T violation without complex entries in the lepton mixing matrix

Abstract

We demonstrate that $T$ invariance can be violated even when the Pontecorvo-Maki-Nakagawa-Sakata lepton mixing matrix is real. We obtain a sufficient condition of $T$ violation in neutrino oscillations in matter and electromagnetic field. In the two-flavor model we derive the $T$-violating spin-flavor transition probabilities. Then we prove that the transition probabilities for neutrino in a moving medium in electromagnetic field differ from those for antineutrino in matter composed of antiparticles and electromagnetic field only in the sign of the $T$-violating term.