Self-consistent Calculation of the Sommerfeld Enhancement

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.