Abstract
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 = sqrt(1 + delta) > 1. Lepton-pair creation due to a Cerenkov-radiation-like process (nu -> nu + e^- + e^+) becomes possible above a certain energy threshold, and bounds on the Lorentz-violating parameter delta can be derived. Here, we investigate a related process, nu_i -> nu_i + nu_f + bar_nu_f, where nu_i is an incoming neutrino mass eigenstate, while nu_f 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)-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.
Highlights
A possible Lorentz violation in the neutrino sector has been the subject of intense investigations in recent years, with a rich texture of interesting models and corresponding scenarios having been explored in the literature
We show that the NPCR process is not parametrically suppressed in comparison to LPCR
While the relative differences among Lorentzviolating parameters for the neutrino mass and flavor eigenstates are otherwise tightly constrained [19,20,21], our assumption is supported by the fact that the corresponding mass terms mi in Eq (11) are different from each other. (ii) We here confirm the results obtained for LPCR obtained in Refs. [17,26], including the model dependence derived in Ref. [17]
Summary
A possible Lorentz violation in the neutrino sector has been the subject of intense investigations in recent years, with a rich texture of interesting models and corresponding scenarios having been explored in the literature (see Refs. [1,2,3,4,5,6,7,8,9]). In terms of the formulation of the vacuum pair emission [17,26], one faces a certain dilemma: On one hand, if the charged fermions and the neutrinos are grouped in an SUð2ÞL doublet, and if the Lorentz-breaking parameters are assigned uniformly over all generations, both NPCR and LPCR decays are kinematically forbidden in the Lorentz-violating Standard Model extension. [17,26] and here are based on two assumptions, namely, (i) that Lorentz violation is confined to the neutrino sector, and that (ii) the effective Fermi theory, possibly with some modifications, still holds for the description of the decay and energy loss processes
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
