Experimental Aspects of Extra Dimensions

1
Experimental Aspects of Extra Dimensions

• Andy Parker
• Cambridge University

2
Outline

• Experimentalists view of the theory
• Gravity experiments
• Other limits
• Large extra dimensions at LHC
• Real and virtual effects
• Tevatron limits
• NLC
• Warped extra dimensions
• Black hole production

3
An experimentalists view of the theory

• SM is wonderful!
• All experimental data is explained to high
  precision
• Theory checked at distance scales of 1/MW 2.5 x
  10-18 m
• Only one state is unaccounted for - the Higgs
• There is only one free parameter which is unknown
  - MH
• No contradiction between the best fit Higgs mass
  and search limit.
• But theorists dont agree!
• Higgs mass is unstable against quantum
  corrections
• Hierarchy problem - MW80 GeV, MHlt1 TeV, MPl1019
  GeV

4
Higgs search limit at LEP

• In SM framework, Higgs mass is well constrained.
• Only a matter of time .
• In SUSY models, very difficult to raise lightest
  higgs mass

5
Two views of the world.

• Supersymmetry . Extra dimensions.

different scales
.hidden perfection
6
Epicycles

• Typical Ptolemaic planetary model
• Symmetry is assumed all orbits are based on
  circles
• But the Earth is not at the centre of the circle
  (the eccentric)
• The planet moves on an epicycle
• The epicycle moves around the equant

From Michael J. Crowe, Theories of the World
from Antiquity to the Copernican Revolution.
7
Supersymmetry

• Conventional method to fix Higgs mass
• Invoke SUSY
• Double the number of states in model
• Invoke SUSY breaking
• Fermion/boson loops cancel (GIM)
• Higgs mass stabilised!
• 105 new parameters (MSSM)
• 48 more free parameters if RP not conserved

gt SUSY is a good pension plan for
experimentalists!
8
Extra Dimensions

• Hypothesize that there are extra space dimensions
• Volume of bulk space gtgt volume of 3-D space
• Hypothesize that gravity operates throughout the
  bulk
• SM fields confined to 3-D
• Then unified field will have diluted gravity,
  as seen in 3-D
• If we choose n-D gravity scaleweak scale then
• Only one scale -gt no hierarchy problem!
• Can experimentally access quantum gravity!
• But extra dimension is different scale from
  normal ones
• -gt new scale to explain

Extra dimensions are more of a lottery bet than a
pension plan!
9
Scale of extra dimensions

• For 4n space-time dimensions
• For MPl(4n) MW
• n1, R1013 cm ruled out by planetary orbits
• n2, R100 mm-1mm OK (see later)
• -gt Conclude extra dimensions must be compactified
  at lt1mm

10
Kaluza Klein modes

• Particles in compact extra dimension
• Wavelength set by periodic boundary condition
• States will be evenly spaced in mass
• tower of Kaluza-Klein modes
• Spacing depends on scale of ED
• For large ED (order of mm) spacing is very small
  - use density of states
• For small ED, spacing can be very large.

M
4-D brane
1/R
r
Compactified dimension
11
Why are SM fields confined to 3-D space?

• Interactions of SM fields measured to very high
  precision at scales of 10-18 m
• If gauge forces acted in bulk, deviations would
  have been measured
• KK modes would exist for SM particles
• For large ED, mass splitting would be small.

12
H1 results on excited fermions
95 cl

• Many channels examined no evidence for f.

13
Gravity in 3-D space

• Gausss theorem
• Field at r given by

M
r
m
14
Gravity in 4-D space
4-sphere

• Compute volume of 4-sphere

r
r sinq
q
3-sphere
15
ED signature in Gravity experiments

• r gt R Get 3-D result
• r lt R Get 4-D result

F
Gaussian surfaces
r
R
16
Measuring Gravity in the lab

• Torsion balance
• Henry Cavendish 1778 (apparatus by Michell)
• Measured mean density of Earth (no definition of
  the unit of force).
• Sir Charles Boys inferred G6.664x10-11Nm2/kg2
  from Cavendishs data a century later.
• Modern value
• G (6.6726 0.0001)x10-11 Nm2/kg2.

17
Measuring Gravity in the lab

• Recent experiment of Long et al
• hep-ph/0009062
• Source mass oscillates at 1kHz
• Signal is oscillation of test mass
• Must isolate masses from acoustic vibrations, EM
  coupling
• Run in vacuum
• Isolation stacks
• Conducting shield
• Low temperature

Capacitor
Detector
1 kHz
Shield
Source mass
18
Deviations from Newtonian gravity

• Gravity experiments present results in terms of
  Yukawa interaction of form
• l gives range of force
• a gives strength relative to Newtonian gravity.
• a depends on geometry of extra dimensions
• Sensitive to forces of 4x10-14 N
• Limited by thermal noise next step, cool
  detector

19
Limits on deviations from Newtonian gravity

• Planetary orbits set very strong limits on
  gravity at large distances.
• but forces many orders of magnitude stronger
  than gravity are not excluded at micron scales.
• Parameterized as a Yukawa interaction of strength
  a relative to gravity and range l
• moduli scalars in string theories

hep-ph/0009062
1mm
20
Submillimetre gravity measurements Eot-Wash

• Torsion pendulum experiment
• Masses are 10 holes in each ring
• Lower attractor has two rings with displaced
  holes, rotates slowly
• Geometry designed to suppress long range signals
  without affecting shortrange ones
• Membrane shields EM forces
• All surfaces gold plated.
• Separation down to 218mm

21
Torsional pendulum data

• Data from one turn of base plate, with fitted
  expected curve
• Angular precision 8nrad
• Signal would have higher harmonic content and
  different dependence on distance.

22
Deviations in data

• Measured torques at 3 frequencies
• Deviations from Newtonian prediction

a3 l250mm
23
Limit from torsional pendulum

• New limit sensitive to scales lt3.5 TeV for n2

n2
24
Casimir effect
r

• Casimir (1948) predicted force between 2 plates
  from field fluctuations
• This will become a background at distances around
  1mm
• Scan gold probe across surface
• Fgrav varies as probe moves, but Fc is constant.

Plate area A
Gold probe
d
d
2d
25
Pioneer 10

• Pioneer 10 is leaving the solar system after 30
  years in flight.
• Orbit shows deccelaration from force of 10-10 g
• Radiation pressure?
• Solar?
• Antenna?
• Heat?
• Gas leaks
• Time dependence?

26
Limits from g-2 experiments

• g-2 is best measured number in physics
• Theory
• aSM (g-2)/2
• 11659159.7(6.7)x10-10
• Experiment (PDG)
• 11659160(6)x10-10
• LED can give contributions from KK excitations of
  W, Z, g, O(10-10)
• (Cirelli, Moriond)
• Brookhaven experiment hep-ph/0105077

27
Astrophysical Constraints

• Supernova remnants lose energy into ED, but
  production of KK states restricted to O(10MeV)
• Remnant cools faster
• Data from SN1987A implies
• MD gt 50 TeV for n2
• PRL 83(1999)268

28
Neutrino oscillations

• Neutrino oscillations could occur into sterile
  neutrinos
• KK excitations of SM fermion singlets can mix
  with neutrinos to form sterile states
• Oscillation data (SNO, Super-Kamiokande) are
  well fitted by oscillations into standard
  neutrino states
• -gt little room for sterile states
• -gt bound on ED models
• -gt model dependent limits on parameters
• Eg LBNL-49369 gives Rlt0.82 mm

29
Signatures for Large Extra Dimensions at Colliders

• ADD model (hep-ph/9803315)
• Each excited graviton state has normal
  gravitational couplings
• -gt negligible effect
• LED very large number of KK states in tower
• Sum over states is large.
• gt Missing energy signature with massless
  gravitons escaping into the extra dimensions

G
30
LEP Searches for Extra Dimensions

• Search for real graviton production
• Cross section
• No evidence for excess rate in photonEtmiss -gt
  Set limits
• Search for deviations in di-lepton and di-boson
  production

31
LEP Limits on direct graviton production
32
LEP limits on virtual graviton interactions

• Search for deviations from SM in dilepton and
  diboson production
• MS 1TeV? Set 95 CL
• l depends on quantum gravity theory

MS limits
33
Signatures at the LHC

• Good signatures are LBNL-45198
• Jet missing energy channels ATL-PHYS-2001-012
• gg -gt gG
• qg -gt qG
• qq -gt Gg
• Photon channels
• qq -gt Gg
• pp -gt ggX Virtual graviton exchange
• Lepton channels
• pp -gt l l X Virtual graviton exchange

34
Real graviton production

• Cross section
• Note ED mass scale and n do not separate -gt
• difficult to extract n
• Can use cutoff in MD from parton distributions
• For ngt6, cross section unobservable at LHC
• Quantum gravity theory above MD unknown -gt
• Calculation only reliable at energies below MD

35
Missing ET analysis

• pp -gt jet ETMiss Jet energies gt 1 TeV
• Dominant backgrounds
• Jet Z -gt n n
• Jet W-gt t n
• Jet W-gt e n
• Veto isolated leptons (lt10 GeV within DR0.2)
• Instrumental background to ETMiss is small

Use lepton veto
36
High PT jet cross section

• ETJet gt 1 TeV
• h Jet lt 3
• 100fb-1 of data expected
• SM Background 500 events
• No prediction for ngt4

SM Background
37
Lepton veto and trigger

• Veto efficiency 98 per lepton
• Reject
• 0.2 signal
• 23.3 JWt
• 74.3 JWe
• 61.1 JWm

38
Jet multiplicity - signal scenarios

• Jet multiplicity in signal increased by gg
  production process and higher mass
• Mean 2.5

39
Jet multiplicity background

• Background lower jet multiplicity
• Lower mass
• Less gg production
• Mean 2.0
• But at high ET, mean 4 is similar

40
PT and h distributions

• PT of jet is harder in signal
• Discrimination in h is too poor to be useful

41
Rejection of W(tn) background

• W(tn) background has jet near missing ET
• Cut at df0.5
• Reject
• 6 signal
• 27 W(tn)
• 11 total background

42
Final missing ET distributions

• Signal and backgrounds after cuts for 100fb-1

43
Missing ET signal

• Signal
• Excess of events at high ET
• Dominant background
• Z-gtnn

44
Calibration of Z-gt nn background

• Use Z-gt ee
• Two isolated electrons, PTgt15, Mee within 10 GeV
  of MZ
• Account for acceptance differences e, m, n
• BRs differ by factor 3, so calibration sample
  has less statistics

45
Background estimates
46
Signal event numbers ETgt1TeV
47
Discovery potential
5s discovery limits, ETgt1 TeV, 100fb-1
48
Single photon signal at LHC

• Potential confirmation of discovery
• Main background
• Other backgrounds from W small, not simulated.
• Require Etggt60 GeV and hlt2.5 for trigger
• Signal in region Etggt500 GeV
• Calibrate background with gZ-gt ee sample
• pTegt20 GeV, invariant mass within 10 GeV of Z
• Sample is 6x smaller than sample, use S/sqr(6B)

49
Significance of single photon signal
Background
Signal
Only useful if n and MD small
50
Extracting n and MD
Cannot separate n and MD at fixed energy Run LHC
at 10 TeV as well as 14 TeV MD limited
kinematically by pdfs -gt can separate n and MD
with precise cross section measurement
51
Variation with ECM at LHC

• Cross section ratio
• (10 TeV/14TeV)
• Need to measure to 5 to distinguish n2,3
• Need O(10) more L at 10 TeV
• Need luminosity to lt5

52
Virtual graviton processes at LHC

• s-channel graviton exchange contributes to
• Potential information from angular distribution
  differences and interference between SM
  background and graviton exchange
• ATL-PHYS-2001-012

53
Diphoton production at LHC

• SM background peaks at high h
• Signal events central

54
Diphoton signals at LHC

• gg invariant mass distributions
• (log scale)
• Signal can be optimised with cut on MgggtMmin

55
Diphoton reach at LHC
Cut value

• 5s reach for diphoton signal for
• 10 fb-1 and 100 fb-1
• Can optimise reach at any n with cut on Mmin

56
Dilepton signals at LHC

• Invariant mass of ll- pair
• (log scale)

57
Forward-backward asymmetry in dileptons

• Interference between G and SM modifies predicted
  FB asymmetry
• 100fb-1

58
Dilepton reach at LHC

• 5s reach for diphoton signal for
• 10 fb-1 and 100 fb-1
• Can optimise reach at any n with cut on Mmin

59
Limits from the Tevatron

• Searches performed by D0 and CDF
• D0 Run I data taken without B field
• -gt use EM clusters only
• Fake background from miss id jets
• No evidence for excess events
• hep-ex/0108015

60
D0 data

• Compare data and MC in
• Mass/cosq plane
• Data compatible with expected backgrounds from SM
  and miss ID jets
• hep-ex/0103009

61
D0 LED Signature

• Dedicated MC generator includes SM, ED and
  interference terms.
• Signal appears at large M, low cosq
• MDgt1.44 TeV for n3
• MDgt0.97 TeV for n7
• Run II will extend reach to
• 3-4 TeV
• Luminosity? 2? 10? 30 fb-1

62
Single photons at the NLC

• Finding signal is one thing
• interpreting it is another
• Single photonETMiss signal at NLC
• SM background from

n2,4,6
63
Single photon angular distribution at NLC

• Assume
• 500 GeV LC
• Pol(e-)80
• Pol(e)60
• Cross-section measured to 1 precision
• (gt270fb-1 required)
• Distinguish n2 from n3 up to MD4.6 TeV
• Gravitino production is indistinguishable from
  n6!

64
Warped 5-d spacetime
Higgs vev suppressed by Warp Factor
Gravity
Planck scale brane
Our brane
5th space dimension r
65
Warped Extra dimensions

• Consider Randall and Sundrum type models as test
  case
• Gravity propagates in a 5-D non-factorizable
  geometry
• Hierarchy between MPlanck and MWeak generated by
  warp factor
• Need no fine tuning
• Gravitons have KK excitations with scale
• This gives a spectrum of graviton excitations
  which can be detected as resonances at colliders.
• First excitation is at
• where
• Analysis is model independent this model used
  for illustration

66
Implementation in Herwig

• Model implemented in Herwig to calculate general
  spin-2 resonance cross sections and decays.
• Can handle fermion and boson final states,
  including the effect of finite W and Z masses.
• Interfaced to the ATLAS simulation (ATLFAST) to
  use realistic model of LHC events and detector
  resolutions.
• Coupling
• Worst case when giving smallest couplings.
• For m1500 GeV, Lp13 TeV
• Other choices give larger cross-sections and
  widths

67
Angular distributions

• Angular distributions expected of decay products
  in CM are
• qq -gt G -gt ff
• gg -gt G -gt ff
• qq -gt G -gt BB
• gg -gt G -gt BB
• This gives potential to discriminate from
  Drell-Yan background with

68
Angular distributions of ee- in graviton frame

• Angular distributions are very different
  depending on the spin of the resonance and the
  production mechanism.
• gtget information on the spin and couplings of
  the resonance

69
ATLAS Detector Effects
Best channel G-gtee- Good energy and angular
resolution Jets good rate, poor energy/angle
resolution, large background Muons worse mass
resolution at high mass Z/W rate and
reconstruction problems. Main background
Drell-Yan Acceptance for leptons hlt2.5
Tracking and identification efficiency included
Energy resolution Mass
resolution
70
Graviton Resonance

• Graviton resonance is very prominent above small
  SM background, for 100fb-1 of integrated
  luminosity
• Plot shows signal for a 1.5 TeV resonance, in the
  test model.
• The Drell-Yan background can be measured and
  subtracted from the sidebands.
• Detector acceptance and efficiency included.

71

• Signal and background for increasing graviton mass

1000 GeV
500 GeV
1.5 TeV
2.0 TeV
72
Events expected from Graviton resonance
Signal
Background
100fb-1
Limit
Mass window is 3x the mass resolution
73
Production Cross Section
10 events produced for 100fb-1 at mG2.2 TeV.
With detector acceptance and efficiency, search
limit is at 2080 GeV, for a signal of 10 events
and S/vBgt5
10 events
74

• Angular distribution changes with graviton mass
• Production more from qq because of PDFs as
  graviton mass rises

75
Angular distribution observed in ATLAS

• 1.5 TeV resonance mass
• Production dominantly from gluon fusion
• Statistics for 100fb-1 of integrated luminosity
  (1 year at high luminosity)
• Acceptance removes events at high cos q

76
Determination of the spin of the resonance

• With data, the spin can be determined from a fit
  to the angular distribution, including background
  and a mix of qq and gg production mechanisms.
• Establish how much data is needed for such a fit
  to give a significant determination of the spin
• 1. Generate NDY background events (with
  statistical fluctuations)
• 2. Add NS signal events
• 3. Take likelihood ratio for a spin-1 prediction
  and a spin-2 prediction from the test model
• 4. Increase NS until the 90 confidence level is
  reached.
• 5. Repeat 1-4 many times, to get the average
  NSMIN needed for spin-2 to be favoured over
  spin-1 at 90 confidence
• 6. Repeat 1-5 for 95 and 99 confidence levels

One ATLAS run
77
Angular distribution observed in ATLAS

• Model independent minimum cross sections needed
  to distinguish spin-2 from spin-1 at 90,95 and
  99 confidence.
• Assumes 100fb-1 of integrated luminosity
• For test model case, can establish spin-2 nature
  of resonance at 90 confidence up to 1720 GeV
  resonance mass

78
Graviton discovery contours

• Confidence limits in plane of Lp vs graviton mass
• Coupling 1/ Lp
• Test model has k/MPl0.01, giving small coupling.
  
• For large k/MPl coupling is large enough for
  width to be measured.
• (Analysis assumes widthltltresolution)

79
Muon analysis

• Muon mass resolution much worse than electron at
  high mass ?
• Discovery reach in muon channel for MGlt1700 GeV
• Muons may be useful to establish universality of
  graviton coupling

80
Measurement of the graviton coupling to mm-

• Confidence limits in plane of Lp vs graviton mass
• Coupling 1/ Lp
• Test model has k/MPl0.01, giving small coupling.
  
• For large k/MPl coupling is large enough for
  width to be measured.
• (Analysis assumes widthltltresolution)

Ds.B/s.B
81
Photon analysis

• Photon pair mass resolution as good as electrons
• But background uncertain. For standard model
  (ptmin150 GeV)
• sHERWIG0.36 pb
• Included
• Not included
• for example
• FNAL data indicates sHERWIG is 5x too small ? use
  1.8 pb
• Do not trust cosq distribution for background.

Graviton mass (GeV)
82
Measurement of the graviton coupling to gg

• Confidence limits in plane of Lp vs graviton mass
• Coupling 1/ Lp
• Test model has k/MPl0.01, giving small coupling.
  
• For large k/MPl coupling is large enough for
  width to be measured.
• (Analysis assumes widthltltresolution)

83
Graviton to jet-jet backgrounds

• k/MPl 0.08
• (64x higher cross-section)

84
Graviton to jet-jet signal at 1.9 TeV

• Significant signal after background subtraction
• k/MPl 0.08
• (64x higher cross-section)

85
Graviton to jet-jet search reach

• Reach is limited because of high background

86
Graviton to WW

• Look for
• Select 1e, 0 m, 2 jets, PTmiss from ATLFAST
• hjet lt2
• Require Mjj compatible with W mass
• take highest pT pair in mass window
• Solve for pzn using W mass constraint
• Plot MWW look for resonance above SM background
• SM background from WW, WZ and ttbar

87
Graviton to WW signal and background

• WW channel is viable for graviton

88
Graviton to WW channel
Efficiency drops at very high jet ET

• Reach of Wjets channel - low cuts

89
Exploring the extra dimension

• Check that the coupling of the resonance is
  universal measure rate in as many channels as
  possible mm,gg,jj,bb,tt,WW,ZZ
• Use information from angular distribution to
  separate gg and qq couplings
• Estimate model parameters k and rc from resonance
  mass and s.B
• For example, in test model with MG1.5 TeV, get
  mass to 1 GeV
• and s.B to 14 from ee channel alone (dominated
  by statistics).
• Then measure

90
Black hole production

• Low scale gravity in extra dimensions allows
  black hole production at colliders.
• Decay by Hawking radiation (without eating the
  planet)
• 8 TeV mass black hole decaying to leptons and
  jets in ATLAS
• 8 partons produced with
• pTgt500 GeV
• Work in progress Richardson, Harris

91
Black hole production cross-sections at LHC
10000 evs/yr

• Classical approximation to cross-section
• (Controversial)
• Very large rates for n2-6 hep-ph/0111230

92
Black hole decay

• Decay occurs by Hawking radiation
• Hawking Temperature TH
• Black Hole radius rh
• Use observed final state energy spectrum to
  measure TH and hence n?

93
Particle spectra from black hole decays

• Example
• n6 extra dimensions
• MD 2 TeV
• Mh 7-7.5 TeV
• Hawking Temperature TH 400 GeV
• Multiplicity N Mh/2 TH 9
• Electron spectrum deviates from Black body
• effect of isolation cut?
• recoil effect?
• Fit gives 388 GeV

All jets
Isolated es
Black body
Fit
94
Extracting n from Black Holes
Preliminary!

• Fit TH against Black Hole mass
• No experimental resolution yet (500 GeV bins)
• Effect of heating?
• Input n6
• Fit gives
• n5.7-0.2

95
Black hole production at the Tevatron
pb
105

• Rate expected to be large at Tevatron
• n4 extra dimensions
• Cross-section drops rapidly at high mass
• Assume 10fb-1
• Non-observation implies MDgt1.4 TeV
• hep-ph/0112186

Events/yr
102
100
s
10-2
10-5
1.0
1.3
1.6
0.7
MD
96
Conclusions

• Extra dimensional theories provide an exciting
  alternative to the normal picture of physics
  beyond the standard model
• A wide variety of new phenomena are predicted
  within reach of experiments.
• Time to bet on the lottery!