Sterile neutrino rates for general $M$, $T$, $\mu$, $k$: review of a theoretical framework

TL;DR

This paper reviews a comprehensive theoretical framework for calculating sterile neutrino rates across various mass and temperature regimes, providing integral representations and gauge-independent expressions crucial for understanding leptogenesis.

Contribution

It introduces a unified set of integral representations for rate coefficients and mass corrections applicable to all regimes, including the intermediate case where M is comparable to πT, filling a gap in existing effective theory methods.

Findings

Provides gauge-independent rate expressions in all regimes.

Offers integral representations extrapolating to known limits.

Guides towards numerical evaluation of sterile neutrino rates.

Abstract

The temperature of sphaleron freeze-out, $T\approx 130$ GeV, sets a scale for mechanisms for generating lepton asymmetries and converting them to baryon asymmetry (leptogenesis). For Majorana masses $M \gg \pi T$, leptogenesis takes place in the non-relativistic regime, while for $M \ll \pi T$, the dynamics is ultrarelativistic. The intermediate case $M \sim \pi T$ is the most cumbersome, as no effective theory methods are available. We review the definitions of and provide integral representations for all rate coefficients and mass corrections of $\mathcal{O}(h_\nu^2)$ in this regime, such that the expressions extrapolate to known limits and are gauge independent to the order computed, both in the symmetric and the Higgs phase, for any helicity, momentum, and set of chemical potentials. Road signs towards a numerical evaluation are offered.