Formal Developments for Lorentz-Violating Dirac Fermions and Neutrinos

TL;DR

This paper derives the full propagator for Lorentz-violating Dirac fermions and the dispersion relation for multiple neutrino flavors, providing theoretical tools for phenomenological studies of Lorentz violation in fermions and neutrinos.

Contribution

It presents the first derivation of the full propagator for Lorentz-violating Dirac fermions and the dispersion equation for multiple neutrino flavors, including Dirac and Majorana types.

Findings

Neutrino dispersion equations have the same structure as Lorentz-violating Dirac theory.

Derived the full propagator for Lorentz-violating Dirac fermions.

Provided a framework for phenomenological analysis of Lorentz violation in neutrinos.

Abstract

The current paper is a technical work that is focused on Lorentz violation for Dirac fermions as well as neutrinos, described within the nonminimal Standard-Model Extension. We intend to derive two theoretical results. The first is the full propagator of the single-fermion Dirac theory modified by Lorentz violation. The second is the dispersion equation for a theory of $N$ neutrino flavors that enables the description of both Dirac and Majorana neutrinos. As the matrix structure of the neutrino field operator is very involved for generic $N$, we will use sophisticated methods of linear algebra to achieve our objectives. Our main finding is that the neutrino dispersion equation has the same structure in terms of Lorentz-violating operators as that of a modified single-fermion Dirac theory. The results will be valuable for phenomenological studies of Lorentz-violating Dirac fermions and neutrinos.