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Neutrinos propagating through matter may participate in forward coherentneutral-current-like scattering arising from non-standard interactions as wellas from the Mikheyev-Smirnov-Wolfenstein matter potential $V_e$. We show thatat fixed long baselines through matter of constant density, the non-standardinteraction potential $\epsilon_{\mu\tau} V_e$ can contribute an additionalterm to the oscillation phase whose sign differs for $\anumu$ versus $\numu$propagation in matter. Its presence can cause different apparent $\Delta m^2$to be erroneously inferred on the basis of oscillations in vacuum, with valueslying above (for $\anumu$) or below (for $\numu$) the actual $\Delta m^2_{32}$for the case where $\epsilon_{\mu\tau}$ is predominantly real-valued and ofsign opposite to $\Delta m_{32}^2$. An NSI scenario invoking only$\Re(\epsilon_{\mu\tau})$ is shown to be capable of accounting for a disparityrecently reported between oscillation survival for $\anumu$ and $\numu$ fluxesmeasured at $735~\mathrm{km}$ by the MINOS experiment. Implications for mantletraversal by atmospheric neutrinos are examined. The NSI matter potential withnon-maximal mixing could evade conventional atmospheric neutrino analyses whichdo not distinguish $\numu$ from $\anumu$ on an event-by-event basis.

Apparent multiple Delta m^2_32 in muon anti-neutrino and muon neutrino survival oscillations from non-standard interaction matter effect