Lorentz-violating neutrino parameters have been severely constrained on the basis of astrophysical considerations. In the high-energy limit, one generally assumes a superluminal dispersion relation of an incoming neutrino of the form E≈ |p ⃗|v , where E is the energy, p ⃗ is the momentum and v ₌ √(1+ δ) > 1. Lepton-pair creation due to a Cerenkov-radiation-like process (ν → ν + е-+e+) becomes possible above a certain energy threshold, and bounds on the Lorentz-violating parameter δ can be derived. Here, we investigate a related process, νi→ νi+ νf+ ν ‾f, where νi is an incoming neutrino mass eigenstate, while νf is the final neutrino mass eigenstate, with a superluminal velocity that is slightly slower than that of the initial state. This process is kinematically allowed if the Lorentz-violating parameters at high energy differ for the different neutrino mass eigenstates. Neutrino splitting is not subject to any significant energy threshold condition and could yield quite a substantial contribution to decay and energy loss processes at high energy, even if the differential Lorentz violation among neutrino flavors is severely constrained by other experiments. We also discuss the SU(2)L-gauge invariance of the superluminal models and briefly discuss the use of a generalized vierbein formalism in the formulation of the Lorentz-violating Dirac equation.
G. Somogyi et al., "Neutrino Splitting for Lorentz-Violating Neutrinos: Detailed Analysis," Physical Review D, vol. 100, no. 3, American Physical Society (APS), Aug 2019.
The definitive version is available at https://doi.org/10.1103/PhysRevD.100.035036
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01 Aug 2019