  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.
