Significant enhancement of Binolike dark matter annihilation cross

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 ”

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

Introduction • Many observations indicate the existence of nonbaryonic 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. gov

Influential candidate for cold dark matter • 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. The composition of the lightest neutralino depends on SUSY breaking scenario.

Parameter in the CMSSM Higgsino-like DM region (constrained by WMAP) Bino–stau coannihilation region Bulk region Bino is degenerate We focus on this region !with stau so that coannihilation is Stau LSP region effective. J. Ellis et al. Phys. Lett. B 565 (2003) 176

Coannihilation If Bino is degenerate with stau, 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.

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

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

Cherenkov telescopes in the world

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. Flux m E Line spectrum is distinct signature against the diffused gamma ray background The observation of the line gamma rays strongly suggests the existence of DM.

We calculate the cross section of Bino dark matter pair annihilation to two gammas for indirect detection. We ① ② ③ consider the case that dark matter is Bino-like neutralino, Bino is degenerate with stau in mass, 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.

DM pair annihilation for indirect detection • DM pair annihilation to two gammas is radiative process. • The full one-loop calculations have been performed. 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.

CP violating process • 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. CP = - 1 in an S-wave CP = + 1 in an S-wave • On the other hand, when CP is conserved, Bino DM pair annihilates to stau-antistau state in a P-wave. suppressed by

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

CP Violating phase in the stau mass term • 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.

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

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

Summary • Heavy Bino dark matter is degenerate with stau in mass. • CP violating phase is in the stau mass term. 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.