Thermal right-handed neutrino production rate in the relativistic regime

The production rate of right-handed neutrinos from a Standard Model plasma at a temperature above a hundred GeV is evaluated up to NLO in Standard Model couplings. The results apply in the so-called relativistic regime, referring parametrically to a mass M similar to pi T, generalizing thereby previous NLO results which only apply in the non-relativistic regime M >> pi T. The non-relativistic expansion is observed to converge for M greater than or similar to 15T, but the smallness of any loop corrections allows it to be used in practice already for M greater than or similar to 4T. In the latter regime any non-covariant dependence of the differential rate on the spatial momentum is shown to be mild. The loop expansion breaks down in the ultrarelativistic regime M << pi T, but after a simple mass resummation it nevertheless extrapolates reasonably well towards a result obtained previously through complete LPM resummation, apparently confirming a strong enhancement of the rate at high temperatures (which facilitates chemical equilibration). When combined with other ingredients the results may help to improve upon the accuracy of leptogenesis computations operating above the electroweak scale.