Collider Signals From Extra Dimensions

Collider Signals From Extra Dimensions

Greg Landsberg

Berkeley 2000 A Workshop to Study the Physics

and Detectors of Future ee Colliders

March 29-31, 2000

NLC Meeting, 3/29-31/2000 Greg Landsberg, Collider Searches for Extra Dimensions

Outline

Basic PhenomenologyGraviton Production and Virtual Graviton ExchangeLEP2 SearchesRun I Tevatron SearchesRun II Tevatron and LHC Sensitivity StudiesProjections for NLCConclusions


Theory of Large Extra Dimensions

New idea, inspired by the string theory, with direct connection to the observables!Main goal: to bring the GUT scale to the EW scale in order to solve the infamous hierarchy problemReplace standard RGE equations by the new ones that take into account virtual gravitons from the extra dimensionsDimopoulos, Arkani-Hamed, Dvali, 1998 – found a serious loophole in the current Newton’s law tests: no one looked at gravity below 1mm scale!Therefore, large spatial extra dimensions compactified at sub-millimeter scale are, in principle, allowed!

3

2

1

MZ MGUT MPl

RGE evolution

MSM’GUT

What we think is the Planck scale: MPl = GN-1/2 is just an effect of the

“parallax” due to the modification of the Newton’s lawMGUT is also lower due to the “parallax” of the 3+1-dimensional RGE evolution

nnSPl RMM 22


Alternative EWSB Mechanism

Since large extra dimensions bring the GUT and gravity scales right at the EWSB scale, they solve the hierarchy problemThere are multiple mechanisms that allow gauge fields in the bulk to communicate symmetry breaking to our braneA new mechanism, “shining” is a powerful way of introducing a small parameter into the theory, and explain many yet unsolved phenomena, such as CP violation, etc.New framework, possibly explaining neutrino masses, EWSB mechanism, and other puzzling phenomenaA significant theoretical interest to the subject ensures rapid development of this fieldOver 150 theoretical papers on this subject over the past two years – truly a topic du jour

SM

bulk

gauge

fields

gravity

bulk

big bang

“CP-

bran

e”“shining”

SM


Compactified Extra Dimensions

Compactified dimensions offer a way to increase tremendously gravitational interaction due to a large number of available “winding” modesThis tower of excitations is known as Kaluza-Klein modes, and such gravitons propagating in the compactified extra dimensions are called Kaluza-Klein gravitons, GKK

For MS 1 TeV, n=1 is already excluded from Cavendish-type of experimentsFor n = 2 minimum allowed scale MS is > 30-100 TeV from SN1987A neutrino flux and distortion of CMB; for n > 3 cosmological limits are weakSince the mass per excitation mode is so small (e.g. 400 eV for n = 3, or 0.2 MeV for n = 4), a very large number of modes can be excited at high energies

CompactifieddimensionR

GKK

Flat dimension

2 1 0 2 ,, , k kR x x

nnSPln

S

Pln

n

nn

SPlN

RMMM

MVR

VMMG

222

2

22

11

4106

33

270

1108

2

1

12

12

2

nm

nnm

nmm

nm

M

M

MR

n

S

Pl

S

,

,

, .

,/

M(GKK) = Px2 = 2k/R


Examples of Compactified Spatial Dimensions

M.C.Escher, Mobius Strip II (1963) M.C.Escher, Relativity (1953)


Collider Signatures for Extra Dimensions

Kaluza-Klein gravitons couple to the momentum tensor, and therefore contribute to most of the SM processesFor Feynman rules for GKK see, e.g. [Han, Lykken, Zhang, PR D59 (1999) 105006]Since it is possible for a graviton to propagate into the bulk, energy and momentum are not conserved in the GKK emission from the point of view of our 3+1 space-timeSince the spin 2 graviton in generally has a bulk momentum component, its spin from the point of view of our brane can appear as 0, 1, or 2Depending on whether the GKK leaves our world or remains virtual, the collider signatures include single photons/Z/jets with missing ET or fermion/vector boson pair production

Real Graviton EmissionMonojets at hadron colliders

Single VB at hadron or e+e- colliders

Virtual Graviton Emission Fermion or VB pairs at hadron or e+e- colliders


LEP2 Searches for Direct Graviton Production - I

ee GPhoton + MET signature

“Recycling” of the GMSB analysesALEPH (2D-fit), DELPHI, L3 (x)

95 = 0.17 pb

442222

2

1

2

2

2

13121

12,

cos,2

,,32

2

2

zxzxxxxxzx

xzxf

zs

Exzxf

M

s

sdxdz

d

n

n n

Sn

Theory:[Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and corrected version: hep-ph/9811291]Experiment:ALEPH-CONF-2000-005DELPHI 2000 CONF 344L3: Phys. Lett. B470, 268 (1999)

MS = 1 TeV, n=2

MS = 1 TeV, n=2

ALEPH, 99 DELPHI, 00

Results:MS > 1.3-0.6 TeVfor n=2-6 (DELPHI)ALEPH, L3 – slightlyworse


LEP2 Searches for Direct Graviton Production - II

ee GZ(jj) + MET signature

“Recycling” of the invisible Higgs analyses

ALEPH: Z(jj)G, 184 GeV, total cross section method

L3: Z(jj)G, 189 GeV, increased sensitivity via analysis of the visible mass distribution

MS > 0.35-0.12 TeV

(ALEPH) for n = 2-6

MS > 0.60-0.21 TeV (L3)

for n = 2-6

xyyxAx

AAxydydxI

IM

M

nZ

GZ

x

n

n

S

Z

nn

41,16

12

23

1

4

1

ff

ff

21

0

1

0 22

2

2 22

22

Theory:[Balazs, Dicus, He, Repko, Yuan, Phys. Rev. Lett. 83, 2112 (1999) – width ratio][Cheung, Keung, Phys. Rev. D60, 112003 (1999) – mass distribution]

Experiment:ALEPH-CONF-99-027L3: Phys. Lett. B470, 281 (1999)

MS = 0.5 TeV, n=2

189 GeV


LEP2 Searches for Virtual Graviton Effects - ff

ee ffRecycle QED analysesLook at angular and energy dependencesBhabha scattering is the most sensitive channelL3: uses compositeness framework by Hewett with the GKK coupling given by /MS

4, with O(1) constant = 1 [L3, PL B464, 135 (1999)]A lot of confusion about the sign of the interference term; published L3 papers are internally inconsistentALEPH: uses GRW framework, but uses two signs of T. Apart from Bhabha, L3 and ALEPH limits are related by: MS(L3)+- = 0.89T(ALEPH)-+DELPHI, OPAL: use Hewett’s convention

fNzzM

sN

zaazvvMMs

MsszQQ

M

sN

dz

d

dz

d

CS

C

fefeZZZ

Zfe

S

C

SM

fermion of colors of number - ,43132

)31(2)(

)(2

4

428

23

232222

23

4

N.B. This is identical to Hewett’s

notation, but the sign of is flipped!

222244

4

32233

32232

2233

1

48

2

23

22

2

23

22

2

14

14812441,

12155,

918105,

30239,

,16

,,,,,

2

tstssttstsF

tsttsstsF

tsttsstsF

sttss

t

t

stsF

tsFsM

Mt

stFastFv

Ms

tsFatsFvtsF

sM

dz

eeeed

dz

eeeed

S

Z

ee

Z

ee

S

SM

N.B. This is identical to Rizzo’s notation; results of GRW differ slightly

L3: ee ffDrell-Yan production

L3: ee eeBhabha scattering

Theory:[Hewett, Phys. Rev. Lett. 82, 4765 (1999) - DY][Giudice, Rattazzi, Wells Nucl. Phys. B544, 3 (1999) and corrected version, hep-ph/9811291 – DY, Bhabha][Rizzo, Phys. Rev. D59, 115010 (1999) - Bhabha]

11

1

41

2

RizzoS

HewettS

GRWT

HewettS

MM

M


LEP2 Searches for Virtual Graviton Effects - ff

Had L3 really reversed the sign? – Doubtful!

ALEPH CONF 99-027

PL B470, 281 (1999)

L3 Note 2516 (2000)

DELPHI CONF 355 (2000)

DELPHI CONF 355 (2000)

OPAL CERN-EP/99-097

189 GeV

192-202 GeV

192-202 GeV

189 GeV202 GeV

189 GeV

ee

ee

ee

PL B470, 281 (1999)

MS>0.8-

1.0 TeV


LEP2 Searches for Virtual Graviton Effects - VV

ee ALEPH: GRW convention [ALEPH CONF 2000-005]

DELPHI: GRW convention w/ errors [DELPHI CONF 324 (1999)]

L3: AD convention [Phys. Lett. B464, 135 (1999)]

OPAL: based on old GRW w/ wrong direct term [Phys. Lett. B465, 303 (1999)]

Theory:[Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and corrected version, hep-ph/9811291][Agashe, Deshpande, Phys. Lett. B456, 60 (1999)]

xFxx

xFxx

xxxF

zF

M

szF

sdz

eed

S

12

2

1

2

24

2

1

4

1,

)1(

221

2

14

2

1

AD convention:

48

32

42

22

2

24

2

1

164

141

1

2

12

2

1

zs

zs

z

z

sd

d

zF

szF

sdz

eed

TT

T

GRW convention:

GRWT

HewettS

ADS MM

4 2

11

AD convention is equivalent to Hewett’s with a flipped sign of

1

4

182

42

22

;1

121

1

Hewett

SDELPHIS

SS

MMM

OzM

s

z

z

sd

d

1

4 2482

32

422

22

;164

11

1

Hewett

SMGzG

sz

G

s

z

z

sd

d

11

3

Hewett

SLS MM

14

2 Hewett

SGRWT M



ee Recycle anomalous Z couplings analysesLook at angular dependence of the diphoton production

MS>0.7-

0.8 TeV

N.B. DELPHI and OPAL results are likely to have problems

ALEPH CONF 2000-005189-202 GeV

PL B470, 281 (1999) DELPHI CONF 363 (2000)

OPAL PN 420 (1999)

202 GeV

200 GeV

189-200 GeV

189 GeV



ee WW/ZZRecycle WW cross section and anomalous ZZ couplings analysesL3 used angular distributions (WW) and mass variables (ZZ) to set limits

Theory:[Agashe, Deshpande, Phys. Lett. B456, 60 (1999)]

11 Hewett

SADS MM

AD convention is equivalent to Hewett’s with a flipped sign of

MS > 520-650 GeV (WW); MS > 460-470 GeV (ZZ)

PL B470, 281 (1999)

PL B470, 281 (1999)

PL B470, 281 (1999) 189 GeV 189 GeV

189 GeV

Also:ZZ qqqqZZ qqZZ llZZ llll


LEP2 Lower 95% CL MS(Hewett) Limits (TeV)

Experiment ee qq f f WW ZZ Combined

ALEPH (T)

0.80 1.03

0.63 0.68

0.57 0.59

0.66/0.61 0.55/0.55 (bb)

0.82 1.04

0.91 0.92

0.84/1.12 (<189) MS > 0.75/1.00

DELPHI 0.59 0.73

0.56 0.65

0.60 0.76

0.69 0.71

0.60/0.76 (ff) (<202) MS for is wrong?

L3 (???) 0.91 0.99

0.56 0.69

0.58 0.54

0.49 0.49

0.84 1.00

0.80 0.79

0.68 0.79

0.76 0.77

0.87/1.07 (<189) ??? 0.82/0.89 (VV)

OPAL 0.63 0.60

0.50 0.63

0.61 0.68

0.63 0.64

0.61/0.68 (ff) (<189) MS for is wrong?

ee G ee ZG

Experiment

n=2

n=3

n=4

n=5

n=6

n=2 n=3

n=4 n=5 n=6

ALEPH 1.10 0.86 0.70 0.60 0.52 0.35 0.22 0.17 0.14 0.12

DELPHI 1.25 0.97 0.79 0.68 0.59

L3 1.02 0.81 0.67 0.58 0.51 0.60 0.38 0.29 0.24 0.21

OPAL

Color coding

184 GeV

189 GeV

202 GeV=-1 =+1 GL

Virtual Graviton Exchange


Virtual graviton Drell-Yan and diphoton productionMass spectrum has been looked at [Gupta, Mondal, Raychaudhuri, hep-ph/9904234, Cheung, Phys. Rev. D61, 015005 (2000), Phys. Lett. B460, 383 (1999),…]Key improvement [Cheung, GL, hep-ph/9909218]: simultaneous analysis of the mass and angular distributions, as a spin 2 graviton would result in different angular distributions compared to the SM backgroundsThere are three terms: SM, interference, and graviton contribution

Tevatron Search for Virtual Graviton Effects

Note that the term in [ ] is a full square!

SM

interferencetermGKK terms

4SM

f

222

22

n,n

ns,Mf S

After [Han, Lykken, Zhang,Phys. Rev. D59, 105006 (1999)](explicit n-dependence of thevirtual graviton exchange)

DY:

Diphotons:

2,2 4

1

1

nMM

nSS HLZHewett


Two-Dimensional Analysis

Parameterize cross section as a bilinear form in scale Use Bayesian fit to the data (real one or MC one) to get the best estimate of For sensitivity studies, repeat the MC gedankenexperiment many times and use the median of the resulting to obtain the sensitivityNote the asymmetry of the interference term, 4, for ll productionSensitivity is 20-30% (in terms of Ldt) higher than for 1-dimensional analysis

llSM

4ll

8ll

SM4

8 [Cheung, GL – hep-ph/9909218]

284 llllll

SMll

284

SM


Search for Extra Dimensions in the di-EM channel at DØ

Basic idea: combine dielectron and diphoton channels to increase efficiency, and hence, sensitivity:

2 EM clusters w/ ET > 45 GeV, ||<1.1 or 1.5<||<2.5 80%Ldt = 127 pb1 – entire Run I statistics

Adding theoretical cross sections is OK, since at LO the relative contribution of each channel is known preciselyNLO corrections are modeled via a constant K-factor of 1.3 ± 0.1


DØ Results


DØ Limits on Large Extra Dimensions

Comparison w/ Hewett’s and GRW frameworks:

GRWHLZ

HLZHewett TSSS MMM

1;

2 444

FF

2,2 4

1

1

nMM

nSS HLZHewett

51

nSS MM HLZHewett

M() = 574 GeVcos* = 0.86

4

nST M HLZGRW

MS > 1.1 TeV

T > 1.2 TeV


Tevatron: Real Graviton Emission

qq gG (dominant channel)jets + MET final stateZ()+jet irreducible backgroundImportant instrumental backgrounds from jet mismeasurement, cosmics, etc.Both CDF and DØ are pursuing this search

)41(216161861

221141

1,

,1

36

3232

21

2

12

xyxxyxxxy

xxxxxyx

yxF

s

m

s

tF

sMgGqq

dt

d

S

S

Theory:[Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999) and corrected version, hep-ph/9811291][Mirabelli, Perelstein, Peskin, PRL 82, 2236 (1999)]

n MS reach, Run I

MS reach, Run II

2 1100 GeV

1400 GeV

3 950 GeV 1150 GeV

4 850 GeV 1000 GeV

5 700 GeV 900 GeV

Note that non-perturbative effects could become important at high n

Note that this sensitivity estimate is probably optimistic, as it does not take into account copious instrumental backgrounds[M.Spiropulu]

Tevatron Run I/II reach, CDF+DØ [Giudice et al.]


DØ Run I (preliminary):1.0-1.3 TeV

)1(,4

2

OcM

fc

S

n

Dependence on the cut-off scale = cMS:

222

22

n,n

ns,Mf S

n=3n=5n=7

n=3n=5n=7

n=3n=5n=7

c=O(1) is natural in string theory (from exponential suppression of the GKK couplings [Antoniadis et al, hep-

ph/9904232] or from the brane tension [Bando et al,

hep-ph/9906549])

Virtual exchange: expected sensitivity @95% CL:

Run II and LHC Reach in Virtual Graviton Exchange


LHC Reach in Direct Graviton Production

qg qG and qq G reach at the LHC

s = 2000 GeV

[Giudice, Rattazzi, Wells, NP B544, 3 (1999)]

qG ETmin spectrum

qG cross section

G cross section

G ETmin spectrum

Caveat: instrumentalbackgrounds are ignored

Note that non-perturbative effects could become important at high n

n MS reach

Perturbativity

2 8.5 TeV 3.8 TeV

3 6.8 TeV 4.3 TeV

4 5.8 TeV 4.8 TeV

5 5.0 TeV 5.4 TeV

LHC reach in j+MET channelfor Ldt = 100 fb1


Real Graviton Emission at the NLC

ee G/ZGSimilar to LEP2 StudiesPolarization helps to reduce SM backgroundsLow background gives an edge above LHCGiudice, Rattazzi, Wells, NP B544, 3 (1999)Mirabelli, Perelstein, Peskin, PRL 82, 2236 (1999)Cheung, Keung, PR D60, 112003 (1999)Many others…

MS reach200 fb-1

Giudice

MS reach? fb-1

Mirabelli

MS reach50 fb-1

Cheung

n 1 TeV, P = 90%, G 1 TeV, P=0, G/ZG

2 7.7 TeV 5.7 TeV 4.5 TeV3.2-4.2 TeV

3 4.0 TeV

4 4.5 TeV 3.0 TeV

5 2.4 TeV

6 3.1 TeV

[Giudice et al., NP B544, 3 (1999)] [Cheung et al., PR D60, 11203 (1999)]

G G

ZG

ETmin spectrum MS dependence

s-dependence


Virtual Graviton Effects at the NLC

ee ff, WW, ZZ, etc.Similar to LEP2 StudiesPolarization helps to reduce SM backgroundsSensitivity comparable to that at the LHCHewett, Phys. Rev. Lett. 82, 4765 (1999)

Giudice, Rattazzi, Wells, NP B544, 3 (1999)Rizzo, Phys. Rev. D59, 115010 (1999)

Cheung, Phys.Rev. D61, 015005 (2000)Davoudiasl, Phys.Rev. D61, 044018 (2000) Many others…

Hewett Giudice

Rizzo Cheung Davoudiasl

Luminosity

200 fb-1 ? fb-1 100-500 fb-1

10 fb-1 200 fb-1

3.8 TeV

3.5-4.0 TeV

ff 6.0-7.0 TeV

6.0-7.5 TeV

ff 3.5-4.5 TeV

Compton 6 TeV

[Cheung, PR D61, 015005 (1999)]


NLC Reach for Large Extra Dimensions

If LED do exist, LHC is likely to discover themFor real graviton emission NLC has an edge for low number of extra dimensions Phenomenology of LED could be very rich, and some effects (e.g., s-channel Kaluza-Klein resonances) could be studied only at NLCPolarized beams, a unique NLC capability, could be very helpful in studying the virtual graviton effects, and to suppress SM backgrounds to direct graviton emission

[M.Spiropulu]

Run I

LEP2

LHCRun II

NLC

n=4, G (ee), gG (pp)

Note that LHC reach exceedsthat for NLC for n = 6, 7


Conclusion: WWW Search for Extra Dimensions

Stay tuned – next generation of colliders has a good chance to solve the mystery of large extra dimensions!

http://www.extradimensions.com

Extra Dimensions TV Show

On 2/15/00 patent 6,025,810 was issued to David Strom for a "hyper-light-speed antenna." The concept is deceptively simple: "The present invention takes a transmission of energy, and instead of sending it through normal time and space, it pokes a small hole into another dimension, thus sending the energy through a place which allows transmission of energy to exceed the speed of light." According to the patent, this portal "allows energy from another dimension to accelerate plant growth." - from APS “What’s New”, 3/17/00

Carolina’s Extra Dimensions

Documents

Collider Signals From Extra Dimensions