Dark matter from universal extra dimensions
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Dark Matter from Universal Extra Dimensions. Mitsuru Kakizaki (Bonn Univ. & ICRR, Univ. of Tokyo). 18 November, 2005 @ Bonn Univ. Collaborated with Shigeki Matsumoto (KEK) Yoshio Sato (Saitama Univ.) Masato Senami (ICRR, Univ. of Tokyo). Refs: PRD 71 (2005) 123522 [hep-ph/0502059]

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Dark Matter from Universal Extra Dimensions

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Dark Matter from Universal Extra Dimensions

Mitsuru Kakizaki (Bonn Univ. & ICRR, Univ. of Tokyo)

18 November, 2005 @ Bonn Univ.

Collaborated with

  • Shigeki Matsumoto (KEK)

  • Yoshio Sato (Saitama Univ.)

  • Masato Senami (ICRR, Univ. of Tokyo)


  • PRD 71 (2005) 123522 [hep-ph/0502059]

  • hep-ph/0508283

1. Motivation

  • Rotation curve of galaxies:

[Begeman, Broeils, Sanders (1991)]

  • Mass-to-light ratio of galaxy clusters:

e.g. the Coma cluster:

  • Cosmic microwave background anisotropies:


Existence of non-baryonic cold dark matter

Mitsuru Kakizaki

What is the constituent of dark matter?

  • We need physics beyond standard model (SM) of particle physics

  • Stable, neutral, weakly interacting massive particles are good candidates:

  • Lightest supersymmetric particle (LSP) in supersymmetric (SUSY) models: e.g. neutralino, gravitino

  • Lightest Kaluza-Klein particle (LKP) in universal extra dimension models

  • etc.

Today’s topic

Mitsuru Kakizaki

Cosmic-ray positron experiments

  • The HEAT experiment indicatedan excess in the positron flux:

The positron excess could originate from the annihilation of DM particles in the Galactic halo

  • Unnatural DM substructure is required to match the data in SUSY models

[From Beatty et al., PRL93 (2004) 241102)]

[Hooper, Taylor, Silk, PRD69 (2004) 103509)]

  • KK dark matter may explain the excess without any exceptional substructure

[Hooper, Kribs, PRD70, (2004) 115004)]

  • Future experiments (PAMELA, AMS-02, …) will confirm or exclude the positron excess

Mitsuru Kakizaki


  • In universal extra dimension (UED) models, Kaluza-Klein (KK) dark matter physics is drastically affected by second KK particles

  • Reevaluation of relic density of KK dark matter including coannihilation and resonance effects Dark matter particle mass consistent with WMAP increases


Universal extra dimension (UED) models

Relic abundance of KK dark matter

Resonant KK dark matter annihilation

Relic abundance including full coannihilation effects



Mitsuru Kakizaki

Mass spectrum for

2. Review of universal extra dimension (UED) models

[Appelquist, Cheng, Dobrescu, PRD64 (2001) 035002]


Idea: All SM particles propagate flat compact spatial extra dimensions



  • 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

Minimal UED model

  • In order to obtain chiral fermions at zeroth KK level, the extra dimension is compactified on an orbifold

  • Conservation of KK parity [+ (--) for even (odd) ]

The lightest KK particle (LKP) is stable

c.f. R-parity and LSP

The LKP is a good candidate for dark matter

  • Only two new parameters in the minimal UED (MUED) model:

: Size of extra dimension

: Cutoff scale

  • Constraints from electroweak measurements are weak:

[Appelquist, Cheng, Dobrescu(2001); Appelquist, Yee, PRD67 (2003)]

: Inclusion of 2-loop SM contributions and LEP2 data

[Flacke, Hooper, March-Russel, hep-ph/0509352 (2005)]

Mitsuru Kakizaki

Mass spectra of KK states

1-loop corrected mass spectrum at the first KK level

  • KK modes are degenerate in mass at each KK level:

  • Compactification  5D Lor. inv. Orbifolding  trans. Inv. in 5th dim.

Radiative corrections relax the degeneracy

  • Lightest KK Particle (LKP):Next to LKP: SU(2)L singlet leptons:

: Cutoff scale

[From Cheng, Matchev, Schmaltz, PRD 036005 (2002)]

Mitsuru Kakizaki

3. Relic abundance of KK dark matter

Co-moving number density

  • Thermal relic abundance


  • Dark matter was at thermal equilibrium in the early universe


  • After the annihilation rate dropped below the expansion rate, the number density per comoving volume is fixed

  • SUSY vs UED

Neutralino (LSP)Majorana fermion




Dark matter particleNature of spin

Annihilation cross section

Relic density

Allowed mass of DM particle

(LKP)Spin-1 boson




Mitsuru Kakizaki

Relic abundance of KK dark matter (without resonance)

[Servant, Tait, NPB650 (2003) 391]

  • Processes relevant to the calculation of the relic abundance of the LKP:

[zero mode (SM) particle pair]

3 flavors

Without coannihilation

e.g. t-channel exchange of 1st KK particle:

Including coannihilation

  • Processes relevant to coannihilation with NLKP:

[From Servant, Tait, NPB650 (2003)391]

SM particles

However, only tree level diagramswhich involve extensively 1st KK modes are considered

Mitsuru Kakizaki


4. Resonant KK dark matter annihilation

  • Dark matter is non-relativistic in the early universe

(Incident energy of two LKPs)

(Masses of 2nd KK modes)

  • Mass splitting in MUED:

  • The annihilation cross section for the LKP is enhanced due to the resonance by s-channel 2nd KK Higgs boson at loop level

Mitsuru Kakizaki

Thermal average of annihilation cross section for LKP

Smaller The averaged cross section becomes maximum at later time and has larger maximum value

Mitsuru Kakizaki

Relic abundance of LKP (without coannihilation)

  • The resonant annihilation by effectively reduces the number density of dark matter

  • The resonance effect raises the LKP mass consistent with the WMAP data

2nd KK modes play an important role in calculation of the relic density of the LKP dark matter

Mitsuru Kakizaki

Coannihilation with NLKP

  • We can systematically survey effects of 2nd KK resonances:

  • -resonance in : sizable

  • -resonance in : relatively small

  • No second KK resonance in

  • Evolution of dark matter abundance

[Three flavors: ]

The number density gradually decreases even after decoupling

Mitsuru Kakizaki

Allowed mass region

Tree level results

Including resonance

Mitsuru Kakizaki

5. Relic abundance including full coannihilation effects

[Burnell, Kribs, hep-ph/0509118; Kong, Matchev, hep-ph/0509119]

Relic abundance including coannihilation processes with all level one KK particles (ignoring resonance effects)

  • Colored KK particles can be degenerate with the LKP in mass

Disfavored byEWPT

Inclusion of full coannihilation modes change the abundance

  • In MUED, inclusion of full coanninilation effects lowers favored range of

  • Resonance effects may sizably shift the allowed mass scale


[From Kong, Matchev, hep-ph/0509119]

Mitsuru Kakizaki

6. Summary

  • UED models provide a viable dark matter candidate:

The lightest Kaluza-Klein particle (LKP)

  • (Masses of 2nd KK particles)

(Masses of 1st KK particles)

Resonant annihilation

  • We evaluated the relic abundance of the LKP dark matter including the resonance and coannihilation effects (with the NLKPs)

  • The LKP mass consistent with WMAP is sizably raised due to the s-channel second KK resonance

Mitsuru Kakizaki

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