New Kinetic Equation for Pair-annihilating Particles: Generalization of the Boltzmann Equation

TL;DR

This paper derives a generalized kinetic equation for pair-annihilating particles, incorporating off-shell effects, to improve dark matter relic abundance calculations in cosmology.

Contribution

It introduces a new kinetic equation extending the Boltzmann equation with off-shell effects, enhancing dark matter relic abundance modeling.

Findings

Supports previous thermal field theory results for equilibrium abundance

Provides temperature dependence of equilibrium value at low temperatures

Enables relic abundance estimation via sudden freeze-out approximation

Abstract

A convenient form of kinetic equation is derived for pair annihilation of heavy stable particles relevant to the dark matter problem in cosmology. The kinetic equation thus derived extends the on-shell Boltzmann equation in a most straightforward way, including the off-shell effect. A detailed balance equation for the equilibrium abundance is further analyzed. Perturbative analysis of this equation supports a previous result for the equilibrium abundance using the thermal field theory, and gives the temperature power dependence of equilibrium value at low temperatures. Estimate of the relic abundance is possible using this new equilibrium abundance in the sudden freeze-out approximation.