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The production and decay rate of massive sterile neutrinos at finitetemperature receives next-to-leading order corrections from the gaugeinteractions of lepton and Higgs doublets. Using the Closed-Time-Path approach,we demonstrate that the perturbatively obtained inclusive rate is finite. Forthis purpose, we show that soft, collinear and Bose divergences cancel whenadding the tree-level rates from 1<->3 and 2<->2 processes to vertex andwave-function corrections to 1<->2 processes. These results hold for a generalmomentum of the sterile neutrino with respect to the plasma frame. Moreover,they do not rely on non-relativistic approximations, such that the fullquantum-statistical effects are accounted for to the given order inperturbation theory. While the neutrino production rate is of relevance forLeptogenesis, the proposed methods may as well be suitable for application to amore general class of relativistic transport phenomena.

Right-Handed Neutrino Production at Finite Temperature: Radiative Corrections, Soft and Collinear Divergences