Kadanoff-Baym approach to the thermal resonant leptogenesis

Abstract

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 $|M_i^2-M_j^2|\ll M_i^2$. The resonantly enhanced $CP$-violating parameter ${\epsilon }_i$ associated with the decay of the RH neutrino $N_i$ is obtained. It is proportional to an enhancement factor $(M_i^2-M_j^2)M_i{\Gamma }_j/((M_i^2-M_j^2{)}^2+R_{ij}^2)$ with the regulator $R_{ij}=M_i{\Gamma }_i+M_j{\Gamma }_j$. 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 $R_{ij}=M_i{\Gamma }_i-M_j{\Gamma }_j$.

Comments: 51 pages + appendices (46 pages), 5 figures; typos corrected, references added