Gauged L_mu - L_tau and different Muon Neutrino and Anti-Neutrino Oscillations: MINOS and beyond

If a Z' gauge boson of a gauged L_mu - L_tau symmetry is very light, it is associated with a long-range leptonic force. In this case the particles in the Sun create via mixing of Z' with the Standard Model Z a flavor-dependent potential for muon neutrinos in terrestrial long-baseline experiments. The potential changes sign for anti-neutrinos and hence can lead to apparent differences in neutrino and anti-neutrino oscillations without introducing CP or CPT violation. This could for instance explain the recently found discrepancy in the survival probabilities of muon neutrinos and anti-neutrinos in the MINOS experiment. We obtain the associated parameters of gauged L_mu - L_tau required to explain this anomaly. The consequences for future long-baseline experiments and for the anomalous magnetic moment of the muon are discussed. The main feature of our explanation is that atmospheric neutrino mixing has to be non-maximal. Neutrino masses tend to be quasi-degenerate.