CP violation in mixing and oscillations for leptogenesis: Part II. The highly degenerate case

Abstract

We extend to the highly degenerate case a recent approach for analyzing the sources of CP violation in baryogenesis models with quasi-degenerate neutrinos. In this approach an expansion of the resummed propagator around the poles is plugged into a quantum field theory model of neutrino oscillations and a source term for the time evolution of the lepton asymmetry is built directly from the probabilities of lepton number violating processes involving only stable particles. This allows for a transparent consideration of unitarity requirements. The source term has contributions that can be identified with CP violation from mixing, oscillations and interference between both. For the highly degenerate case, i.e. when the mass difference between two neutrinos is similar or smaller than their decay widths, we find that in general the mixing and oscillation terms contribute with opposite signs to the generation of lepton asymmetry and the contribution of the interference term is typically very relevant and crucial to ensure unitarity is satisfied. Moreover, the expressions we obtain are finite in the double degenerate limit of equal masses and couplings. The calculations are done in a simple scalar toy model.