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### Introduction to universal extra dimensions (UEDs)

Mitsuru Kakizaki (ICRR, University of Tokyo)

May 10, 2005 @ KEK

- Refs:Original idea: Appelquist, Cheng, Dobrescu, PRD67 (2000) 035002Second KK particle physics: MK, Matsumoto, Sato, Senami, hep-ph/0502059UED vs SUSY at CLIC: Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/0502041

- Pedagogical introduction to UED models
- Comparison of UED and SUSY phenomenology

- Probing extra dimensions at linear colliders

Prof. Raychaudhuri’s talk

Dr. Matsumoto’s talk

- UED cosmology and astrophysics

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) 035002]

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.

Mitsuru Kakizaki

SM

SM

UED is similar to SUSYUED

SUSY

- 1st KK mode mass

- Superparticle mass

- KK parity stabilizes the LKP

SUSY breaking mass

- R parity stabilizes the LSP

- Same spin

SUSY

- Different spin

- 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

Mitsuru Kakizaki

Mass spectrum for 2. Universal extra dimensions

[Appelquist, Cheng, Dobrescu, PRD67 (2000) 035002]

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

For compactification with radius ,

is quantized

- Momentum conservation in the extra dimension

Conservation of KK number in each vertex

Mitsuru Kakizaki

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

: Cutoff scale

: Size of extra dimension

c.f. minimal SUGRA:

and

Mitsuru Kakizaki

Dirac

Dirac

Chiral

Minimal UED- In 5D spacetime, spinor representation has 4 complex components

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

Mitsuru Kakizaki

Particle contents in minimal UED

KK level

Fermion (SU(2)L)

Gauge boson

Scalar (SU(2)L)

New particles:

Complex scalar

Dirac

Massive

(Mass )

SM particles:

Massive

Dirac

Real scalar

Massless

Chiral

(Mass )

Electroweak symmetry breaking effects are suppressed for higher KK modes

There appear infinite towers of KK modes with quantum numbers identical to SM particles

Mitsuru Kakizaki

5DInteractions in UED models

- e.g. gauge interaction of fermion:

4D

SM

For

KK expansion

KK

Couplings in UED models are determined by corresponding SM ones

Mitsuru Kakizaki

Radiative corrections to mass spectra of KK modes

[Cheng, Matchev, Schmaltz, PRD66, 036005 (2002)]

- Compactification 5-dimensional Lorentz invariance Orbifolding translational invariance in the 5th dimensionRadiative corrections generate KK mass splitting

One-loop corrected masses of 1st KK modes

Tree level masses spectrum of 1st KK modes

c.f. SUSY: Universal soft mass at cutoff scale

Mass splitting at weak scale

Mitsuru Kakizaki

3. UED vs SUSY

- LHC:

[Cheng, Matchev, Schmaltz PRD 66 (2002) 056006]

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

Mitsuru Kakizaki

Contrasting SUSY and UED at CLIC (Multi-TeV collider)

[Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/0502041]

- 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)

Mitsuru Kakizaki

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/0502041]

Mitsuru Kakizaki

Discrimination of UED from SUSY

- Photon energy spectrum in

- Cross section for

resonance

Includingbeamstrahlung

[From Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/0502041]

c.f. SUSY: at threshold region, no sharp peak due to resonance

Mitsuru Kakizaki

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

Mitsuru Kakizaki

Backup slides

Mitsuru Kakizaki

Collider signatures at LHC

[Cheng, Matchev, Schmaltz PRD66 (2002) 056006]

Discovery reach

Decay chains of 1st KK modes

- The discovery reach:
- Signals of 1st KK modes are similar to those of superparticles

Mitsuru Kakizaki

One-loop corrected masses of 1st KK modes

[From Cheng, Matchev, Schmaltz PRD66 (2002) 056006]

Mitsuru Kakizaki

Muon energy spectrum

[From Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/0502041]

Mitsuru Kakizaki

Threshold scan

- Cross section for

[From Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/0502041]

Mitsuru Kakizaki

Radiative return to

- Photon energy spectrum in

[From Battaglia, Datta, De Roeck, Kong, Matchev, hep-ph/0502041]

Mitsuru Kakizaki

e.g.

New

Second KK particle physics[MK, Matsumoto, Sato, Senami, hep-ph/0502059]

- 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

Mitsuru Kakizaki

KK quarkonium

Idea

Threshold singularity[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

Mitsuru Kakizaki

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