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=λ(ψγ_μψψγ^μψ)^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 λ=-(0.5-1.6)x10^-4. The self-interaction Lagrangian V=λ(ψγ_μψψγ^μψ) with the coupling constant λ=-(0.7-0.9)x10^-4 yields the same result. Scalar interaction V=λ(ψψ)^b and scalar-vector interaction λ(ψ^{+}ψ)^{b+1}/(ψψ)^b cannot be responsible for the observed superluminal neutrino.

13 pages, no figures

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