Introduction to universal extra dimensions UEDs

1
Introduction to universal extra dimensions
(UEDs)
Mitsuru Kakizaki (ICRR, University of Tokyo)
May 10, 2005 _at_ 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

• Probing extra dimensions at linear colliders

Prof. Raychaudhuris talk

• UED cosmology and astrophysics

Dr. Matsumotos talk
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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
Todays 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.

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UED is similar to SUSY
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
4
Contents

• Motivation
• Universal extra dimensions (UEDs)
• UED vs SUSY
• Summary

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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
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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
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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
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Particle contents in minimal UED
KK level
Gauge boson
Fermion (SU(2)L)
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
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Interactions 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
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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 dimension
  Radiative 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
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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

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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 gt 2.5 TeV
• transverse energy lt 150 GeV
• event sphericity gt 0.05
• missing trans. energy gt 50 GeV

(small polar angle)
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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
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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
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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

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Backup slides
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Second KK particle physics
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
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Threshold singularity
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
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Higgs mass vs 1/R
Appelquist, Yee, PRD 67 (2003) 055002

• KK modes of top-bottom quark doublet

? T positive

• For large Higgs mass, SM Higgs and KK Higgs

? T negative

• KK quarks and KK HIggs

? S positive
Combined analysis
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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

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One-loop corrected masses of 1st KK modes
From Cheng, Matchev, Schmaltz PRD66 (2002)
056006
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Muon energy spectrum
From Battaglia, Datta, De Roeck, Kong, Matchev,
hep-ph/0502041
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Threshold scan

• Cross section for

From Battaglia, Datta, De Roeck, Kong, Matchev,
hep-ph/0502041
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Radiative return to

• Photon energy spectrum in

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