Cosmic evolution of lepton flavor charges

Chee Sheng Fong

doi:10.1103/physrevd.105.043004

Abstract

In the early Universe above the weak scale, both baryon $B$ and lepton $L$ numbers are violated by nonperturabive effects in the Standard Model while $B\ensuremath{-}L$ remains conserved. Introducing new physics which violates perturbatively $L$ and/or $B$, one can generate dynamically a nonzero $B\ensuremath{-}L$ charge and hence a nonzero $B$ charge. In this work, we focus on the former scenario, which is also known as leptogenesis. We show how to describe the evolutions of lepton flavor charges taking into account the complete Standard Model lepton flavor and spectator effects in a unified and lepton flavor basis--independent way. The recipe we develop can be applied to any leptogenesis model with arbitrary number of new scalars carrying nonzero hypercharges and is valid for cosmic temperature ranging from ${10}^{15}\text{ }\text{ }\mathrm{GeV}$ down to the weak scale. We demonstrate that in order to describe the physics in a basis-independent manner and to include lepton flavor effect consistently it is necessary to describe both left-handed and right-handed lepton charges in terms of density matrices. This is a crucial point since physics should be basis independent. As examples, we apply the formalism to type-I and type-II leptogenesis models where in the latter case a flavor-covariant formalism is indispensable.

Highlights

In the early Universe, if the cosmic temperature is above the weak scale, the thermal bath contains all the degrees of freedom of the Standard Model (SM) and perhaps other new physics degrees of freedom as well if they are kinematically accessible
To generate a cosmic baryon asymmetry dynamically, one needs to violate at least the baryon number B of the SM
The weak scale when the SM B-violating process is in thermal equilibrium [1], one needs to identify other charges which are not in thermal equilibrium such that the charge is effectively conserved and can remain nonzero

Summary

INTRODUCTION

In the early Universe, if the cosmic temperature is above the weak scale, the thermal bath contains all the degrees of freedom of the Standard Model (SM) and perhaps other new physics degrees of freedom as well if they are kinematically accessible. While the computation of leptogenesis is usually carried out in a charged lepton mass basis, one should be cautious that this description has limited validity, and in particular, if the result is basis dependent, it is a red flag that something must be wrong In this flavor-covariant formalism [6,7], the SM lepton flavor effect is consistently taken into account.. III, we write down the flavor-covariant Boltzmann equations, taking into account the complete lepton flavor and spectator effects due to quark Yukawa and the SM sphaleron interactions These results are completely general and, together with the equations in Appendix C, can be applied to any leptogenesis model (with arbitrary number of new scalars carrying nonzero hypercharges) for cosmic temperature ranging from 1015 GeV down to the weak scale. In Appendix A, we discuss how number density asymmetry matrices are related to matrices of chemical potentials; in Appendix B, we show how the flavor-covariant structure can be derived using Sigl-Raffelt formalism [5]; and in Appendix D, we discuss how to determine the transition temperatures related to spectator effects

EFFECTIVE SYMMETRIES AND CHARGES

Standard Model with additional scalar fields

APPLICATIONS

Type-II leptogenesis

CONCLUSIONS