Thermal production of relativistic Majorana neutrinos: Strong enhancement by multiple soft scattering

TL;DR

This paper addresses thermal production of relativistic Majorana neutrinos in the early Universe to inform leptogenesis. It develops a leading-order, all-orders resummation of collinear emissions mediated by soft gauge interactions (an LPM-like approach) to capture $N$ production beyond tree-level Higgs decay and inverse decay. The authors derive an integral equation for the Majorana self-energy that sums ladder diagrams with soft SU(2)×U(1) exchanges, yielding a production rate that is smooth across kinematic thresholds and enhanced by about a factor of 3 at high temperatures. The results show helicity-changing channels dominate at $T\gg M_N$ and produce an infrared-peaked, non-thermal spectrum for the emitted neutrinos, providing a crucial input for accurate leptogenesis calculations. They also outline how soft-gauge contributions could be combined with $2\leftrightarrow 2$ scattering processes for a more complete leading-order treatment.

Abstract

The production rate of heavy Majorana neutrinos is relevant for models of thermal leptogenesis in the early Universe. In the high temperature limit the production can proceed via the 1 <-> 2 (inverse) decays which are allowed by the thermal masses. We consider new production mechanisms which are obtained by including additional soft gauge interactions with the plasma. We show that an arbitrary number of such interactions gives leading order contributions, and we sum all of them. The rate turns out to be smooth in the region where the 1 <-> 2 processes are kinematically forbidden. At higher temperature it is enhanced by a factor 3 compared to the 1 <-> 2 rate.

Figures (8)

• Figure 1: The imaginary part of this diagram gives the production rate due to decay and inverse decay processes. This diagram also determines the inhomogeneous term in Eq. (\ref{['72']}).
• Figure 2: Decay and inverse decay processes that contribute to the production of Majorana neutrinos.
• Figure 3: Example for two processes whose interference needs to be taken into account in a consistent leading order treatment.
• Figure 4: Example for a self-energy diagram whose imaginary part contributes to the leading order production rate.
• Figure 5: 1-loop diagrams with soft external gauge field lines. Only the 2-point function Fig. \ref{['fg:2point']} needs to be calculated explicitly. The $n$-point functions with $n > 2$ are related to the $( n -1 )$-point functions by a recursion relation.