Medium corrections to the CP-violating parameter in leptogenesis

In two recent papers [4,5], it has been demonstrated that one can obtain quantum-corrected Boltzmann kinetic equations for leptogenesis using a top-down approach based on the Schwinger-Keldysh/Kadanoff-Baym formalism. These "Boltzmann-like'' equations are similar to the ones obtained in the conventional bottom-up approach but differ in important details. In particular there is a discrepancy between the CP-violating parameter obtained in the first-principle derivation and in the framework of thermal field theory. Here we demonstrate that the two approaches can be reconciled if causal n-point functions are used in the thermal field theory approach. The new result for the medium correction to the CP-violating parameter is qualitatively different from the conventional one. The analogy to a toy model considered earlier enables us to write down consistent quantum-corrected Boltzmann equations, for thermal leptogenesis in the standard model extended by three right-handed neutrinos, which include quantum statistical terms and medium-corrected expressions for the CP-violating parameter.