NLO thermal corrections to dark matter annihilation cross sections: a novel approach

The dark matter relic density has been increasingly accurately measured by successive generations of experiments. The Boltzmann equation determines the yields using the dark matter annihilation cross section as one of the inputs; the accurate computation of the latter including thermal contributions thus assumes importance. We report here the next-to-leading order (NLO) thermal corrections to the cross sections for (Majorana) dark matter annihilation to standard model fermions: $\chi \chi \to f \overline{f}$, via charged scalars. We use a novel approach, utilising the technique of Grammer and Yennie, extended to thermal field theories, where the cancellation of soft infra-red divergences occurs naturally. We present the NLO thermal cross sections in full detail for both the relativistic case as well as in the non-relativistic limit. Our independent calculation verifies earlier results where the leading contribution at order ${\cal{O}}(T^2)$ was shown to be proportional to the square of the fermion mass in the non-relativistic limit, just as at leading order. We find that the ${\cal{O}}(T^4)$ contributions have the same dependence on the fermion mass as well.