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