CP Asymmetries and Higher-Order Unitarity Relations

TL;DR

This paper introduces a novel method based on $S$-matrix unitarity to calculate CP asymmetries in particle reactions, simplifying the process and making cancellations more transparent, with applications to leptogenesis.

Contribution

It presents a new approach to compute CP asymmetries using unitarity expansion, avoiding complex loop calculations and clarifying symmetry cancellations.

Findings

Framework applied to neutrino and top-quark scattering asymmetries

Simplifies calculations of CP asymmetries in perturbation theory

Demonstrates effectiveness in leptogenesis models

Abstract

The main focus of this paper is to introduce a new method to control perturbative calculations of CP asymmetric reaction rates in the Boltzmann equation. CP asymmetries in particle reactions are traditionally calculated in terms of complex couplings, Feynman integrals, and Cutkosky rules. We use an expansion of the $S$-matrix unitarity condition instead, obtaining a general expression for the asymmetries without reference to the imaginary part of the loops. Asymmetry cancelations implied by CPT and unitarity are manifested in a diagrammatic way and easy to track at any order of perturbation theory. We demonstrate the power of this general framework within the right-handed neutrino and top-quark scattering asymmetries in seesaw type-I leptogenesis.