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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.
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Squeezing the Parameter Space for Lorentz Violation in the Neutrino Sector with Additional Decay Channels
The hypothesis of Lorentz violation in the neutrino sector has intrigued scientists for the last two to three decades. A number of theoretical arguments support the emergence of such violations, first and foremost for neutrinos, which constitute the “most elusive” and “least interacting” particles known to mankind. It is of obvious interest to place stringent bounds on the Lorentz-violating parameters in the neutrino sector. In the past, the most stringent bounds have been placed by calculating the probability of neutrino decay into a lepton pair, a process made kinematically feasible by Lorentz violation in the neutrino sector, above a certain threshold. However, even more stringent bounds can be placed on the Lorentz-violating parameters if one takes into account, additionally, the possibility of neutrino splitting, i.e., of neutrino decay into a neutrino of lower energy, accompanied by “neutrino-pair Čerenkov radiation.” This process has a negligible threshold and can be used to improve the bounds on Lorentz-violating parameters in the neutrino sector. Finally, we take the opportunity to discuss the relation of Lorentz and gauge symmetry breaking, with a special emphasis on the theoretical models employed in our calculations.
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- Award ID(s):
- 1710856
- PAR ID:
- 10285348
- Date Published:
- Journal Name:
- Particles
- Volume:
- 3
- Issue:
- 3
- ISSN:
- 2571-712X
- Page Range / eLocation ID:
- 630 to 641
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/particles3030041
