Neutrino Splitting and Density-Dependent Dispersion Relations

Abstract

We show that particles are unstable with respect to a splitting process, which is the quantum analog of the modulational instability in anomalous dispersive media, only when their group velocity exceeds their phase velocity. In the case of a neutrino, when the concavity results from a term E(P)~Pk, the neutrino will decay to two neutrinos and an antineutrino after traveling a distance proportional to E2+3k. Unlike the Cohen-Glashow instability, the splitting instability exists even if all particles involved in the interaction have the same dispersion relations at the relevant energy scales. We show that this instability leads to strong constraints even if the energy E is a function of both the momentum P and also of the background density ρ; for example, we show that it alone would have been sufficient to eliminate any model of the MINOS/OPERA velocity anomaly which modifies the neutrino dispersion relation while leaving those of other particles intact.