Self-consistent Calculation of the Sommerfeld Enhancement

TL;DR

This paper presents a self-consistent method for calculating the Sommerfeld enhancement in dark matter annihilation, accurately incorporating short-range scattering effects and ensuring unitarity, with analytic solutions for relevant potentials.

Contribution

It introduces a novel, consistent approach that combines short-range and long-range interactions in the Sommerfeld enhancement calculation, improving upon previous methods.

Findings

Method satisfies partial-wave unitarity

Provides analytic results for key potentials

Enhances accuracy of dark matter annihilation models

Abstract

A calculation of the Sommerfeld enhancement is presented and applied to the problem of s-wave non-relativistic dark matter annihilation. The difference from previous computations in the literature is that the effect of the underlying short-range scattering process is consistently included together with the long-range force in the effective QM Schr\"odinger problem. Our procedure satisfies partial-wave unitarity where previous calculations fail. We provide analytic results for some potentials of phenomenological relevance.