  If a Z' gauge boson from 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 the 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 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 are also discussed, and we compare the
scenario to standard NSIs. When used to explain MINOS, both approaches have
severe difficulties with existing limits.
