Relic density computations at NLO: infrared finiteness and thermal correction

TL;DR

This paper addresses the challenge of accurately computing dark matter relic density at NLO by systematically analyzing finite-temperature effects and demonstrating the cancellation of infrared divergences, thus justifying the conventional freeze-out approach.

Contribution

It provides a systematic method to include finite-temperature corrections in NLO relic density calculations and shows the cancellation of infrared divergences in a realistic model.

Findings

Infrared divergences cancel at finite temperature in the collision term.

Finite-temperature corrections to annihilation cross sections are derived.

The conventional freeze-out equation remains justified at NLO.

Abstract

There is an increasing interest in accurate dark matter relic density predictions, which requires next-to-leading order (NLO) calculations. The method applied up to now uses zero-temperature NLO calculations of annihilation cross sections in the standard Boltzmann equation for freeze-out, and is conceptually problematic, since it ignores the finite-temperature infrared (IR) divergences from soft and collinear radiation and virtual effects. We address this problem systematically by starting from non-equilibrium quantum field theory, and demonstrate on a realistic model that soft and collinear temperature-dependent divergences cancel in the collision term. Our analysis provides justification for the use of the freeze-out equation in its conventional form and determines the leading finite-temperature correction to the annihilation cross section. This turns out to have a remarkably simple structure.