Significant enhancement of Bino-Significant enhancement of Bino-like dark matter annihilation cross like dark matter annihilation cross

section due to section due to CP violationCP violation

Yoshio Sato (Saitama University)

Collaborated withShigeki Matsumoto (ICRR, University of Tokyo)

Joe Sato (Saitama University)

Jan. 14. 2005YITP 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

• 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.

WMAPhttp://map.gsfc.nasa.gov

IntroductionIntroduction

• 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.

Stau LSP region

Bulk region

Bino–stau coannihilation region

J. Ellis et al. Phys. Lett. B565 (2003) 176

129.0094.0 2 h

Bino is　degenerate with stau so that coannihilation is effective.

Higgsino-like DM region

We focus on this region !We focus on this region !

(constrained by WMAP)

Parameter in the CMSSM

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

• Direct detection

• Indirect detection

- Cosmic gamma rays

- High energy neutrinos from the Sun

- Positron and anti-proton excess

Dark matter searches

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

Cherenkov telescopes in the worldCherenkov 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.

The observation of the line gamma The observation of the line gamma

raysrays　　 strongly strongly suggests the suggests the existence of DM.existence of DM.

Line spectrum is distinct signature against the diffused gamma ray background

Flux

Em

We calculate the cross section of We calculate the cross section of Bino dark matter pair annihilation to Bino dark matter pair annihilation to two gammas for indirect detection.two gammas for indirect detection.

We consider the case that① 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.

• DM pair annihilation to two gammas is radiative process.

• The full one-loop calculations have been performed.

DM pair annihilation for indirect DM pair annihilation for indirect detectiondetection

L. Bergstroem and P. Ullio 　　 NPB 504, 27 (1997)

ButBut, in this case that we consider, the cross , in this case that we consider, the cross section can be much larger than the one-loop section can be much larger than the one-loop calculation.calculation.

• 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 = - 1in an S-wave

CP = + 1in an S-wave

suppressed by

CP violating processCP violating process

• 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.The higher-order calculation becomes important.

almost on-shellnon-relativistic >1

• 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

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 calculationThe method of calculation

non-relativistic limit

introduce the auxiliary fields for two-body state

optical theorem

Numerical ResultNumerical Result

1-loop @ 300GeV

1-loop @ 1 TeV

parameters

:Sfermion mixing parameter

: CP phase of

Our result is much larger than the one-loop Our result is much larger than the one-loop calculation at the typical DM velocity.calculation at the typical DM velocity.

• Heavy Bino dark matter is degenerate with stau in mass.

• CP violating phase is in the stau mass term .

SummarySummary

　　 For sizable parameter, the cross section of For sizable parameter, the cross section of

heavy Bino DM pair annihilation to two heavy Bino DM pair annihilation to two

gammas is enhanced due to the threshold gammas is enhanced due to the threshold

singularity, compared with the one-loop singularity, compared with the one-loop

calculation.calculation.