Right-Handed Neutrino Production at Finite Temperature: Radiative Corrections, Soft and Collinear Divergences

TL;DR

This paper calculates the sterile neutrino production rate at finite temperature, demonstrating the cancellation of divergences at next-to-leading order using the Closed-Time-Path approach, relevant for leptogenesis and other relativistic transport phenomena.

Contribution

It provides a finite, gauge-invariant calculation of neutrino production rates including radiative corrections without non-relativistic approximations.

Findings

Soft, collinear, and Bose divergences cancel at NLO.

The inclusive rate is finite and gauge-invariant.

Results apply to general neutrino momenta in plasma.

Abstract

The production and decay rate of massive sterile neutrinos at finite temperature receives next-to-leading order corrections from the gauge interactions of lepton and Higgs doublets. Using the Closed-Time-Path approach, we demonstrate that the perturbatively obtained inclusive rate is finite. For this purpose, we show that soft, collinear and Bose divergences cancel when adding the tree-level rates from 1<->3 and 2<->2 processes to vertex and wave-function corrections to 1<->2 processes. These results hold for a general momentum of the sterile neutrino with respect to the plasma frame. Moreover, they do not rely on non-relativistic approximations, such that the full quantum-statistical effects are accounted for to the given order in perturbation theory. While the neutrino production rate is of relevance for Leptogenesis, the proposed methods may as well be suitable for application to a more general class of relativistic transport phenomena.