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

Neutrinos propagating through matter may participate in forward coherent neutral-current-like scattering arising from non-standard interactions as well as from the Mikheyev-Smirnov-Wolfenstein matter potential $V_e$. We show that at fixed long baselines through matter of constant density, the non-standard interaction potential ${ϵ}_{\mu \tau }{V}_e$ can contribute an additional term to the oscillation phase whose sign differs for $\text{anumu}$ versus $\text{numu}$ propagation in matter. Its presence can cause different apparent $\mathrm{\Delta }{m}^2$ to be erroneously inferred on the basis of oscillations in vacuum, with values lying above (for $\text{anumu}$) or below (for $\text{numu}$) the actual $\mathrm{\Delta }{m}_{32}^2$ for the case where ${ϵ}_{\mu \tau }$ is predominantly real-valued and of sign opposite to $\mathrm{\Delta }{m}_{32}^2$. An NSI scenario invoking only $\mathrm{\Re }({ϵ}_{\mu \tau })$ is shown to be capable of accounting for a disparity recently reported between oscillation survival for $\text{anumu}$ and $\text{numu}$ fluxes measured at $735\mathrm{k}\mathrm{m}$ by the MINOS experiment. Implications for mantle traversal by atmospheric neutrinos are examined. The NSI matter potential with non-maximal mixing could evade conventional atmospheric neutrino analyses which do not distinguish $\text{numu}$ from $\text{anumu}$ on an event-by-event basis.