Superluminal Neutrinos from OPERA Experiment and Weyl Equation

Abstract

By analyzing the structure of the Weyl spinor field in the Clifford bundle formalism we show that in each spinorial frame it is represented by F\insec(\doublebarwedge^0 T^\starM + \doublebarwedge^2 T^\star M + \doublebarwedge^{4} T^\star M)\hookrightarrowsecC\ell(M,g) satisfying the equation \partialF=0, where \partial is the Dirac operator acting on sections of the Clifford bundle C\ell(M,g). With this result we show that introducing a generalized potential A=(A + \gamma_5 B)\insec(\doublebarwedge^{1}T^{\star}M + \doublebarwedge^3 T^\star M)\hookrightarrowsecC\ell(M,g) for the Weyl field such that F=\partialA it is possible to exhibit superluminal solutions (including one with a front moving at superluminal speed) for Weyl equation, which surprisingly describes the propagation of a massive tachyonic neutrino. We propose to interpret these extraordinary solutions in order that eventually they may serve as possible models for the emission process and propagation of the superluminal neutrinos observed at the OPERA experiment. Moreover, complementing this study we show that general local chiral invariance of Weyl equation implies that it describes for all solutions that are eigenstates of the parity operator a pair of `sub-particles' carrying opposite magnetic charges (thus possibly carrying a small magnetic moment) which thus interact with an external electromagnetic field. Even if at the Earth's electromagnetic field the effect may result negligible, eventually the idea may be a useful one to study neutrinos leaving the electromagnetic field of stars.