Collaboration

DELPHI 1.000 4- 0.05

L3 1.000 4- 0.08

OPAL 0.996 + 0.03

All four LEP detectors are capable of selecting data samples enriched in b quarks, either by requiring events with high pt leptons, or by selecting events tha t have a displaced vertex. If the puri ty of the selected data sample is known, and it can be obtained from Monte Carlo methods, a value of as for the b quark to gluon coupling can be extracted. The values obtained for the ratio of the couphng to b quarks to that of the lighter quarks [36,38,37] are given in Table 3. A L E P H will release a number at the upcoming Glasgow conference. In addition, OPAL [35] have independent ly determined the coupling ratios given in Ta-

Table 4 OPAL results indicating that the strong interaction is flavor independent

b I t ,d ,s lc c%/c~, 1.017 ± 0.036

c I~ l tTd j spc 5 , / , 0.918 ± 0.115

ct:/a~ '~ .... 1.158 4- 0.164

a,=d'/c~, ~'d .... 1.038 4- 0.221

ble 4, by analyzing the jet rates and event compositions. They obtained an enriched b quark data sample by requiring high pt leptons, and an enriched c quark sample by tagging D *± mesons. By tagging K°s they ob- tain a sample enriched in s quarks, and furthermore they find that high x stable charged particles tend to originate in events where the initial quark-antiquark pair produced were u, d, or s quarks.

2.4. Spin of the Oluon

;> ¢ )

5000

2500

o;

• data - - vector .... scalar

. .~ ......................... !

i w

0'2 0 ' 4 ' ' 0~6 ~ : ' X 3

Fig. 8. The scaled energy distribution of the least energetic jet as determined by the L3 collaboration in 3-jet events with the predictions for vector (QCD) and scalar gluons

In its most general form the differential 3-jet

192 IL Stone~Nuclear Physics B (Proc. Suppl.) 39B, C (1995) 184-197

Jet l

Fig. 9. The scaled energy distribution of the least energetic jet as determined by the L3 collaboration in 3-jet events with the predictions for vector (QCD) and scalar gluons

cross-section can be writ ten as

do 4s~ns do.i dz~dx2dcosOdx = ~ fi (cosO,X) dxldx2

i=1 ,4

where xl and x2 are the energies of the quark and ant iquark respectively normahzed to the beam energy, so that xl+x2+x3 = 2, and the jets are energy ordered so that xl > x2 > x3. The angles are defined in Figure 9. The sum over spins apphes to the different spin states of the Z, or 7, and interference terms between them. The do';/dxldz2 term however, depends on the spin of the gluon.

When the angles are integrated out for the QCD case where the gluon spin is 1 and for the case of scalar gluons one finds:

dctQCD x2 _~ 2 _ _ ~ q x~ (3) d.ld - ( 1 - -

do.Scalar 2 - - ~ ( 4 )

- ( 1 - -

In the case that xg --~ 0, both xq and x~ --~ 1 and the cross-section for vector gluons be- comes large, while for scalar gluons it remains finite. The distribution of the je t energies is thus sensitive to the spin of the gluon. This is shown in Figure 8 for the energy of the least energetic je t reconstructed in the L3 detector.

2.5. Gluon Self Coupling

The underlying symmet ry of QCD is com- pletely defined by the generators of the group corresponding to the symmetry. The group generators, T, are related to the s t ructure functions of the group by:

[T i, T j] = i ~ flJkTk k

The Feynman diagrams that enter into the calculation of the 4-jet cross-section are shown in Figure 10. Squaring the ver tex terms from these diagrams and summing over the final states introduces color factors CF, CA and TF which are related to the underlying group by:

E k k

k,n

j,k

a,b

The differential cross-section for the q~gg final state, which is the one that explictly in- volves the triple gluon vertex can be writ ten a s

l do.q~gg(y~j ) = (a, Cf )~ [A(y~j) + O" o 7V

CA C ]

and the corresponding differential cross-section for the q~q~ final s tate is

(NFTF l do'@@(yij) = ] D(ylj) +

H. Stone~Nuclear Physics B (Proc. Suppl.) 39B, C (1995) 184-197 1 9 3

G % t - -

! . . . . i . . . . n ' ' '

O Abelian gluon model, U(1)$

* O P A L

- - 687, C.L.

; . . . . . . . 9 5 % C.L. ;] so(z)

..... SO(N)

~z

uo) ~ so(3).~s I QCD = SU(3)

'. =x,~ "~,: f - - [ . . . . . ? . . . ~

'. p ~ ~, " 3 . * ~ . " ~ ( ' :

.~ ...................... ~c:!~~Z~...::'_._.

1 . . . . I . . . . I . . . . i

0 1 2 5 CJC~

ferred to as intra-jet effects.

3.1. The string effect

, , \ \ I

Fig. 12. The particle flow associated with the breaking of a string with a kink, where the kink represents a gluon.

Fig. 11. Color factor ratios obtained by the OPAL experiment. Models based on groups shown with circles or squares are already excluded as they cannot accommodate 3 colors.

confidence level. This is very strong experimental evidence that QCD does have SU(3) as its basic symmetry.

Within the string models, gluons are t rea ted as "kinks" in the strings. The configuration of a string corresponding to a q@ event is illustrated in Figure 12. Based on this model it is expected that there will be more final s tate hadrons in the regions between the quarks and the gluon than in the region between the quarks themselves; this is known as the string effect.

3. N o n - p e r t u r b a t i v e Q C D R e s u l t s

When dealing with the individual jets of an event it is possible (to some extent) to utilize per turbat ive QCD calculations. The distinc- tion between hard and soft QCD is vague, and this is reflected in the hadronization uncertainties encountered when trying to relate the data to per turbat ive calculations.

The low Q2 regimes of hadronic events are not amenable to existing per turbat ive calculations, but some general features of this soft physics can be investigated experimentally. The soft physics can be put into two cate- gories, first the dynamics of the event evolution between the jets can be investigated. These effects are known as inter-jet effects. Secondly, the s t ructure of the jets themselves may be investigated. The non-perturbat ive dynamics taking place within the jets is re-

10 ~

10 .z

-3 10

10

_ qg ÷ DELPHI i

S- L /

100 150 200 250 300 350

= yyCner-" f low v (degrees)

Fig. 13. The energy flow, as a function of angle from the most energetic jet in the 3 jet plane.

At LEP it is possible (due to the high statis- tics available) to find events with a hard photon well isolated from two jets, that is, a "3 jet event" where one of the jets is a photon. By comparing events with two jets and an isolated photon to t rue 3 je t events of similar topology, the string effect can be investigated.

194 ILL S t o n e ~ N u c l e a r P h y s i c s B ( P r o c . S u p p l . ) 3 9 B , C ( 1 9 9 5 ) 1 8 ~ 1 9 7

The results of one such study, performed by the DELPHI group [47], are shown in Fig- ure 13. In the QCD 3 jet events, the gluon jet was anti-tagged by requiring that the other two jets contained a displaced vertex (this technique also makes possible studies of differences in quark and gluon fragmentation).

Events are selected such that the angle 0, defined in the 3 jet plane, between the gluon and the most energetic of the two quark jets is 150 ° + 10% The angle between the quark and gluon jets is then approximately the same as the angle between the quark jets. When the events containing two jets and a 3' are subject to the same selection criteria, except that the 3' is treated in the same way as the gluon, 47 events are selected out of an initial q~3' sample of 500 events.

In the 3 jet plane the energy flow as a function of 0 measured from the most energetic jet towards the lower energy jet is plotted as a function of 0. This is what is shown in Fig- ure 13. In the regions close to the jet cores the energy flow is appreciabaly less in the qq7 sample than in the q~g sample. Furthermore, from the q~g sample alone it can be seen that the energy flow is higher between the gluon and quark jets than between the two quark jets. The data supports the string models for hadronic event evolution.

3.1.1. Subjet Structure

In a recent study [48], the ALEPH collaboration analyzed approximately one million hadronic events. Three jet events are initially selected by using the algorithim described in section 2.1.2 with your=0.1, then by applying the double lifetime tag outlined in the preced- ing section, a sub-sample of 1750 3 jet events in which the gluon jet is identified 95% of the time is obtained.

The jet finding algorithim is then applied to the particles within the individual jets, using

2 . 5 .... ~ . . . . . . . . , . . . . . . . . , . . . . . . . . [ . . . . . . . . ,

~ - • A L E P H dota

< 2

I

1.5

1

- - - HEIRWIG ' '/':"'"

.......... ARIADNE ~ 0.5 /

. . . . . N L L j e t

. . . . . t o y m o d e l (C~ - 9 . 4 / . 3 ) @

0 ,,I . . . . . . . . I . . . . . . . . I . . . . . . . . I . . . . ,,,,I

16 5 I ~ 4 I ~ 3 I ~ 2 i ~ I

Yo Fig. 14. ALEPH results for the ratio of the subjet multiplicities in gluon and quark jets. The predictions of several models are also shown.

a yc,~t = y0 and the sub jet multiplicity for the quark and gluon jets is studied as a function of y0- The results are shown in Figure 14.

Within the framework of QCD, gluons carry a larger color charge than quarks. The mag- nitude of this difference is determined by the Casimir factors, or color factors, CA and CF, and the first order perturbative QCD prediction for the ratio is CA/CF = 9/4, see Section 2.5. Since the gluon carries a larger color charge than the quark, the probability of gluon radiation from gluons is larger. QCD, then, predicts that gluon jets have a higher particle multiphcity than corresponding quark jets.

This tendency is evident in the data shown in Figure 14. In the region near y0 = 0.002 the data agree relatively well with the QCD prediction. As y0 is reduced and the central core of the jet is probed, the ratio seen in the data tends to fall below the perturba- tire QCD value. Note, however, that there is in general good agreement between the data and the QCD inspired fragmentation models shown in the figure. The toy model shows the expected distribution for the case where

H. Stone~Nuclear Physics B (Proc.

the quarks and gluons carry the same color charge.

4. S u m m a r y and Conclusions

To summarize, LEP is an ideal place for studying QCD, and as more data is analyzed many of the results presented here will improve sub- stantially. There are many other QCD related results coming from the LEP data that have not been included in this review. In particular, studies of particle spectra, Bose-Einstein correlations, color coherence and intermittency have been omitted.

Much theoretical progress has been made in the treatment of higher order terms in calculations for jet cross sections, and as a result the theoretical uncertainties quoted for c~s measurements are small.

The strong coupling constant has been measured in a variety of ways and they all give consistent values. From a combined fit to event shape variables using resummed O(a~) calculations it is

0.123 + 0.006 }

The running of as has been clearly established

The flavor independence of the strong interaction has been experimentally established.

The vector nature of the gluon has been definitively established.

That the strong interaction is based on a non- abelian SU(3) group symmetry is verified, and many competing groups have been excluded.

The notion that hadronization occurs through some sort of color-string breaking mechanism has gained strong experimental support.

Suppl.) 39B. C (1995) 184-197 195

In the perturbative, or near to non-perturbative, regime QCD is in good agreement with the data. In the highly non-perturbative regime, QCD is still not well understood. Monte Carlo models, motivated by the ideas of QCD, do describe the non-perturbative regime reason- ably well.

5. A c k n o w l e d g e m e n t s

I would like to thank all my collegues on LEP experiments for making their data available to me before publication. In particular I thank Glen Cowan and Miriam Watson for explain- ing certain results to me, and Andreas Gougas for help with the presentation at Montpel- lier. I especially thank Sunanda Banerjee for many informative conversations and for help directly, and indirectly, in the preparation of this document.

None of the results presented here would be possible were it not for the efforts of the CERN- SL division in keeping the LEP collider oper- ating.

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Documents

Review of QCD results from LEP