Quantum transport theory for neutrinos with flavor and particle-antiparticle mixing

TL;DR

This paper develops a comprehensive quantum kinetic framework for neutrino flavor and particle-antiparticle mixing, incorporating collision effects and coherence, applicable to diverse physical environments.

Contribution

It derives a generalized density matrix equation from Kadanoff--Baym equations that includes both flavor and particle-antiparticle coherences for arbitrary neutrino masses.

Findings

Includes collision integrals with coherence information

Identifies a spectral shell structure underlying mixing

Provides simplified limits for ultra-relativistic neutrinos

Abstract

We derive quantum kinetic equations for mixing neutrinos including consistent forward scattering terms and collision integrals for coherent neutrino states. In practice, we reduce the general Kadanoff--Baym equations in a few clearly justified steps to a generalized density matrix equation that describes both the flavour- and particle-antiparticle coherences and is valid for arbitrary neutrino masses and kinematics. We then reduce this equation to a simpler particle-antiparticle diagonal limit and eventually to the ultra-relativistic limit. Our derivation includes simple Feynman rules for computing collision integrals with the coherence information. We also expose a novel spectral shell structure underlying the mixing phenomenon and quantify how the prior information on the system impacts on the QKE's, leading to a direct effect on its evolution. Our results can be used for example to accurately model neutrino distributions in hot and dense environments and to study the production and decay of mixing heavy neutrinos in colliders.