Dirac equation for superluminal neutrinos and mass matrix

Abstract

The superluminal is reported in OPERA neutrino experiment (arXiv:1109.4897v2), this result is consistent with previous MINOS experiment about neutrino velocity (Phys. Rev. D 76, 072005 (2007)). Here we propose a Dirac equation of tachyon for superluminal neutrino in which the mass matrix is anti-hermitian. Additionally we find that this anti-hermitian mass matrix which is responsible for superluminal can only be for neutrinos, while other results of Standard Model are unchanged. In case that Lorentz invariant is remained, the masses of neutrinos are estimated based on available data of experiments.