$1\leftrightarrow 2$ processes of a sterile neutrino around the electroweak scale in a thermal plasma

In this paper, we apply the Goldstone equivalence gauge to calculate the $1\leftrightarrow 2$ processes of a sterile neutrino in a thermal plasma below the standard model (SM) critical temperature $T_c\approx 160\mathrm{GeV}$. The sterile neutrino’s mass is around the electroweak scale, $50\mathrm{GeV}\le m_N\le 200\mathrm{GeV}$, and the acquired thermal averaged effective width ${\overline{\mathrm{\Gamma }}}_{\mathrm{tot}}$ does not depend on the gauge selection and is continuous around the crossover. We also apply our results to perform a preliminary calculation of leptogenesis.

Figure 1

$N\to W^{+}{l}^{-}$ $1\leftrightarrow 2$ channel. Since we have applied the Goldstone equivalence gauge, the Goldstone contribution is explicitly contained in the polarization vector, so we also need to calculate the Goldstone part of the diagrams.

Figure 2

$N\to (Z/\gamma )\nu 1\leftrightarrow 2$ channel.

Figure 3

$N\to h\nu 1\leftrightarrow 2$ channel.

Figure 4

Thermal averaged widths plot normalized by $\frac{1}{|y_N{|}^2}$ for $m_N=50$, 100, 150, 200 GeV masses. The meanings in the legends are illustrated in Table 1.

Figure 5

${\overline{\mathrm{\Gamma }}}_{\mathrm{tot}}={\sum }_X{\overline{\mathrm{\Gamma }}}_X$ normalized by $\frac{1}{|y_N{|}^2}$, depending on the temperature $T$ and the sterile neutrino mass $m_N$. To keep the image contrast in the other areas where the $1\leftrightarrow 2$ processes are not suppressed kinematically, we just keep $\frac{{\overline{\mathrm{\Gamma }}}_{\mathrm{tot}}}{|y_N{|}^2}\ge 1.0\times {10}^{-3}\mathrm{GeV}$ in this image. Therefore, most of the red parts in this image are actually much smaller than those plotted here.

Figure 6

$\lg {\epsilon }_{\mathrm{CP}}$ needed to obtain successful leptogenesis. The sterile neutrinos are initially in thermal equilibrium with the plasma.