Table of Contents
ISRN High Energy Physics
Volume 2012 (2012), Article ID 436580, 20 pages
http://dx.doi.org/10.5402/2012/436580
Research Article

Neutrino Splitting and Density-Dependent Dispersion Relations

1TPCSF, IHEP, Chinese Academy of Sciences, Beijing 100049, China
2Key Laboratory of Particle Astrophysics, IHEP, Chinese Academy of Sciences, Beijing 100049, China
3Theoretical Physics Division, IHEP, Chinese Academy of Sciences, YuQuan Lu 19(B), Beijing 100049, China

Received 21 August 2012; Accepted 2 October 2012

Academic Editors: G. Bonvicini, K. Cho, M. V. Garzelli, and O. A. Sampayo

Copyright © 2012 Emilio Ciuffoli et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 , the neutrino will decay to two neutrinos and an antineutrino after traveling a distance proportional to . 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 is a function of both the momentum and also of the background density ; 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.