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 \( \left(0,\frac{1}{2},1\right) \) 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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Acknowledgments
I am grateful to B. Grzadkowski for encouraging me to write this paper and for discussions concerning it. I would also like to thank Károly Seller for a fruitful discussion and bringing my attention to the papers [13–15]. I thank St. Mrówczyński for enabling me to familiarize myself with [19].
This work has been partially supported by the National Science Centre (Poland) under
grants 2017/25/B/ST2/00191 and 2020/37/B/ST2/02746.
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Iglicki, M. Thermal regularization of t-channel singularities in cosmology and particle physics: the general case. J. High Energ. Phys. 2023, 6 (2023). https://doi.org/10.1007/JHEP06(2023)006
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DOI: https://doi.org/10.1007/JHEP06(2023)006