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] hep-ph/0508283

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1. Motivation1. Motivation

Existence of non-baryonic cold dark matterExistence of non-baryonic cold dark matter

Cosmic microwave background anisotropies:

Rotation curve of galaxies:

Mass-to-light ratio of galaxy clusters:

[http://map.gsfc.nasa.gov]

e.g. the Coma cluster:

[Begeman, Broeils, Sanders (1991)]

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What is the constituent of What is the constituent of dark matter? 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

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Cosmic-ray positron Cosmic-ray positron experiments experiments

The HEAT experiment indicated　 an excess in the positron flux:

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

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

KK dark matter may explain the excess without any exceptional substructure

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

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

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

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

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OutlineOutline 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

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

1. Motivation2. Universal extra dimension (UED) models3. Relic abundance of KK dark matter4. Resonant KK dark matter annihilation5. Relic abundance including full coannihilation effects6. Summary

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2. Review of universal extra 2. Review of universal extra dimension (UED) models dimension (UED) models

Idea: All SM particles propagate flat compact spatial extra dimensionsIdea: All SM particles propagate flat compact spatial extra dimensions

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

Dispersion relation:

Momentum along the extra dimension Mass in four-dimensional viewpoint

For compactification with radius , Mass spectrum for

is quantized

Momentum conservation in the extra dimensionConservation of KK number in each vertex

Macroscopic

MicroscopicMagnify

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

The lightest KK particle (LKP) is stable

The LKP is a good candidate for dark matterThe LKP is a good candidate for dark matter

c.f. R-parity and LSP

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

Constraints from electroweak measurements are weak:

Minimal UED modelMinimal UED model

Only two new parameters in the minimal UED (MUED) model:: Size of extra dimension : Cutoff scale

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

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

: Inclusion of 2-loop SM contributions and LEP2 data

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Mass spectra of KK statesMass spectra of KK states KK modes are degenerate in mass at each KK level:

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

Radiative corrections relax the degeneracy

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

1-loop corrected mass spectrum at the first KK level

: Cutoff scale

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

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3. Relic abundance3. Relic abundance of KK dark matter of KK dark matter

Dark matter was at thermal equilibrium in the early universe

Neutralino (LSP)Majorana fermionSmall LargeSmall

(LKP)Spin-1 bosonLargeSmallLarge

Dark matter particleNature of spinAnnihilation cross sectionRelic densityAllowed mass of DM particle

SUSY vs UED

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

Thermal relic abundance

Increasing

Decoupling

Co-moving number density

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Relic abundance of KK dark Relic abundance of KK dark matter (without resonance) matter (without resonance)

[From Servant, Tait, NPB650 (2003)391

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

[zero mode (SM) particle pair]

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

[Servant, Tait, NPB650 (2003) 391]

Inclu

ding

coa

nnih

ilatio

nW

ithou

t coa

nnih

ilatio

n

3 flavors

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

Processes relevant to coannihilation with NLKP: SM particles

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4. Resonant KK dark matter 4. Resonant KK dark matter annihilation annihilation

(Incident energy of two LKPs) Dark matter is non-relativistic in the early universe

(Masses of 2nd KK modes)

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

Mass splitting in MUED:

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Thermal average of Thermal average of annihilation cross section for annihilation cross section for LKPLKP

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

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

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Relic abundance of LKPRelic abundance of LKP (without coannihilation) (without coannihilation)

2nd KK modes play an important role in calculation of the relic density of the LKP dark matter2nd KK modes play an important role in calculation of the relic density of the LKP dark matter

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

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

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Coannihilation Coannihilation with NLKP with NLKP

Evolution of dark matter abundance [Three flavors: ]

-resonance in : relatively small

We can systematically survey effects of 2nd KK resonances: -resonance in : sizable

No second KK resonance in

The number density gradually decreases even after decouplingThe number density gradually decreases even after decoupling

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Allowed mass regionAllowed mass region

Including resonance Tree level results

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5. Relic abundance including 5. Relic abundance including full coannihilation effects full coannihilation effects

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

Colored KK particles can be degenerate with the LKP in mass

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

WMAP

Disfavored byEWPT

In MUED, inclusion of full coanninilation effects lowers favored range of Resonance effects may sizably shift the allowed mass scale

In MUED, inclusion of full coanninilation effects lowers favored range of Resonance effects may sizably shift the allowed mass scale

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

Inclusion of full coannihilation modes change the abundance

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6. Summary6. Summary

UED models provide a viable dark matter candidate:

(Masses of 2nd KK particles)The lightest Kaluza-Klein particle (LKP)

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

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

(Masses of 1st KK particles)

Resonant annihilation