Thermal regularization of t-channel singularities in cosmology and particle physics: the general case

TL;DR

This paper introduces a method to regularize t-channel singularities in particle interactions within a thermal medium, making cross sections finite by incorporating a temperature-dependent width for mediators of any spin.

Contribution

It provides a general analytical framework for regularizing t-channel singularities for particles of any spin in thermal environments, including a derivation of the width and an application to dark matter models.

Findings

Derived analytical expression for the thermal width of mediators.

Demonstrated the regularization method in a Vector-Fermion Dark Matter model.

Showed the cross sections become finite with the introduced width.

Abstract

This paper presents a~way to regularize the $t$-channel singularity (which appears when a~massive, stable $t$-channel mediator of a~given process is allowed to be on-shell, making the cross section infinite) in a~general case of particles of any spin (0,~\nicefrac12,~1) interacting within a~thermal medium. Those interactions result in a~finite lifetime of the mediator and allow to introduce an~effective momentum- and temperature-dependent width. As a result, the would-be-singular cross section becomes finite. A~complete derivation and an analytical result for the width are provided. For an illustration, the method is used to calculate the thermal widths and cross sections within the~Vector-Fermion Dark Matter model.