Lorentz Breaking and SU(2)L x 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 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 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 SU(2)L x U(1)Y, 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 SU(2)L x U(1)Y gauge invariance, involves flavor-dependent Lorentz-breaking parameters, and still allows for Cerenkov-type decays to proceed.




The authors would like to acknowledge support from the National Science Foundation (Grant PHY-1710856). This work was also supported by the ÚNKP-17-3 New National Excellence Program of the Ministry of Human Capacities of Hungary and by the Grant K 125105 of the National Research, Development and Innovation Fund in Hungary.

Keywords and Phrases

Fundamental Symmetries; Gauge Invariance; Lorentz-Violation; Neutrinos; Relation Of Lorentz-Symmetry Breaking And Gauge Invariance; Spontaneous Lorentz-Symmetry Breaking

International Standard Serial Number (ISSN)

0218-3013; 1793-6608

Document Type

Article - Journal

Document Version


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Publication Date

01 Sep 2019