Radiative corrections to vectorlike portal dark matter

A massive real scalar dark matter particle $S$ can couple to Standard Model leptons or quarks through a vector-like fermionic mediator $\psi$, a scenario known as the Vector-like portal. Due to helicity suppression of the annihilation cross section into a pair of SM fermions, it has been shown in previous works that radiative corrections, either at one-loop or through radiation of gauge bosons, may play a significant role both in determining the relic abundance and for indirect detection. All previous works considered the limit of massless final state quarks or leptons. In this work, we focus on a technical issue, which is to reliably determine the annihilation cross sections taking into account finite fermion masses. Following previous works in the framework of simplified supersymmetric dark matter scenarios, and building on an analogy with Higgs decay into fermions, we address the issue of infrared and collinear divergences that plagues the cross section by adopting an effective operator description, which captures most of the relevant physics and give explicit expressions for the annihilation cross sections. We then develop several approximations for the differential and total cross sections, which simplify greatly their expressions, and which can then be used in various phenomenological studies of similar models. Finally, we describe our method to compute the final gamma-ray spectrum, including hadronisation of the heavy fermions, and provide some illustrative spectra for specific dark matter candidates.