Kadanoff-Baym approach to the thermal resonant leptogenesis

Using the non-equilibrium Green function method (Kadanoff-Baym equations) in the expanding universe, we investigate evolution of the lepton number asymmetry when the right-handed (RH) neutrinos have almost degenerate masses \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ |M_i^2-M_j^2| \ll M_i^2 $$\end{document}. The resonantly enhanced CP-violating parameter εi associated with the decay of the RH neutrino Ni is obtained under an assumption that the off-diagonal component of the Yukawa coupling is smaller than the diagonal one. It is proportional to an enhancement factor \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left( {M_i^2-M_j^2} \right){{{{M_i}{\varGamma_j}}} \left/ {{\left( {{{{\left( {M_i^2-M_j^2} \right)}}^2}+R_{ij}^2} \right)}} \right.} $$\end{document} with the regulator Rij = MiΓi + Mj Γj. The result is consistent with the previous result obtained by Garny et al., in a constant background with an out-of-equilibrium initial state. We discuss the origin of such a regulator, and why it is not like Rij = MiΓi − MjΓj.