Thermal right-handed neutrino production rate in the relativistic regime

TL;DR

This paper calculates the production rate of right-handed neutrinos in a hot plasma at high temperatures, extending previous results to the relativistic regime and providing insights for leptogenesis models.

Contribution

It generalizes NLO production rate calculations to the relativistic regime, bridging non-relativistic and ultrarelativistic limits with improved accuracy.

Findings

Non-relativistic expansion converges for M > 15 T

Loop corrections are small, valid for M > 4 T

Mass resummation aligns with LPM resummation results

Abstract

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 ~ 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 > 15 T, but the smallness of any loop corrections allows it to be used in practice already for M > 4 T. 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.