1. Introduction to universal extra dimensions (UEDs)
Mitsuru Kakizaki (ICRR, University of Tokyo)
May 10, KEK
Refs: Original idea: Appelquist, Cheng, Dobrescu, PRD67 (2000) Second KK particle physics: MK, Matsumoto, Sato, Senami, hep-ph/ UED vs SUSY at CLIC: Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/
Pedagogical introduction to UED models
Comparison of UED and SUSY phenomenology
Probing extra dimensions at linear colliders
Prof. Raychaudhuri’s talk
UED cosmology and astrophysics
Dr. Matsumoto’s talk

2. 1. Motivation
Extra-dimension scenarios provide new views of various problems
Hierarchy problem:
Large extra dimensions
[Arkani-hamed, Dimopoulos, Dvali PLB 429 (1998) 263]
Warped extra dimensions
[Randall, Sundrum PRL 83 (1999) 3370]
Fermion mass hierarchy
[Arkani-hamed, Schmaltz PRD 61 (2000)]
Existence of dark matter
Universal extra dimensions (UEDs) [Appelquist, Cheng, Dobrescu, PRD67 (2000) ]
Today’s topic
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]
etc.
May 10, 2005
Mitsuru Kakizaki

3. Study at linear colliders is mandatory
UED is similar to SUSY
SUSY
UED
1st KK mode mass
Superparticle mass
 SUSY breaking mass
KK parity stabilizes the LKP
R parity stabilizes the LSP SM
Same spin
SUSY
Different spin SM
Kinematics of 1st KK modes resembles that of superparticles with degenerate mass
Attention to spins of new particles and second KK modes
Study at linear colliders is mandatory
May 10, 2005
Mitsuru Kakizaki

4. Contents Motivation Universal extra dimensions (UEDs) UED vs SUSY
Summary
May 10, 2005
Mitsuru Kakizaki

5. 2. Universal extra dimensions
[Appelquist, Cheng, Dobrescu, PRD67 (2000) ]
Idea: All SM particles propagate compact spatial extra dimensions
For definiteness, we concentrate on one-extra dimensional cases in this talk
Dispersion relation:
Momentum along the extra dimension  Mass in four-dimensional viewpoint
Mass spectrum for
For compactification with radius ,
is quantized
Momentum conservation in the extra dimension
Conservation of KK number in each vertex
May 10, 2005
Mitsuru Kakizaki

6. Parameters in UED models
Kaluza-Klein expansion (Fourier expansion):
Zero modes are identified with SM fields
Parameters in UED models are completely specified in terms of the SM parameters
Only three free parameters in minimal UED model:
: Higgs boson mass
: Size of extra dimension
: Cutoff scale
c.f. minimal SUGRA:
and
May 10, 2005
Mitsuru Kakizaki

7. Minimal UED
In 5D spacetime, spinor representation has 4 complex components
Dirac
Chiral
Reflection sym. under
 Chiral fermions in 4D
e.g.
Conservation of KK parity [+ (--) for even (odd) ] {
The lightest KK particle (LKP) is stable
Dark matter
Single KK particle cannot be produced
c.f. R-parity and the LSP in SUSY models
Experimental limit on is weaker than other extra-dimensional models:
Electroweak precision tests
May 10, 2005
Mitsuru Kakizaki

8. Particle contents in minimal UED
KK level
Gauge boson
Fermion (SU(2)L)
Scalar (SU(2)L)
New particles:
Massive
Dirac
Complex scalar
(Mass )
SM particles:
Massive
Dirac
Real scalar
(Mass )
Massless
Chiral
Electroweak symmetry breaking effects are suppressed for higher KK modes
There appear infinite towers of KK modes with quantum numbers identical to SM particles
May 10, 2005
Mitsuru Kakizaki

9. Interactions in UED models
e.g. gauge interaction of fermion: 5D 4D SM
For
KK expansion KK
Couplings in UED models are determined by corresponding SM ones
May 10, 2005
Mitsuru Kakizaki

10. Radiative corrections to mass spectra of KK modes
[Cheng, Matchev, Schmaltz, PRD66, (2002)]
Compactification  5-dimensional Lorentz invariance Orbifolding  translational invariance in the 5th dimension Radiative corrections generate KK mass splitting
Tree level masses spectrum of 1st KK modes
One-loop corrected masses of 1st KK modes
c.f. SUSY: Universal soft mass at cutoff scale
Mass splitting at weak scale
May 10, 2005
Mitsuru Kakizaki

11. 3. UED vs SUSY LHC: Discovery reach for minimal UED:
[Cheng, Matchev, Schmaltz PRD 66 (2002) ]
Discovery reach for minimal UED:
Signals of 1st KK modes are similar to those of superparticles
(UED is called “Bosonic supersymmetry”)
Future colliders is promising for distinguishing UED and SUSY
Observation of effects caused by second KK modes
Determination of spins of new particles
May 10, 2005
Mitsuru Kakizaki

12. Contrasting SUSY and UED at CLIC (Multi-TeV collider)
[Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/ ]
Comparison of
Rad. cor.
in UED
UED parameters:
with
Missing
in SUSY
MSSM parameters are adjusted to reproduce UED kinematics
SM background:
Event seletion:
missing energy > 2.5 TeV
transverse energy < 150 GeV
event sphericity > 0.05
missing trans. energy > 50 GeV
(small polar angle)
May 10, 2005
Mitsuru Kakizaki

13. Angular distribution and spin measurements
UED:
: Spin 1/2
Factor
SUSY:
: Spin 0 at
: signal + background
: signal
[From Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/ ]
May 10, 2005
Mitsuru Kakizaki

14. Discrimination of UED from SUSY
Cross section for
Photon energy spectrum in
resonance
Including beamstrahlung
[From Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/ ]
c.f. SUSY: at threshold region, no sharp peak due to resonance
May 10, 2005
Mitsuru Kakizaki

15. 4. Summary Remarkable features of UED models:
Excellent dark matter candidate: LKP
Small number of free parameters
Towers of KK modes with spins identical to corresponding SM particles
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
May 10, 2005
Mitsuru Kakizaki

16. Backup slides
May 10, 2005
Mitsuru Kakizaki

17. Collider signatures at LHC
[Cheng, Matchev, Schmaltz PRD66 (2002) ]
Decay chains of 1st KK modes
Discovery reach
The discovery reach:
Signals of 1st KK modes are similar to those of superparticles
May 10, 2005
Mitsuru Kakizaki

18. One-loop corrected masses of 1st KK modes
[From Cheng, Matchev, Schmaltz PRD66 (2002) ]
May 10, 2005
Mitsuru Kakizaki

19. Muon energy spectrum
[From Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/ ]
May 10, 2005
Mitsuru Kakizaki

20. Threshold scan Cross section for
[From Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/ ]
May 10, 2005
Mitsuru Kakizaki

21. Radiative return to Photon energy spectrum in
[From Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/ ]
May 10, 2005
Mitsuru Kakizaki

22. Second KK particle physics
New
Second KK particle physics
[MK, Matsumoto, Sato, Senami, hep-ph/ ]
e.g.
Radiative corrections KK number violating couplings
(2nd KK mode mass)
(1st KK mode mass)
pair production is naturally enhanced by resonance in the s-channel
Signal of 2 lepton + large missing energy is expected to have large cross section and be almost background free
May 10, 2005
Mitsuru Kakizaki

23. Threshold singularity
Idea
Threshold singularity
KK quarkonium
[MK, Matsumoto, Okada, Yamashita, …]
Threshold cross section for KK quarkonium at linear collider
KK quarkonium cross section
for small decay width
Energy of bound state:
Precise determination of parameters is possible
May 10, 2005
Mitsuru Kakizaki