Abstract
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.
Highlights
Neutrinos are the most elusive particles within the standard model of elementary interactions
Lorentz-violating neutrinos undergo stronger decay and energy loss mechanisms than “ordinary” neutrinos because of their dispersion relation E = p2 v2 + m2 ≈ |p| v, which makes a number of decay channels kinematically possible
E2 − p2 = p2(v2 − 1) ≈ E2(v2 − 1) = E2 δ of a neutrino becomes large for large energy, rendering a number of decay processes kinematically possible
Summary
Neutrinos are the most elusive particles within the standard model of elementary interactions. In reference [18], it has been suggested that the invariant arena for nonquantum physics is a phase space rather than spacetime, and the locality of an even in space-time is replaced by relative locality in which different observers see different spacetimes, and the spacetimes they observe are energy and momentum dependent This hypothesis can lead to a modified dispersion relation of the kind investigated here. If photons themselves propagate faster than c (the limiting velocity of massive standard fermions) in some Lorentz-violating theories, as long as information propagates along or inside the modified lightcone (as defined by a modified effective metric), it can propagate faster than c without implying causality issues (see, e.g., the paragraph around Equation (9) in reference [31]).
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