CP
 asymmetries and higher-order unitarity relations

Tomáš Blažek,Peter Maták

doi:10.1103/physrevd.103.l091302

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.

Highlights

In physics, cancelations among terms in calculations may occasionally lead to small numbers or exact zero results that do not show up until the calculations’ last steps are done
We introduce a diagrammatic representation of asymmetries and reaction rates and formulate a general algorithm identifying the complete set of contributions
We briefly discuss technical aspects of the diagrammatic representation used in Eq (14) and comment on their relation to previous works

Summary

INTRODUCTION

Cancelations among terms in calculations may occasionally lead to small numbers or exact zero results that do not show up until the calculations’ last steps are done If this happens it may be suggestive that the language we use—the way we cut reality into pieces [1]—is not fitting the description of the phenomenon. The effect of the asymmetric lH ↔ ̄l Hscattering has to be taken into account as well canceling the asymmetry in equilibrium This is an example of what is known as a real intermediate state subtraction introduced in order to avoid doublecounting in the Boltzmann collision term [2]. Our approach is fully general and can be applied both to real intermediate state subtractions and higher-order terms with complex loops

CP VIOLATION AND S-MATRIX EXPANSION

ASYMMETRIES IN BOLTZMANN COLLISION INTEGRAL

NEUTRINO-QUARK SCATTERING AND OðY4Y2t Þ UNITARITY RELATIONS

EVALUATION OF ASYMMETRIES AND INFRARED FINITENESS

Ktree Kloop: cuts ð19Þ

SUMMARY