Thermal production of Majorana fermions in the early Universe

Majorana fermions, spin 1/2 fermions which are their own antiparticles, play a prominent role in the evolution of the Universe, both as an essential ingredient for thermal leptogenesis and as potential dark matter candidates. Since the early universe was in the state of a hot and dense plasma, it is mandatory to take finite temperature effects into account to compute the resulting baryon asymmetry from leptogenesis, or the abundance of thermally produced dark matter particles. Yet a consistent computation to leading order in the coupling is still an open issue. As a first step to a consistent finite temperature treatment of thermal leptogenesis, we compute the thermal production rate of Majorana neutrinos whose decays create the lepton asymmetry, to leading order in the electroweak gauge and top Yukawa coupling. In particular we present a method to deal with the Landau-Pomeranchuk-Migdal (LPM) effect whose relevance in fermion production from (inverse) decays was overlooked so far. Our method is sufficiently general that it can also be applied to the production of other particles, such as e.g. axinos or gravitinos where the role of the LPM effect has never been studied either. To obtain the leading order production rate of Majorana neutrinos, we study in addition 2-body scattering processes and show how to cure the arising IR divergencies with the so-called Braaten-Yuan prescription.