Thermal abundance of non-relativistic relics with Sommerfeld enhancement

TL;DR

This paper develops an analytic method to accurately compute the relic abundances of non-relativistic particles with Sommerfeld-enhanced annihilation rates, achieving high precision in predictions.

Contribution

It introduces approximate rational functions for thermally-averaged Sommerfeld-enhanced cross sections, enabling precise relic abundance calculations with standard analytic methods.

Findings

Approximate rational functions fit Sommerfeld-enhanced cross sections within 1% accuracy.

Standard analytic relic abundance calculations remain accurate with Sommerfeld enhancement.

Method applies to massless force carriers in s- and p-wave annihilations.

Abstract

We propose an analytic treatment for computing the relic abundances of non-relativistic particles whose annihilation rate at chemical decoupling is increased by Sommerfeld enhancement. We find approximate rational functions that closely fit the thermal average of Sommerfeld-enhanced cross sections in the massless limit of force carriers for s- and p-wave annihilations. We demonstrate that, with the approximate thermally-averaged cross sections implemented, the standard analytic method for the final relic abundances provides accuracy to within 1% even for the case of Sommerfeld enhancement.