Towards leptogenesis at NLO: the right-handed neutrino interaction rate

We compute quantum and thermal corrections to the right-handed neutrino interaction rate in the early universe at next-to-leading order in all the relevant SM couplings (gauge, top Yukawa and higgs couplings). Previous computations considered 2 -> 2 scatterings, finding infra-red divergences. The KLN theorem demands that infra-red divergences cancel in the full result: after adding 1 -> 3 and one-loop virtual corrections that enter at the same order we find a simple result.