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

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