Gauged Lμ–Lτ and different muon neutrino and anti-neutrino oscillations: MINOS and beyond

If a Z' gauge boson of a gauged Lμ–Lτ 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 can 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 Lμ–Lτ required to explain this anomaly, and compare our scenario to usually considered non-standard interactions. When applied to MINOS, both approaches have difficulties with existing limits. The consequences for future long-baseline experiments and for the anomalous magnetic moment of the muon are discussed. The main feature is that atmospheric neutrino mixing has to be non-maximal in order to have an effect. Neutrino masses tend to have a mild hierarchy.