  The MINOS experiment at Fermilab has recently reported a tension between the
oscillation results for neutrinos and anti-neutrinos. We show that this
tension, if it persists, can be understood in the framework of non-standard
neutrino interactions (NSI). While neutral current NSI (non-standard matter
effects) are disfavored by atmospheric neutrinos, a new charged current
coupling between tau neutrinos and nucleons can fit the MINOS data without
violating other constraints. In particular, we show that loop-level
contributions to flavor-violating tau decays are sufficiently suppressed.
However, conflicts with existing bounds could arise once the effective theory
considered here is embedded into a complete renormalizable model. We predict
the future sensitivity of the T2K and NOvA experiments to the NSI parameter
region favored by the MINOS fit, and show that both experiments are excellent
tools to test the NSI interpretation of the MINOS data.
