Thermal production rate of non-relativistic Majorana neutrinos in an effective field theory framework

Abstract

Heavy Majorana neutrinos represent an attempt to explain the smallness of the nu_e, nu_mu and nu_tau masses via the See-Saw mechanism. Moreover heavy Majorana neutrinos have been considered to play a relevant role in the dark matter problem and the leptogenesis mechanism as well. In the latter a heavy Majorana neutrino decays within a hot and dense plasma of particles producing an imbalance of leptons and anti-leptons. Hence a thermal treatment is needed and we focus here on the temperature regime M>>T, which may be relevant for the leptogenesis scenario. Building on QCD thermal field theory methods, we develop an effective theory for non-relativistic Majorana neutrinos which simplifies computations in a thermal medium of standard model particles. As a proof of concept, we perform the computation of the decay rate for the Majorana neutrinos to test our effective Lagrangian, reproducing a result already known in the literature. Moreover the present effective field theory approach may be considered within different models involving non-relativistic Majorana fermions.