1. Large enhancement of KK dark matter annihilation rate due 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

2. １． Motivation 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)]

3. 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

4. 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

5. Positron detection The milky way In the neighborhood of our solar system: (Almost at rest) Dark matter halo DM Primary is monoenergetic: signal is broadened during propagation: Flux

6. 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)]

7. Purpose 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)]

8. Contents 1.Motivation 2.Universal extra dimension (UED) 3.Annihilation cross section of KK dark matter 4.Threshold cross section in the NR limit 5.Summary

9. 2. Universal extra dimension Idea: 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:

10. 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 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 :

11. 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

12. 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:

13. 4. Threshold cross section in the NR limit Higher 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

14. Strategy 1.5-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

15. 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

16. Non-relativistic approximation Definition of non-relativistic field: NR region: Non-relativistic : On-shell Particle Anti-particle

17. Non-relativistic action Kinetic terms Coulomb potential generated by exchange (electron exchange) Imaginary part leading to annihilation:

18. 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

19. 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

20. Numerical result for The annihilation cross section is significantly enhanced when and are degenerate

21. 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 The lightest Kaluza-Klein particle (LKP)

22. 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)]

23. Backup slides

24. Inclusion of