Cutting rules on a cylinder and simplified diagrammatic approach to $CP$ violation in quantum kinetic theory

TL;DR

This paper introduces a novel, diagrammatic method using cylindrical cuttings and windings to incorporate thermal corrections into $CP$ violation rates within quantum kinetic theory, simplifying calculations and ensuring unitarity and CPT invariance.

Contribution

It presents a simplified, diagrammatic approach to include thermal effects in $CP$ asymmetry calculations, avoiding complex real-time formalism methods.

Findings

The method reproduces known thermal correction results.

It simplifies the calculation of $CP$ violation rates.

The approach maintains unitarity and CPT invariance.

Abstract

We briefly explain a novel diagrammatic method for including thermal corrections in $CP$ asymmetric reaction rates entering the quantum Boltzmann equation. In thermal equilibrium, the asymmetries have to cancel precisely due to the $S$-matrix unitarity and $CPT$ invariance. Such cancelations are easy to track in zero-temperature leading-order calculations. However, accounting for medium effects requires modification of the on-shell part of propagators and, consequently, the $CP$ violating rates. In the literature, the correct form of the statistical factors in the asymmetry source term has been obtained employing the real-time-formalism of non-equilibrium field theory in a certain approximation. We demonstrate that the same results can be obtained by summing an infinite sequence of zero-temperature asymmetries. Those are derived from cuttings of forward diagrams drawn on a cylindrical surface, while thermal corrections come from windings of their propagators. The procedure is entirely diagrammatic, and the $CPT$ and unitarity cancelations are formulated for thermally corrected reaction rate asymmetries. The simplification achieved is the primary focus of our work. The aspect of infrared finiteness in higher-order corrections will also be discussed.