Efficient numerical integration of thermal interaction rates

TL;DR

This paper introduces an algorithm for efficiently computing thermal interaction rates in particle cosmology, accounting for virtual corrections and resummation effects, applicable to general momenta, masses, and chemical potentials.

Contribution

It presents a novel automated method to evaluate thermal 2↔2 and 1↔3 interaction rates, including virtual corrections and IR divergence elimination, for diverse particle parameters.

Findings

Algorithm effectively regularizes IR divergences.

Inclusion of virtual corrections improves accuracy.

Applicable to a wide range of particle parameters.

Abstract

In many problems in particle cosmology, interaction rates are dominated by ${2}\leftrightarrow{2}$ scatterings, or get a substantial contribution from them, given that ${1}\leftrightarrow{2}$ and ${1}\leftrightarrow{3}$ reactions are phase-space suppressed. We describe an algorithm to represent, regularize, and evaluate a class of thermal ${2}\leftrightarrow{2}$ and ${1}\leftrightarrow{3}$ interaction rates for general momenta, masses, chemical potentials, and helicity projections. A key ingredient is an automated inclusion of virtual corrections to ${1}\leftrightarrow{2}$ scatterings, which eliminate logarithmic and double-logarithmic IR divergences from the real ${2}\leftrightarrow{2}$ and ${1}\leftrightarrow{3}$ processes. We also review thermal and chemical potential induced contributions that require resummation if plasma particles are ultrarelativistic.