Introduction to Introduction to universal extra dimensions (UEDs) universal extra dimensions (UEDs)
Mitsuru Kakizaki (ICRR, University of Tokyo)May 10, 2005 @ KEK
Refs: Original idea: Appelquist, Cheng, Dobrescu, PRD67 (2000) 035002 Second KK particle physics: MK, Matsumoto, Sato, Senami, hep-ph/0502059 UED vs SUSY at CLIC: Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/0502041
Pedagogical introduction to UED models Comparison of UED and SUSY phenomenology
Pedagogical introduction to UED models Comparison of UED and SUSY phenomenology
UED cosmology and astrophysics Dr. Matsumoto’s talk
Probing extra dimensions at linear colliders Prof. Raychaudhuri’s talk
May 10, 2005 Mitsuru Kakizaki 2
Large extra dimensionsWarped extra dimensions
Today’s topic
[Arkani-hamed, Dimopoulos, Dvali PLB 429 (1998) 263][Randall, Sundrum PRL 83 (1999) 3370]
1. Motivation1. Motivation
etc.
Extra-dimension scenarios provide new views of various problemsExtra-dimension scenarios provide new views of various problems
Hierarchy problem:
Fermion mass hierarchy Existence of dark matter
[Arkani-hamed, Schmaltz PRD 61 (2000)]
Universal extra dimensions (UEDs) [Appelquist, Cheng, Dobrescu, PRD67 (2000) 035002]
Universal extra dimensions (UEDs) [Appelquist, Cheng, Dobrescu, PRD67 (2000) 035002]The Lightest Kaluza-Klein particle (LKP) in UED models is an excellent candidate for dark matter due to Kaluza-Klein (KK) parity [Servant, Tait, NPB 650 (2003) 391]
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Study at linear colliders is mandatoryStudy at linear colliders is mandatory
UEDSUSY
R parity stabilizes the LSP
Kinematics of 1st KK modes resembles that of superparticles with degenerate mass
KK parity stabilizes the LKP
Attention to spins of new particles and second KK modes
Superparticle mass 1st KK mode mass
UED is similar to SUSYUED is similar to SUSY
SUSY breaking mass
SMSM
SUSY Same spin
Different spin
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ContentsContents
1. Motivation2. Universal extra dimensions (UEDs)3. UED vs SUSY4. Summary
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2. Universal extra dimensions2. Universal extra dimensions
For definiteness, we concentrate on one-extra dimensional cases in this talk
Idea: All SM particles propagate compact spatial extra dimensionsIdea: All SM particles propagate compact spatial extra dimensions
[Appelquist, Cheng, Dobrescu, PRD67 (2000) 035002]
Dispersion relation: Momentum along the extra dimension Mass in four-dimensional viewpoint
For compactification with radius ,
Mass spectrum for
is quantized
Momentum conservation in the extra dimensionConservation of KK number in each vertex
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Parameters in UED modelsParameters in UED models
c.f. minimal SUGRA:
: Cutoff scale: Size of extra dimension : Higgs boson mass
Kaluza-Klein expansion (Fourier expansion):
Parameters in UED models are completely specified in terms of the SM parametersParameters in UED models are completely specified in terms of the SM parameters
and
Only three free parameters in minimal UED model:
Zero modes are identified with SM fields
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Minimal UEDMinimal UED
Conservation of KK parity [+ (--) for even (odd) ]The lightest KK particle (LKP) is stable
c.f. R-parity and the LSP in SUSY models
Reflection sym. under
Experimental limit on is weaker than other extra-dimensional models:
Electroweak precision tests
Single KK particle cannot be produced{ Dark matter
In 5D spacetime, spinor representation has 4 complex components
Chiral fermions in 4D e.g.
DiracDiracChiral
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Particle contents in minimal Particle contents in minimal UEDUED
Electroweak symmetry breaking effects are suppressed for higher KK modesThere appear infinite towers of KK modes
with quantum numbers identical to SM particlesThere appear infinite towers of KK modes with quantum numbers identical to SM particles
KK level
New particles:
MasslessMassive
Massive(Mass )
Dirac
Gauge boson Fermion (SU(2)L)
Real scalar
Scalar (SU(2)L)
SM particles:(Mass )
DiracChiral
Complex scalar
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Interactions in UED modelsInteractions in UED models e.g. gauge interaction of fermion:
KK expansion
5D
Couplings in UED models are determined by corresponding SM onesCouplings in UED models are determined by corresponding SM ones
4DFor
SM
KK
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Compactification 5-dimensional Lorentz invariance Orbifolding translational invariance in the 5th dimension Radiative corrections generate KK mass splitting
Compactification 5-dimensional Lorentz invariance Orbifolding translational invariance in the 5th dimension Radiative corrections generate KK mass splitting
Radiative corrections to Radiative corrections to mass spectra of KK modesmass spectra of KK modes
[Cheng, Matchev, Schmaltz, PRD66, 036005 (2002)]
One-loop corrected masses of 1st KK modes
c.f. SUSY: Universal soft mass at cutoff scale Mass splitting at weak scale
Tree level masses spectrum of 1st KK modes
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LHC:[Cheng, Matchev, Schmaltz PRD 66 (2002) 056006]
Signals of 1st KK modes are similar to those of superparticles
Discovery reach for minimal UED:
3. UED vs SUSY3. UED vs SUSY
Future colliders is promising for distinguishing UED and SUSY
(UED is called “Bosonic supersymmetry”)
Observation of effects caused by second KK modes Determination of spins of new particles
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Contrasting SUSY and UED at CLICContrasting SUSY and UED at CLIC (Multi-TeV collid (Multi-TeV collider)er)
[Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/0502041]
missing energy > 2.5 TeV transverse energy < 150 GeV event sphericity > 0.05 missing trans. energy > 50 GeV
Event seletion: SM background:
(small polar angle)
MSSM parameters are adjusted to reproduce UED kinematics
Comparison of
with in UED
in SUSY
UED parameters:
Missing
Rad. cor.
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Angular distribution Angular distribution and spin measurements and spin measurements
: Spin 1/2
: Spin 0
: signal + background: signal
UED:
SUSY:at
Factor
[From Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/0502041]
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Discrimination of UED from Discrimination of UED from SUSYSUSY Cross section for
resonanceIncludingbeamstrahlung
Photon energy spectrum in
c.f. SUSY: at threshold region, no sharp peak due to resonance
[From Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/0502041]
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4. Summary4. Summary
LHC would not distinguish UED from SUSY models
Study at linear colliders is mandatory
Attention to Spins of new particles Effects caused by second KK particles
Attention to Spins of new particles Effects caused by second KK particles
Remarkable features of UED models:
Towers of KK modes with spins identical to corresponding SM particlesSmall number of free parametersExcellent dark matter candidate: LKP
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Backup slidesBackup slides
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Collider signatures at LHCCollider signatures at LHC
The discovery reach: Signals of 1st KK modes are similar to those of superparticles
The discovery reach: Signals of 1st KK modes are similar to those of superparticles
[Cheng, Matchev, Schmaltz PRD66 (2002) 056006]
Discovery reachDecay chains of 1st KK modes
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One-loop corrected massesOne-loop corrected masses of 1st KK modes of 1st KK modes
[From Cheng, Matchev, Schmaltz PRD66 (2002) 056006]
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Muon energy spectrumMuon energy spectrum
[From Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/0502041]
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Threshold scanThreshold scan Cross section for
[From Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/0502041]
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Radiative return toRadiative return to
[From Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/0502041]
Photon energy spectrum in
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Radiative corrections KK number violating couplings
pair production is naturally enhanced by -resonance in the s-channel
Second KK particle physicsSecond KK particle physics
Signal of 2 lepton + large missing energy is expected to have large cross section and be almost background freeSignal of 2 lepton + large missing energy is expected to have large cross section and be almost background free
(2nd KK mode mass)(1st KK mode mass)
[MK, Matsumoto, Sato, Senami, hep-ph/0502059]
e.g.
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Threshold Threshold singularitysingularity
Threshold cross section for KK quarkonium at linear collider
Precise determination of parameters is possible Precise determination of parameters is possible
[MK, Matsumoto, Okada, Yamashita, …]
KK quarkonium
KK quarkonium cross section for small decay width
Energy of bound state:
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