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 left(0,frac{1}{2},1right) 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.
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