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.

48 pages, programs as ancillary files. v2: clarifications added