Neutrino Oscillations and Superluminal Propagation, in OPERA or Otherwise

Abstract

We digress on the implications of recent claims of superluminal neutrino propagation. No matter how we turn it around such behaviour is very odd and sits uncomfortably even within "far-fetched" theories. In the context of non-linear realizations of the Lorentz group (where superluminal misbehaviour is run of the mill) one has to accept rather contrived constructions to predict superluminal properties for the neutrino. The simplest explanation is to require that at least one of the mass states be tachyonic. We show that due to neutrino mixing, the flavor energy does not suffer from the usual runaway pathologies of tachyons. For non-tachyonic mass states the theories become more speculative. A neutrino specific dispersion relation is exhibited, rendering the amplitude of the effect reasonable for a standard Planck energy. This uses the fact that the beam energy is close to the geometrical average of the neutrino and Planck mass; or, seen in another way, the beam energy is unexceptional but its gamma factor is very large. A dispersion relation crossing over from a low energy bradyonic branch to a high energy tachyonic one is also considered. We comment on consistency with SN 1987A within these models.

Neutrino processes with power law dispersion relations

“…1. Deformed Lorentz symmetry models [17,18,19,20,21,22,23] where the dispersion relations change from the usual p 2 = m 2 form to a different form which is still covariant under the modified Lorentz transformations. In this picture the processes which are forbidden in one reference frame (like the rest frame of the massive neutrinos) will be forbidden also in the lab frame.…”