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 1987Awithin these models.
Highlights
No particle can claim to have caused as much havoc in modern physics as the neutrino
We digress on the implications of recent claims of superluminal neutrino propagation
We show that due to neutrino mixing, the flavor energy does not suffer from the usual runaway pathologies of tachyons
Summary
No particle can claim to have caused as much havoc in modern physics as the neutrino. Faster than light propagation has been envisaged in the context of varying speed of light theories, in particular those where the speed of light is energy dependent [12,13,14,15] The latter may be realized in a variety of ways, for example via a deformation of the usual dispersion relations, made invariant by adopting a nonlinear representation of the Lorentz group [16]. We do not want to wed our considerations to this debate, but since one of our models results from this discussion we briefly review the issues at stake It was shown in [20] that it is possible to define a Hilbert space of flavor states, with a well defined vac-.
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