Sommerfeld Enhancement of DM Annihilation: Resonance Structure, Freeze-Out and CMB Spectral Bound

TL;DR

This paper analytically and numerically investigates the Sommerfeld enhancement in dark matter annihilation, exploring resonance structures, relic density implications, and constraints from CMB spectral distortions.

Contribution

It provides universal analytic expressions for the Sommerfeld boost factor across different potentials and performs detailed relic density and CMB distortion calculations.

Findings

Resonance patterns are universal across potentials.

Only a small parameter space is excluded by FIRAS constraints.

Numerical solutions match analytic expressions for the boost factor.

Abstract

In the last few years there has been some interest in WIMP Dark Matter models featuring a velocity dependent cross section through the Sommerfeld enhancement mechanism, which is a nonrelativistic effect due to massive bosons in the dark sector. In the first part of this article, we find analytic expressions for the boost factor for three different model potentials, the Coulomb potential, the spherical well and the spherical cone well and compare with the numerical solution of the Yukawa potential. We find that the resonance pattern of all the potentials can be cast into the same universal form. In the second part of the article we perform a detailed computation of the Dark Matter relic density for models having Sommerfeld enhancement by solving the Boltzmann equation numerically. We calculate the expected distortions of the CMB blackbody spectrum from WIMP annihilations and compare these to the bounds set by FIRAS. We conclude that only a small part of the parameter space can be ruled out by the FIRAS observations.