Superluminal self-interacting neutrino

Abstract

The effect of nonlinear self-interaction can be associated with superluminal velocity of neutrino. The power energy spectrum E=p+Cp^a is derived from the nonlinear Dirac equation when interaction term V=\lambda (\psi \gamma_\mu \psi \psi \gamma^\mu \psi)^a is added to the Lagrangian of a free spin-1/2 particle. The superluminal velocity recorded by the OPERA and MINOS collaborations is achieved when the coupling constants are taken in the range a=0.4-1.18 and \lambda =-(0.5-1.6)x10^-4. The self-interaction Lagrangian V=\lambda (\psi \gamma_\mu \psi \psi \gamma ^\mu \psi) with the coupling constant \lambda =-(0.7-0.9)x10^-4 yields the same result. Scalar interaction V=\lambda (\psi \psi)^b and scalar-vector interaction \lambda(\psi^{+}\psi)^{b+1}/(\psi \psi)^b cannot be responsible for the observed superluminal neutrino.