1. Significant enhancement of Bino-like dark matter annihilation cross section due to CP violation Yoshio Sato (Saitama University) Collaborated with Shigeki Matsumoto (ICRR, University of Tokyo) Joe Sato (Saitama University) Jan. 14. 2005 YITP workshop on “ CP violation and Matter and anti-matter asymmetry ”

2. Plan of Talk Introduction Dark matter pair annihilation for indirect detection CP violating process in Bino pair annihilation The method of calculation Numerical Result Summary

3. Many observations indicate the existence of non- baryonic dark matter (DM). Next question is what the constituent of non-baryonic DM is. A study of the beyond standard model (SM) is mandatory. WMAP http://map.gsfc.nasa.govIntroduction

4. In the Minimal Supersymmetric Standard Model (MSSM), the lightest neutralino is a candidate for non-baryonic DM. Neutralino is a linear combination of SUSY particle. R-parity conservation ensures the stability of the lightest neutralino. Influential candidate for cold dark matter The composition of the lightest neutralino depends on SUSY breaking scenario.

5. Stau LSP region Bulk region Bino–stau coannihilation region J. Ellis et al. Phys. Lett. B565 (2003) 176 Bino is degenerate with stau so that coannihilation is effective. Higgsino-like DM region We focus on this region ! (constrained by WMAP) Parameter in the CMSSM

6. 1.When Bino freeze out, the number of stau is almost same as Bino. 2.The number of Bino decrease compared with the case when Bino is not degenerate with stau. 3.To satisfy the relic abundance, Bino must be heavy. If Bino is degenerate with stau, Coannihilation

7. Direct detection Indirect detection - Cosmic gamma rays - High energy neutrinos from the Sun - Positron and anti-proton excess Dark matter searches

8. Halo Dark Matter (Halo) is associated with the galaxy, and distributes spherically. DM accumulates in the Galactic center. bulge = solar system The Milky Way (Our Galaxy) disk Where is dark matter in the current Universe? The typical velocity of DM

9. Cherenkov telescopes in the world

10. Gamma ray detection from the DM pair annihilation Gamma rays from DM pair annihilation have a line spectrum. The diffused gamma ray background induced from astrophysical sources has a continuum spectrum. The observation of the line gamma rays strongly suggests the existence of DM. Line spectrum is distinct signature against the diffused gamma ray background Flux E m

11. We calculate the cross section of Bino dark matter pair annihilation to two gammas for indirect detection. We consider the case that ① dark matter is Bino-like neutralino, ② Bino is degenerate with stau in mass, ③ CP violating phase is in the stau mass matrix. We found that the cross section of Bino pair annihilation to two gammas can be enhanced due to the threshold singularity, compared with the one-loop calculation.

12. DM pair annihilation to two gammas is radiative process. The full one-loop calculations have been performed. DM pair annihilation for indirect detection L. Bergstroem and P. Ullio NPB 504, 27 (1997) But, in this case that we consider, the cross section can be much larger than the one-loop calculation.

13. When CP is violated, the transition between Bino two-body state in an S-wave and stau-antistau state in an S-wave can take place. On the other hand, when CP is conserved, Bino DM pair annihilates to stau-antistau state in a P-wave. CP = - 1 in an S-wave CP = + 1 in an S-wave suppressed by CP violating process

14. Ladder diagrams of photon exchange The higher-order contributions are enhanced due to the threshold singularity. Threshold singularity in the CP violating process The higher-order calculation becomes important. almost on-shell non-relativistic >1

15. Stau mass matrix CP violating phase cannot be in, but can still be in. We consider the case that the CP violating phase is only in the. CP Violating phase in the stau mass term

16. i)Effective action for Bino and stau ii)Non-relativistic Lagrangian iii)Bino and stau two-body states effective action iv)Equation of motion (= Schroedinger equation) for Bino and stau two-body states v)Annihilation cross section The method of calculation non-relativistic limit introduce the auxiliary fields for two-body state optical theorem

17. Numerical Result 1-loop @ 300GeV 1-loop @ 1 TeV parameters :Sfermion mixing parameter : CP phase of Our result is much larger than the one-loop calculation at the typical DM velocity.

18. Heavy Bino dark matter is degenerate with stau in mass. CP violating phase is in the stau mass term. Summary For sizable parameter, the cross section of heavy Bino DM pair annihilation to two gammas is enhanced due to the threshold singularity, compared with the one-loop calculation. For sizable parameter, the cross section of heavy Bino DM pair annihilation to two gammas is enhanced due to the threshold singularity, compared with the one-loop calculation.