CP violation in mixing and oscillations for leptogenesis with quasi-degenerate neutrinos

TL;DR

This paper investigates CP violation sources in leptogenesis with quasi-degenerate neutrinos using a quantum field theory approach, identifying contributions from mixing, oscillations, and interference, and deriving a source term for lepton asymmetry evolution.

Contribution

It introduces a novel method to analyze CP violation in neutrino oscillations using the renormalized propagator, avoiding complex density calculations and real intermediate state subtractions.

Findings

Source term cancels in equilibrium due to unitarity and CPT invariance.

CP violation contributions from mixing and oscillations are explicitly identified.

Interference effects become more significant with increased degeneracy.

Abstract

We study the sources of CP violation for baryogenesis models with quasi-degenerate neutrinos. Our approach is to use the renormalized propagator in a quantum field theory model of neutrino oscillations, paying close attention to unitarity requirements. From the probabilities of lepton number violating processes obtained in this way, we derive a source term for the time evolution of the lepton asymmetry. The source term has contributions that can be identified with CP violation from mixing, oscillations and interference between both. Given that this source term does not involve processes with unstable particles in the initial or final states, neither does it require to calculate number densities of neutrinos, no subtraction of real intermediate states must be performed. In equilibrium the source term is null, as demanded by unitarity and CPT invariance, due to a cancellation between the terms coming from CP violation in mixing and oscillations. The calculations are done in a simple scalar toy model, and the resummed propagator is diagonalized at first order in the decay widths over the mass difference. We also comment on the effect of the interference term, which is mild at the order we work, but seems to become more important with increasing degeneracy.