$1 \leftrightarrow 2$ Processes of a Sterile Neutrino Around Electroweak Scale in the Thermal Plasma

Abstract

In this paper, we will apply the Goldstone equivalence gauge to calculate the $1 \leftrightarrow 2$ processes of a sterile neutrino in the thermal plasma below the standard model (SM) critical temperature $T_c \approx 160 \text{ GeV}$. The sterile neutrino's mass is around the electroweak scale $50 \text{ GeV} \leq m_N \leq 200 \text{ GeV}$, and the acquired thermal averaged effective width $\bar{\Gamma}_{\text{tot}}$ is continuous around the cross-over. We will also apply our results to perform a preliminary calculation of the leptogenesis.