Cosmic Evolution of Lepton Flavor Charges

TL;DR

This paper develops a comprehensive, basis-independent formalism for describing the evolution of lepton flavor charges in leptogenesis, accounting for Standard Model effects and applicable across a wide temperature range.

Contribution

It introduces a unified, flavor basis-independent method to analyze lepton flavor charge evolution, including both left- and right-handed leptons, for various leptogenesis models.

Findings

Formalism applies to any leptogenesis model with arbitrary scalars.

Includes complete Standard Model lepton flavor and spectator effects.

Demonstrates basis independence using density matrices.

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 $B-L$ remains conserved. Introducing new physics which violates perturbatively $L$ and/or $B$, one can generate dynamically a nonzero $B-L$ 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 $10^{15}$ 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.