Coherent Flavour Oscillation and CP Violating Parameter in Thermal Resonant Leptogenesis

Abstract

Solving the Kadanoff-Baym (KB) equations in a different method from our previous analysis, we obtain the CP violating parameter $\varepsilon$ in the thermal resonant leptogenesis without assuming smallness of the off-diagonal Yukawa couplings. For that purpose, we first derive a kinetic equation for density matrix of RH neutrinos with almost degenerate masses $M_i \ (i=1,2) \sim M$. If the deviation from thermal equilibrium is small, the differential equation is reduced to a linear algebraic equation and the density matrix can be solved explicitly in terms of the time variation of (local) equilibrium distribution function. The obtained CP-violating parameter $\varepsilon_i$ is proportional to an enhancement factor $(M^{2}_{i}-M^{2}_{j}) M_i \Gamma_j/ ((M^{2}_{i}-M^{2}_{j})^2 +R_{ij}^2)$ with a regulator $R_{ij}=M (\Gamma_i + \Gamma_j)$, consistent with the previous analysis. The decay width can be determined systematically by the 1PI self-energy of the RH neutrinos in the 2PI formalism.