# Lorentz Breaking and SU(2)_L x U(1)_Y Gauge Invariance for Neutrino Decays

## TL;DR

This paper explores how Lorentz violation can occur in neutrino interactions without breaking the fundamental SU(2)_L x U(1)_Y gauge symmetry, analyzing different scenarios and their implications for neutrino decay processes.

## Contribution

It introduces a gauge-invariant model of Lorentz violation in the neutrino sector that permits neutrino decay processes like NPCR and LPCR.

## Key findings

- Lorentz violation can be compatible with gauge invariance in neutrino interactions.
- Flavor-dependent Lorentz-breaking parameters enable neutrino decay processes.
- The model preserves SU(2)_L x U(1)_Y gauge symmetry while allowing Lorentz violation.

## Abstract

Conceivable Lorentz-violating effects in the neutrino sector remain a research area of great general interest, as they touch upon the very foundations on which the Standard Model and our general understanding of fundamental interactions is laid. Here, we investigate the relation of Lorentz violation in the neutrino sector in light of the fact that neutrinos and corresponding left-handed charged leptons form SU(2)_L doublets under the electroweak gauge group. Lorentz-violating effects thus cannot be fully separated from questions related to gauge invariance. The model dependence of the effective interaction Lagrangians used in various recent investigations is investigated, with a special emphasis on neutrino splitting, otherwise known as neutrino-pair Cerenkov radiation, NPCR, and vacuum pair emission (electron-positron-pair Cerenkov radiation, LPCR). We investigate two scenarios in which Lorentz violating effects do not necessarily also break electroweak gauge invarianceThe first of these involves a restricted set of gauge transformation, a subgroup of SU(2)_L x U(1)_Y, while in the second, differential Lorentz violation is exclusively introduced by the mixing of the neutrino flavor and mass eigenstates. Our study culminates in a model which fully preserves SU(2)_L x U(1)_Y gauge invariance, involves flavor-dependent Lorentz-breaking parameters, and still allows for NPCR and LPCR decays to proceed.