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In this paper, we will apply the Goldstone equivalence gauge to calculate the$1 \leftrightarrow 2$ processes of a sterile neutrino in the thermal plasmabelow 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 averagedeffective width $\bar{\Gamma}_{\text{tot}}$ is continuous around thecross-over. We will also apply our results to perform a preliminary calculationof the leptogenesis.

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