Thermal production of ultrarelativistic right-handed neutrinos: Complete leading-order results

TL;DR

This work completes the leading-order calculation of the thermal production rate of ultrarelativistic right-handed Majorana neutrinos in the symmetric phase of the electroweak theory, valid for $M_N \ll T$. It combines the previously analyzed $1 \leftrightarrow 2$ (and inverse) decays with soft gauge exchanges and the full set of $2 \to 2$ scatterings involving electroweak gauge bosons and third-generation quarks, employing HTL resummation and ladder resummation techniques. A compact analytic form for the $2 \to 2$ rate is derived, with gauge-boson contributions parameterized by constants $c_Q$ and $c_V$, and a new sum rule for the HTL-resummed fermion propagator is established. The results show that gauge interactions dominate the LO production rate across a wide temperature range, with a transition from $1 \leftrightarrow 2$-dominated at low $T$ to $2 \to 2$-dominated at high $T$, providing a crucial input for leptogenesis kinetics and CP asymmetry calculations.

Abstract

The thermal production of relativistic right-handed Majorana neutrinos is of importance for models of thermal leptogenesis in the early Universe. Right-handed neutrinos can be produced both by 1 <-> 2 decay or inverse decay and by 2 -> 2 scattering processes. In a previous publication, we have studied the production via 1 <-> 2 (inverse) decay processes. There we have shown that multiple scattering mediated by soft gauge boson exchange also contributes to the production rate at leading order, and gives a strong enhancement. Here we complete the leading order calculation by adding 2 -> 2 scattering processes involving either electroweak gauge bosons or third-generation quarks. We find that processes with gauge interactions give the most important contributions. We also obtain a new sum rule for the Hard Thermal Loop resummed fermion propagator.

Figures (7)

• Figure 1: Leading order contributions to the production of right-handed neutrinos $N$. ($a$) Decay and recombination processes which occur when the asymptotic thermal masses are such that they are kinematically allowed. ($b$) Examples for processes, where exchanges of soft gauge bosons with particles in the plasma have been added. Higgs bosons are denoted with a dashed line and gauge bosons with a wiggled line. Fermions are represented by solid lines.
• Figure 2: $2 \to 2$ scattering contributions to Majorana neutrino production.
• Figure 3: Example for a self-energy diagram that needs to be taken into account in a consistent leading order calculation of the production rate via Eq. (\ref{['rate']}).
• Figure 4: One-loop self-energy diagram of the Majorana neutrino. The black dot indicates that the lepton propagator is HTL resummed.
• Figure 5: Dependence of the production rate on $z$ for $M _ N = 10 ^ 7$ GeV.