Large enhancement of KK dark matter annihilation ratedue to threshold singularity

Mitsuru Kakizaki (ICRR, University of Tokyo)Dec. 2004 @ Stanford Univ.

Collaborated with Shigeki Matsumoto and Masato Senami (ICRR), in preparation

Kaluza-Klein (KK) dark matter annihilation cross section is significantly enhanced due to the threshold singularity in the non-relativistic (NR) limit

Kaluza-Klein (KK) dark matter annihilation cross section is significantly enhanced due to the threshold singularity in the non-relativistic (NR) limit

１．Motivation

Existence of non-baryonic cold dark matter (CDM)Existence of non-baryonic cold dark matter (CDM)

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)]

What is the constituent of dark matter?

We need physics beyond the standard model (SM)

Candidates:

Lightest supersymmetric (SUSY) particle (LSP) e.g. Neutralino, gravitino Lightest Kaluza-Klein particle (LKP) in universal extra dimensions etc.

Today’s topic

How to detect

Direct detection Indirect detection: Positrons from annihilations in the galactic halo Antiprotons Exotic gamma rays from the galactic center Neutrinos from the sun and earth

Today’s topic

Positron detectionThe milky way In the neighborhood

of our solar system:

(Almost at rest)

Dark matter halo

DM

DM

Primary is monoenergetic: signal is broadened during propagation:

Flux

Positron 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 (2004)] KK dark matter can explain the excess

Unnatural dark matter substructure is required to match the HEAT data in SUSY models [Hooper, Taylor, Kribs (2004)]

Purpose

Reconsideration of pair annihilation processes of dark matter in universal extra dimensions (UED), in which all the SM fields propagate

Reconsideration of pair annihilation processes of dark matter in universal extra dimensions (UED), in which all the SM fields propagate

The 1st excited mode of boson, , is CDM candidate is almost degenerate with other first KK modes The annihilation cross section is enhanced due to the threshold singularity in the non-relativistic limit. Predicted flux can be increased compared with that at the tree level.

[c.f. Cheng, Feng, Matchev (2002)]

Contents

1. Motivation2. Universal extra dimension (UED)3. Annihilation cross section of KK dark matter4. Threshold cross section in the NR limit5. Summary

2. Universal extra dimension

Idea: All SM particles propagate spatial extra dimensionsIdea: All SM particles propagate spatial extra dimensions [Appelquist, Cheng, Dobrescu]

For simplicity, we consider one extra dimension:

Momentum conservation in higher dim.

Mass spectrum

Conservation of KK number

in 4-dim. viewpoint

Eq. of motion:

orbifold provides CDM

Conservation of KK parity [+ (--) for even (odd) ]The lightest KK particle (LKP) is stable

LKP is a good candidate of cold dark matterLKP is a good candidate of cold dark matter

c.f. R-parity and LSP in SUSY models

To obtain chiral fermions at zero mode, we identify with

Electroweak precision measurements restrict the size :

Mass spectra of KK states Fourier expanded modes are degenerate in mass at each KK level

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

Radiative corrections remove the degeneracy is the LKP and nearly degenerate with SU(2)L singlet

1-loop corrected mass spectrum of the first KK level

We treat the mass deference as a free parameter

3. Annihilation cross section of KK dark matter

[Cheng, Feng, Matchev (2002)]

We concentrate on mode:

Bosonic property of the LKP avoids chirality suppression

Annihilation cross section:

4. Threshold cross section in the NR limit

Higher order calculations are importantHigher order calculations are important

Ladder diagrams can give dominant contributions

and in internal lines are almost on-shell when their mass difference is tiny:

+ ++ . . .

is almost at rest

Strategy1. 5-dim. UED action Effective action for and

2. Non-relativistic approximation using NRQED method

3. Eq. of motion of pair and pair

Exact annihilation cross section for

The optical theorem

= Shroedinger equation

Derivation of effective action for and

5-dimensional UED action:

4-dimensional action with KK particles

Fourier transform

The relevant part for our calculation: Photon ( ), electron ( ), 1st-excited boson ( ) and electrons ( ), and their interactions

Integrate out

Effective action for and Effective action for and

Non-relativistic approximation

Definition of non-relativistic field:

NR region:

Non-relativistic :

On-shellParticle

Anti-particle

Non-relativistic action

Kinetic terms

Coulomb potential generated by exchange

(electron exchange)

Imaginary part leading to annihilation:

2-body effective action

: state of pair: Relative distance

Introduce auxiliary fields:

: Center-of-mass coordinate

Integrate fields out 2-body effective action:

Let us replace by composite fields:

exchange Coulomb, centrifugal force

NR pair annihilation cross section for

The exact annihilation cross section:

The eq. of motion is the Shroedinger equation:

The optical theorem

Perturbative expansion of leads to usual loop expansion

We can treat non-perturtatively

Numerical resultfor

The annihilation cross section is significantly enhanced when and are degenerate The annihilation cross section is significantly enhanced when and are degenerate

4. Summary

UED models provide a viable CDM candidate:

LKP is naturally degenerate with other first KK modes in mass

KK dark matter annihilation cross section is significantly enhanced due to the threshold singularity in the NR limit, compared with that at the tree level

KK dark matter annihilation cross section is significantly enhanced due to the threshold singularity in the NR limit, compared with that at the tree level

The lightest Kaluza-Klein particle (LKP)

Future direction

Inclusion of other imaginary parts in potentials Consideration on effects caused by KK quarks and gluon mediated diagrams Re-estimation of the positron flux Investigation of annihilation cross sections to photons

This work is now in progress

[c.f. Bergstroem, Bringmann, Eriksson, Gustafsson (2004)]

Backup slides

Inclusion of