MARIA SPIROPULU

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Experimental Clues From Higher Dimensions
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Outline

• Extra Old
• Variations on a theme
• Embedding the 31 spacetime
• to a higher dimensional
• structure
• Table-top experiments
• Status
• Collider experiments
• Results and prospects

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the 5th dimension is 75 Years Old
Kaluza and Klein started from 5-dim Einstein
gravity and derived 4-dim gravity plus
electromagnetism
The 5th dimension is compactified around a
circle of radius R
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Compactification around a circle of radius R
e.g. For many extra dimensions
BUT in the KK case the compactification radius is
too very small.
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String theory and Extra dimensions
String 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 lt 103
GeV 1/R meV1
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Kaluza-Klein modes
If a spatial dimension is periodic then the
momentum in that dimension is quantized
From our dimensions of view the KK modes get
mass
KK momentum tower of states
p
0
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Gausss Law
If the d extra dimensions are compactifid down to
sizes R, then Gausss Law
4d Planck Scale Ms MD M any scale that in the
higher dimensional theory is taken O(TeV)
The Planck Scale from our dimension of view,
1019GeV
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The size of the extra dimension
Set the higher dimesional Planck scale to mEWK,
the Planck scale to 1019GeV then
No way
Explore in sub-mm gravitational
experiments/collider...
M-theory limits
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The extra world picture
The SM is confined on a 4d wall
Gravity exists in a 4d bulk
Gravity feels week on the wall because of the
enormity of the bulk volume
Each KK-graviton state couples to the wall with
Planck supressed strength

The number of KK-states (ER)d
The sum over all KK-states is not MPl supressed
but MPl(4d) supressed i.e. MEWK supressed so we
have sizable cross sections
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Variations on a theme
many large toroidal extra 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 dimensions in the TeV range
(Antoniadis-Benakli-Quiros) and more...
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Variations on a theme
Energy Desert
Weak-103
Planck
1019
Space Oasis
What (kind of like a U duality) is going on???
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Experimental (Low Scale) Quantum Gravity
Deviations from Newtons law at the mm range
KK excitations of gravitons in the
bulk neutrinos in the bulk gauge bosons in the
bulk
Astrophysics-cosmology constraints
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Torsion Balance Could Archimedeshave measured
G N19 Centuries before Newtons Principia
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Cavendish Type Setups
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Table -Tops
Add a Yukawa term to the Gravitational Potential
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Table Tops
hep-ph/9805217 Long,Chan,Price
1KHz
100u
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Table Tops
Goal Measure gravity to 1 at distances of 100m
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Collider searches forExtra Dimensions
CERN,European Center for Nuclear Research
Protons run the 4 mile ring about 50000/sec
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Particle Detecting
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The Particles and Their Interactions
quarks leptons
up down
charm strange
top bottom
electron electron neutrino
muon muon neutrino
tau tau neutrino
Relative Strength Today
forces carriers
Strong Electromagnetic Weak Gravity
Gluon photon W,Z graviton
1 10-3 10-14 10-42
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Grand Unification
Force Strength
Higher Energy
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The scale of experimental particle physics
Number of researchers
For discovery of
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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
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ee-?Gg
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ee-?GZ
METjets
2 0.64 0.56 0.29 0.60
3 0.08 0.56 0.30 0.38
4 0.01 0.55 0.30 0.29
n sZG(pb) e sZG95(pb) Ms(TeV)
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ee- ?gt gg
Standard Model
Interference Term
Gravity
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Two-photon measurements at LEP-II
161-189GeV
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Two-photon measurements at LEP-II
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Two-photon measurements at LEP-II
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ee- ?gt ff
Giudice,Rattazi,Wells/Hewett/Rizzo
Terms cos3q, cos4q make differential cross
sections a unique signature
For ff other than ee the integrated interference
term for scattering angles from 0 to p is ZERO.
The interference between graviton and t-channel
SM Bhabha is giving sizable contributions ? good
sensitivity
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Bhabha scattering results
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Bhabha scattering results
ALEPH,OPAL,DELPHI,L3 combined (Bourilkov
hep-ph/9907380) MSgt1.26 TeV (l1) Msgt960 TeV
(l-1)
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ee- ?gt ff
tt- MSgt450 GeV (l1) Msgt550 GeV (l-1)
mm- MSgt580 GeV (l1) Msgt510 GeV (l-1)
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ee- ?gt WW, ZZ
T.Han, J.D.Lykken, R.-J.Zhang hep-ph
9811350 K.Agashe, N.G.Deshpande hep-ph 9902263
ZZ MSgt470 GeV (l1) Msgt460 GeV (l-1)
WW- MSgt650 GeV (l1) Msgt520 GeV (l-1)
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LEP summary
Virtual Graviton Exchange Limits on Ultraviolet
Cutoff Scale (TeV)
Real Graviton Production Limits On Extra
Dimensions
gG,ZG 1 TeV to 500 GeV for n2 to n6
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Tevatron (virtual)
Drell-Yan and diphoton production with virtual
graviton exchange
Landsberg,Cheung hep-ph/9909218
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The Three Components
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Tevatron (direct)
Only qqbar-gtg G (PYTHIA 6.115 graviton
process), d2, M1TeV, ?s1.8TeV
Lykken/Matchev/Burkett/Spiropulu
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qq-gtGg
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Case d6
Only qqbar-gtg G (PYTHIA 6.115 graviton
process), d6, M1TeV, ?s1.8TeV
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RUNII Display
Only qqbar-gtg G (PYTHIA 6.115 graviton
process), d6, M1TeV, ?s2TeV, GEANT CDF
preliminary RUNII simulation and display
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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)

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Extra Dimensions Stats
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Neutrinos in the bulk
Dimopulos, Hamed,Dvali Russel, hep-ph/9811448 Mart
in,Wells hep-ph/9903259
If the nR lives in the extra dimensions as a KK
tower of states and the Dirac neutrino masses
arise from ynHnRnL so that mnynu where u is the
Higgs vev 175 GeV then the decay of the Higgs to
nLnR(i) is proportional to the small yn2, but
also to the sum of the KK states (all n with
mltmH) (mHR)d.
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ZH(invisible)
For some reasonable values, mH100GeV, d3,
mn210-6eV2 and MD1 TeV the above ratio is gt 100

Signal
l-
l
n
Background Z(ll)Z(nn) WW,top,mismeasurements..
n
l-
l
PT(l)gt12 GeV, hlt2 mll-mZlt7 GeV no jet with
Etgt10 GeV
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ZH(invisible)
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ZH(invisible)
mH(GeV)
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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 and other form factor
corrections to SM 2-body reactions
Impressive sensitivity of LHC,LC
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Gauge Bosons in the Bulk
Antoniadis,Quiros,Benakli hep-ph/9905311 Rizzo,Wel
ls hep-ph9906234
One motivation is the weak scale SUSY
breaking.The compactification scale of the extra
dimension(s) considered in these scenarios is of
the order of the SUSY breaking scale taken to be
of the order of the EWK scale.
quarks and leptons are confined on a 4d boundary
gauge fields live in the 5d bulk
The gauge boson KK states have an additional ?2
strength in their interactions
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implications
The vector boson KK modes have masses
From precision EWK measurements R-13.5 TeV
Z(n),g(n)
Also limits from
PEWLEP,SLD,NuTeV..,haddirect KK gauge
boson ,ee-deviations in final state fermion
observables
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NLC
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String Resonances
Accomando,Antoniadis,Benakli hep-ph/9912287
Production of a gluon excitation at the
LHC(?s14Te, L100fb-1)
(also with dijet excess TeVII,20fb-1, Rc4 TeV)
W KK excitations at LHC
l n
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Stringy Model BuildingSearches
http//itp.ucsb.edu/online/susy_c99/peskin/
183 GeV ALEPH data Mgt1200 GeV (Msgt400 GeV MHgt810
GeV)
1000 GeV LC projections Mgt8 TeV (Msgt2.7
TeV MHgt5.4 TeV)
MHHewetts ultraviolet cutoff