CP violation at finite temperature

TL;DR

This paper provides a detailed analysis of the finite temperature CP-asymmetry factor crucial for leptogenesis, comparing different thermal quantum field theory methods and offering analytic and numerical results.

Contribution

It introduces a comprehensive comparison of real-time and imaginary-time formalisms for calculating CP asymmetry at finite temperature, ensuring consistency across methods.

Findings

Validated the linearity of the CP-asymmetry factor with statistical factors.

Derived analytic expressions for the CP-asymmetry as triple-integrals.

Provided numerical benchmarks within a specific particle physics model.

Abstract

We present a comprehensive study of the finite temperature CP-asymmetry factor needed in the semi-classical treatment of leptogenesis originating from Majorana fermion decays into a lepton and a scalar particle. The imaginary part of the relevant one-loop integrals are evaluated using both the real time and the imaginary time formalisms of thermal quantum field theory. In the former we consider the retarded-advanced approach as well as the original thermal cutting method developed by Kobes and Semenoff. Specific care is directed towards showing the consistency between the various approaches. We show that the final physical result of the calculation is linear in the statistical factors and is consistent with what is obtained in the Kadanoff-Baym approach. We also present analytic expressions for the full CP-asymmetry factor in the form of well-behaved triple-integrals, and provide numerical benchmark predictions in a specific particle physics model.