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

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 0121\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left(0,\frac{1}{2},1\right) $$\end{document} 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.