A Sommerfeld Toolbox for Colored Dark Sectors

TL;DR

This paper provides analytical formulas for Sommerfeld corrections to the annihilation of massive colored particles, crucial for precise dark matter relic density calculations, applicable to arbitrary spins and gauge groups.

Contribution

It introduces a comprehensive Sommerfeld correction formula for colored particles of any spin and color representation, including higher partial waves and general gauge groups.

Findings

Sommerfeld corrections can modify annihilation cross sections by 10-20% during freeze-out.

Formulas account for particle spin effects on wave function symmetry.

A Mathematica tool is provided for practical computations.

Abstract

We present analytical formulae for the Sommerfeld corrections to the annihilation of massive colored particles into quarks and gluons through the strong interaction. These corrections are essential to accurately compute the dark matter relic density for coannihilation with colored partners. Our formulae allow to compute the Sommerfeld effect, not only for the lowest term in the angular momentum expansion of the amplitude, but for all orders in the partial wave expansion. In particular, we carefully account for the effects of the spin of the annihilating particle on the symmetry of the two-particle wave function. This work focuses on strongly interacting particles of arbitrary spin in the triplet, sextet and octet color representations. For typical velocities during freeze-out, we find that including Sommerfeld corrections on the next-to-leading order partial wave leads to modifications of up to ten to twenty percent on the total annihilation cross section. Complementary to QCD, we generalize our results to particles charged under an arbitrary unbroken SU(N) gauge group, as encountered in dark glueball models. In connection with this paper a Mathematica notebook is provided to compute the Sommerfeld corrections for colored particles up to arbitrary order in the angular momentum expansion.