Limits on Threshold and "Sommerfeld" Enhancements in Dark Matter Annihilation

TL;DR

This paper establishes model-independent upper limits on dark matter annihilation rates, demonstrating that common enhancements like Sommerfeld factors are ineffective, and highlights the significance of small decay widths in saturating unitarity bounds.

Contribution

It provides a comprehensive analysis showing that Sommerfeld enhancements are invalid and identifies small decay widths as the primary mechanism for high annihilation rates.

Findings

Sommerfeld factors do not significantly enhance annihilation cross sections.

Small decay widths can saturate unitarity bounds on annihilation rates.

Wave function normalization effects are minimal in bound state formation.

Abstract

We find model-independent upper limits on rates of dark matter annihilation in galactic halos. The Born approximation generally fails, while exotic threshold enhancements akin to "Sommerfeld factors" also turn out to be baseless The most efficient annihilation mechanism involves perturbatively small decay widths that have largely been ignored. Widths that are very small compared to TeV mass scales suffice to effectively saturate unitarity bounds on annihilation rates. Bound state formation in weakly coupled theories produces small effects due to wave function normalizations. Unitarity shows the Sommerfeld factor cannot produce large changes in cross sections, and serves to identify where those approximations break down.