Calculations of the Sommerfeld Effect in a Unified Wave Function Framework

TL;DR

This paper introduces a unified wave function framework for accurately calculating the Sommerfeld effect in dark matter annihilation, covering both s-wave and p-wave cases with complete formulas.

Contribution

It presents a novel method using equal-time Beth-Salpeter wave functions to comprehensively compute Sommerfeld effects in dark matter interactions.

Findings

Derived complete formulas for cross sections with Sommerfeld effects

Unified treatment of s-wave and p-wave annihilation scenarios

Provides a systematic approach for future dark matter studies

Abstract

In this paper, we suggest a method of a complete calculation of the Sommerfeld effect in both the s-wave and p-wave annihilation situations. The basic idea is to uniformly consider the equal-time Beth-Salpeter wave functions of both the dark matter and the final state particles, then short-distance interactions can be parametrized as a cross-term considering the equations. Solving these equations will result in the complete formulas of the cross sections with the Sommerfeld effects.