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.
Highlights
Gauge-singlet right-handed neutrinos is a natural candidate
In the so-called non-relativistic regime πT ≪ M, next-to-leading order (NLO) corrections can be computed and are in general small [12, 13], in accordance with expectations based on the Operator Product Expansion (OPE) [14]
In addition the structure of the differential production rate is analyzed with the goal of suggesting a numerically affordable and yet relatively accurate approximation scheme that may be used in practical applications
Summary
3.1 Strict NLO expression Each of the master spectral functions can be split into two parts: ρIx = ρvIaxc + ρTIx. The first term must include all divergences, and may be chosen to include finite parts as well. We note that denoted by ρvIaxc, this structure does have an overall temperature dependence, of the same functional form as the leading-order (LO) result which it renormalizes. The purely thermal part ρTIx is, in contrast, finite and of a more complicated functional form. With the choices of ρvIaxc explained in appendix B, we obtain a finite. A numerical evaluation of this expression is shown in figure 1 (parameters and the renormalization scale are chosen as explained in appendix C). Based on this plot one might conclude that loop corrections decrease the production rate but, as will become apparent in section 3.3, such a conclusion is premature
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