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 $\epsilon$ 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 ${\epsilon }_i$ 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 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.

arXiv comment31 pages, 5 figures; typos corrected

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