Lorentz breaking and SU(2)L × U(1)Y gauge invariance for neutrinos
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 are laid. Here, we investigate the relation of Lorentz violation in the neutrino sector in light of the fact that neutrinos and the corresponding left-handed charged leptons form [Formula: see text] 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 explored with a special emphasis on neutrino splitting, otherwise known as the neutrino-pair Cerenkov radiation and vacuum-pair emission (electron–positron-pair Cerenkov radiation). We highlight two scenarios in which Lorentz-violating effects do not necessarily also break electroweak gauge invariance. The first of these involves a restricted set of gauge transformations, a subgroup of [Formula: see text], while in the second where 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 [Formula: see text] gauge invariance, involves flavor-dependent Lorentz-breaking parameters, and still allows for Cerenkov-type decays to proceed.