Dirac equation for superluminal neutrinos and mass matrix

TL;DR

This paper proposes a Dirac equation for superluminal neutrinos with an anti-hermitian mass matrix, explaining superluminal velocities while preserving Standard Model results, and estimates neutrino masses from experimental data.

Contribution

It introduces a novel Dirac equation for tachyonic neutrinos with an anti-hermitian mass matrix, a new theoretical framework for superluminal neutrinos.

Findings

Anti-hermitian mass matrix explains superluminal neutrino velocities.

Neutrino masses estimated from experimental data.

Standard Model results remain unchanged for other particles.

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.