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Introduction to universal extra dimensions (UEDs)

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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

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

Motivation

Universal extra dimensions (UEDs)

UED vs SUSY

Summary

Mitsuru Kakizaki

Mass spectrum for

[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

- 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

- 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

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

5D

- e.g. gauge interaction of fermion:

4D

SM

For

KK expansion

KK

Couplings in UED models are determined by corresponding SM ones

Mitsuru Kakizaki

[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

[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

UED:

: Spin 1/2

Factor

SUSY:

: Spin 0

at

: signal + background

: signal

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

Mitsuru Kakizaki

- 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

- 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

Mitsuru Kakizaki

[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

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

Mitsuru Kakizaki

- Cross section for

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

Mitsuru Kakizaki

- Photon energy spectrum in

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

Mitsuru Kakizaki

e.g.

New

[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

[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