Efficient numerical integration of thermal interaction rates

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.