Lorentz-Violating Regulator Gauge Fields as the Origin of Dynamical Flavour Oscillations

TL;DR

This paper demonstrates how Lorentz-violating gauge fields can dynamically generate fermion flavor mixing and oscillations, with the LIV features acting as a regulator that decouples, restoring Lorentz invariance and producing finite dynamical masses.

Contribution

It introduces a novel mechanism where LIV gauge fields induce dynamical flavor mixing, providing a new perspective on neutrino oscillations and mass generation.

Findings

Dynamical mass mixing matrix generated for massless fermions

LIV features serve as a regulator for gap equations

Finite dynamical masses emerge, restoring Lorentz invariance

Abstract

We show how a mass mixing matrix can be generated dynamically, for two massless fermion flavours coupled to a Lorentz invariance violating (LIV) gauge field. The LIV features play the role of a regulator for the gap equations, and the non-analytic dependence of the dynamical masses, as functions of the gauge coupling, allows to consider the limit where the LIV gauge field eventually decouples from the fermions. Lorentz invariance is then recovered, to describe the oscillation between two free fermion flavours, and we check that the finite dynamical masses are the only effects of the original LIV theory. We also discuss briefly a connection of our results with the case of Majorana neutrinos in both, the standard model, where only left-handed (active) neutrinos are considered, and extensions thereof, with sterile right-handed neutrinos.