Medium corrections to the CP-violating parameter in leptogenesis

TL;DR

This paper reconciles two approaches to calculating medium corrections to the CP-violating parameter in leptogenesis, providing a consistent quantum-corrected framework that includes medium effects and quantum statistical terms.

Contribution

It demonstrates that using causal n-point functions in thermal field theory reconciles previous discrepancies and derives a new, qualitatively different medium correction to the CP-violating parameter.

Findings

Reconciliation of top-down and bottom-up approaches using causal n-point functions.

Derivation of a new medium correction to the CP-violating parameter.

Development of quantum corrected Boltzmann equations including medium effects.

Abstract

In two recent papers, arXiv:0909.1559 and arXiv:0911.4122, 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 (supplemented by three right-handed neutrinos) which include quantum statistical terms and medium corrected expressions for the CP-violating parameter.