Thermal right-handed neutrino production rate in the non-relativistic regime

TL;DR

This paper calculates the next-to-leading order thermal production rate of heavy right-handed neutrinos in the non-relativistic regime, confirming previous results and extending the analysis to higher orders and momentum dependence.

Contribution

It introduces a new OPE-based approach, extends the non-relativistic expansion to the next order, and computes NNLO effects, providing a comprehensive framework for neutrino production rates.

Findings

Confirmed the structure of previous NLO results

Extended analysis to next order in non-relativistic expansion

Revealed leading momentum dependence and NNLO sensitivity

Abstract

We consider the next-to-leading order thermal production rate of heavy right-handed neutrinos in the non-relativistic regime m_top < pi*T << M, where m_top refers to the electroweak scale. Rephrasing the problem in an OPE language and making use of different techniques than a previous analysis by Salvio et al, we confirm the general structure of their result and many of the coefficients. We also extend the analysis to the next order in the non-relativistic expansion, thereby revealing the leading non-trivial momentum dependence, as well as to NNLO in couplings, revealing the leading sensitivity to thermal resummations. Our results are expressed as a sum of simple "master" structures, which renders them a suitable starting point for determining the next-to-leading order rate also in the relativistic regime pi*T ~ M.