On coherence lengths of wave packets II : High energy neutrino

Abstract

In this second paper of the series on the coherence of wave packets, we study neutrinos in high energy experiments where neutrinos are produced by decays of pions or muons which are described using wave packets. The space time position where one neutrino is produced is not fixed to one value but is extended in macroscopic area. Hence the amplitude is defined by a superposition of the amplitudes of different neutrino's production time in the macroscopic region and depends on the absolute value of the neutrino mass. We analyze neutrino interference based on operator product expansion near the light cone and find a new universal term in the time dependent neutrino probability. This new term has an origin in higher order quantum effect in a similar manner as axial anomaly. Roles of Lorentz invariance and the operator product expansion in the light-cone region are clarified and a possibility of measuring the absolute value of neutrino mass from neutrino interference experiments is pointed out.