MARIA SPIROPULU MARCH 30 2000

Vanderbilt UniversityPhysics & Astronomy

Colloquium

Experimental Clues From

Higher Dimensions

Outline Extra Old

Variations on a theme::

Embedding the 3+1 spacetime to a higher dimensional structure

Table-top experiments:

Status

Collider experiments:

Results and prospects

the 5th dimension

is 75 Years Old

Kaluza and Klein started from 5-dimEinstein gravity and derived 4-dim gravity plus electromagnetism

RgxdM 53*

The 5th dimension is compactified around a circle of radius R

RMM P3

*2

]4

1[ 24

FFRgMxd P

Compactification around a circle of radius Re.g. For many extra dimensions

BUT in the KK case the compactification radius is too very small.

GeVR

RMg

P

1815 1010~/1

1~1~

String theory and

Extra dimensionsString Theory, or M-theory implies

the existence of 7 extra spatial dimensions which must be compact

since we do not see them.

Many possible physical scales of string theory :

Ms ~1016 GeV ; 1/R ~ 1016 GeV1

Ms ~1011 GeV ; 1/R ~ 109 GeV1

Ms ~ 104 GeV ; 1/R ~ 103 GeV1

Ms < 103 GeV ; 1/R ~ meV1

Kaluza-Klein modes

If a spatial dimension is periodic thenthe momentum in that dimensionis quantized:

R

np

From our dimensions of view the KK modes get mass:

2

220

2

R

nmm

pR

1

R

2

R

3

R

4

0

R

KK momentumtower of states

Gauss’s Law

Rr r

1

1~)(

Rr 1

~)(

212

)4(

121

2)4(

R

mm

MrV

r

mm

MrV

Pl

Pl

If the δ extra dimensions are compactifid down to sizes R, then Gauss’s Law

2)4(

2 ~ PlPlanck MRM

The Planck Scale from our dimension

of view, 1019GeV

4+ Planck ScaleMsMDM*

…any scale that in the

higher dimensional theoryis taken O(TeV)

The size of the extra dimension

fm 10~ 7,6

nm1~ 3

mm1~ 2

Km10~ 1 9

R

R

R

R

No way

Explore in sub-mm gravitational experiments/collider...

M-theory limits

Set the higher dimesional Planck scale to mEWK, the Planck scale to 1019GeVthen

cm102~ 17

31

R

The extra world picture

The SM is confined on a 4d wall

Gravity exists in a 4+d “bulk”

Gravity feels week on the wallbecause of the enormity ofthe bulk volume

Each KK-graviton state couplesto the wall with Planck supressedstrength

The number of KK-states ~(ER)

The sum over all KK-states is not MPl supressed but MPl(4+)

supressed i.e. MEWK supressedso we have sizable cross sections

Variations on a theme

many large toroidalextra dimensions

(Arkani Hamed-Dimopoulos-Dvali)

one infinite extra dimension(Randall-Sundrum)

one infinite extra dimension for us, and the Planck brane for gravity

(Randall-Lykken)

longitudinal extra dimensionsin the TeV range

(Antoniadis-Benakli-Quiros)

and more...

Variations on a theme

Weak-103 Planck

What (kind of like a U duality) is going on???

Energy Desert

Space Oasis

1019

Experimental (Low Scale) Quantum

Gravity

KK excitations of

gravitons in the bulk

neutrinos in the bulk

gauge bosons in the bulk

Deviations from Newton’s law at the mm range

Astrophysics-cosmology constraints

Torsion Balance :Could Archimedes’have measured G N

19 Centuries before Newton’s

Principia

Cavendish Type Setups

Table -Tops

12

12

2121 -exp 1

)()()( r

r

rrGdrdrrV N

Add a Yukawa term to the Gravitational Potential

][mR

][TeVLs

Table Topshep-ph/9805217 Long,Chan,Price

1KHz

100u

Table Tops

Goal: Measure gravity to 1%

at distances of 100

MITevatron

D0

CDF

Collider searches for

Extra Dimensions

Protons run the 4 mile ring about 50000/sec

CERN,European Center for Nuclear Research

Particle Detecting

trackerMuon chambers

calorimeters

The Particles and Their Interactions

up down

charm strange

top bottom

electron electron neutrino

muon muon neutrino

tau tau neutrino

forces & carriers

quarks & leptons

StrongElectromagnetic

WeakGravity

Gluonphoton

W,Zgraviton

Relative Strength

Today

110-3

10-14

10-42

Grand Unification Fo

rce S

tren

gth

Higher Energy

electromagnetic

strong

weak

gravity

new

The scale of experimental

particle physics

e nmu

pis

c taub

W/Z

t

1

10

100

1000

Num

ber

of

rese

arc

hers

For discovery of

Direct Graviton Emission at electron positron collisions

As no statistically significant signal is observed, 95% Confidence Limits are placed

on the fundamental mass scale MD, as a function of the number of extra dimensions

4422222

12/

22/2

coscos)1(3)1()2()cos1(

)1(2)cos,(

2 )cos,(

)2/(32cos

xxxxxxx

xxf

sE

xxfM

s

sGee

dxd

d

D

e+e-G

cm106.9R TeV49.0 6

cm106.4R TeV55.0 5

cm101.9R TeV65.0 4

cm105.4R TeV78.0 3

cm104.9R TeV99.0 2

12-

11-

9-

7-

-2

D

D

D

D

D

M

M

M

M

M

e+e-G

20.640.560.290.60

30.080.560.300.38

40.010.550.300.29

nZG(pb)

ZG

95%(pb)Ms(TeV)

MET+jets

e+e- >

8

2

42

2

22

1

cos11

4

)cos1(

)cos1(

2)(

cos

T

T

O

s

see

d

d

Standard Model

Interference Term

Gravity

Two-photon measurements at LEP-

II

44

2 sT M

161-189GeV

T(+)>987 GeV (189:>890 GeV)

T(-)>866 GeV (189:>770 GeV)

192-202 GeV

Two-photon measurements at

LEP-II

MS>615 GeV/c2(=+1)

Ms>703 GeV/c2(=-1)

Two-photon measurements at LEP-II

e+e- > ff

),(),(),(ff

2

44ts

Mts

MtsSMee

d

dGRV

sINTF

s

For ff other than ee the integrated interference term for scattering angles from 0 to is ZERO.The interference between graviton and t-channel SM Bhabha is giving sizable contributions good sensitivity

Terms ~cos3, ~cos4 make differential cross sections a unique signature

Giudice,Rattazi,Wells/Hewett/Rizzo

Bhabha scattering results

MS>810 GeV (=+1)

Ms>720 GeV (= -1)

Bhabha scattering results

MS>920 GeV (=+1)

Ms>710 GeV (=-1)ALEPH,OPAL,DELPHI,L3 combined:

(Bourilkov hep-ph/9907380)

MS>1.26 TeV (=+1)

Ms>960 TeV (=-1)

e+e- > ff

MS>580 GeV (=+1)

Ms>510 GeV (=-1)

MS>450 GeV (=+1)

Ms>550 GeV (=-1)

e+e- > WW, ZZ

T.Han, J.D.Lykken, R.-J.Zhang hep-ph 9811350K.Agashe, N.G.Deshpande hep-ph 9902263

k2

k3

k1 MMMM

cos14

4VVGravity ss

M s

W+W-

MS>650 GeV (=+1)

Ms>520 GeV (=-1)

ZZ

MS>470 GeV (=+1)

Ms>460 GeV (=-1)

LEP summary

61.0/75.060./75.50./63..60/.63O

74.0/86.046./47.52./65.67./63.49./49.46./51.49./55.72./81.L

62./59.50./55.51./58.D

75.0/00.169./79.59./54.51./53.56./61..92/.71A

CombZZWWqqee

Virtual Graviton ExchangeLimits on Ultraviolet Cutoff Scale

(TeV)

Real Graviton ProductionLimits On Extra Dimensions

G,ZG~1 TeV to ~500 GeV for n=2 to n=6

Tevatron (virtual)

Landsberg,Cheung hep-ph/9909218

Drell-Yan and diphoton productionwith virtual graviton exchange

The Three Components

Tevatron (direct)

Only qqbar->g G (PYTHIA 6.115 + graviton process), =2, M=1TeV, s=1.8TeV

Lykken/Matchev/Burkett/Spiropulu

qq->Gg

Case =6

Only qqbar->g G (PYTHIA 6.115 + graviton process), =6, M=1TeV, s=1.8TeV

RUNII Display

Only qqbar->g G (PYTHIA 6.115 + graviton process), =6, M=1TeV, s=2TeV, GEANT CDF preliminaryRUNII simulation and display

Outlook

Sub-mm gravity experiments are expected to announce results very

soon (maybe APR00)

More Collider results and projections on the way

LHC and (?) LC will probe effective higher dimensional Planck scales up

to many (tens of) TeV

Very important cosmological constraints and implications

More extra dimensions model building (infinite extra dimensions, trap gravity on the Planck brane,

string phenomenology &tc)

Extra Dimensions Stats

1

10

100

1000

SPIRES, "extra dimensions"

91-949596979899

Neutrinos in the bulk

Dimopulos, Hamed,Dvali Russel, hep-ph/9811448Martin,Wells hep-ph/9903259If the R lives in the extra

dimensions as a KK tower of statesand the Dirac neutrino masses arise from yHRL so that m=yu where u is the Higgs vev 175 GeV thenthe decay of the Higgs to LR

(i) isproportional to the small y

2, but also to the sum of the KK states(all with m<mH) (mHR).

R)my16m

Η H2n

HR (~)

i

Z*H(invisible)

2

2~

)

D

Pl

D

H2R

MM

Mm

3mm

)bbΗB

ΗB

i

For some reasonable values, mH=100GeV, d=3, m

2~10-6eV2 and MD=1 TeV the above ratio is > 100 …

l+

l- ) )((* invisHllZZpp inv

Signal

l+l-

Background: Z(ll)Z()

WW,top,mismeasurements..

PT(l)>12 GeV, ||<2 |mll-mZ|<7 GeVno jet with Et>10 GeV

Z*H(invisible)

TE

Z*H(invisible)

mH(GeV)

Strings again

A lot of work in string phenomenology domain with

large extra dimensions

The dominant new physics effects may come from stringy physics

Look for string resonances andother form factor correctionsto SM 2-body reactions

Impressive sensitivity of LHC,LC

Gauge Bosons in the Bulk

Antoniadis,Quiros,Benakli hep-ph/9905311Rizzo,Wells hep-ph9906234

One motivation is the weak scaleSUSY breaking.The compactification scale of the extra dimension(s)considered in these scenarios is of the order of the SUSY breakingscale taken to be of the order of theEWK scale.

quarks and leptons are confinedon a 4d boundary

gauge fields live in the 5d bulk

The gauge boson KK states have an additional 2 strengthin their interactions

implications

2

220

2

R

nmm

The vector boson KK modes have masses

couplings. mode zero their than larger are fermions to couplings their 2

From precision EWK measurementsR-1~3.5 TeV

Z(n),(n)

f

f

f

fAlso limitsfrom:

PEW:LEP,SLD,NuTeV..,had:direct KK gauge boson,e+e-:deviations in final state fermion observables

NLC

String ResonancesAccomando,Antoniadis,Benakli hep-ph/9912287Production of a gluon

excitationat the LHC(s=14Te, L=100fb-

1)

(also with dijet excessTeVII,20fb-1,

Rc=4 TeV)

l

W KK excitation

sat LHC

Stringy Model Building&Searches

http://itp.ucsb.edu/online/susy_c99/peskin/

1000 GeV LCprojectionsM>8 TeV

(Ms>2.7 TeVMH>5.4 TeV)

183 GeV ALEPHdata

M>1200 GeV(Ms>400 GeVMH>810 GeV)

MH=Hewett’s ultraviolet cutoff