$CPT$ and unitarity constraints for higher-order $CP$ asymmetries at finite temperature

TL;DR

This paper develops a novel diagrammatic approach to formulate $CPT$ and unitarity constraints on higher-order $CP$ asymmetries at finite temperature, incorporating thermal effects and quantum statistics.

Contribution

It introduces an unconventional diagrammatic method using cylindrical surface diagrams to analyze reaction rate asymmetries with thermal mass effects.

Findings

Incorporates thermal-mass effects into $CP$ asymmetry constraints.

Tracks cancellations of reaction rate asymmetries with quantum statistics.

Applies the method to top Yukawa corrections in leptogenesis.

Abstract

We use an unconventional diagrammatic approach to formulate $CPT$ and unitarity constraints for higher-order $CP$ asymmetries entering the source term in the Boltzmann equation. Usually, the reaction rate asymmetries in these constraints are computed within the classical kinetic theory, using zero-temperature quantum field theory to describe particles' interactions. We approximate the rates, otherwise obtained within the closed-time-path formalism, in terms of diagrams drawn on a cylindrical surface and their holomorphic cuts. The resulting equilibrium asymmetry constraints incorporate thermal-mass effects and allow tracking the cancellations of reaction rate asymmetries computed with quantum statistics. We use the top Yukawa corrections to the asymmetries in the seesaw type-I leptogenesis as an example.