Event rates for nu_e and anti-nu_e appearance oscillations reported by the MINOS and T2K long baseline experiments are used to set constraints on the strength of the non-standard interaction epsilon_{e tau}V_e matter potential. The ranges allowed for
the magnitude and phase of epsilon_{e tau} are delineated for scenarios wherein i) other non-standard interactions for neutrinos propagating through the terrestrial crust are negligible, and ii) the real-valued, flavor-diagonal couplings epsilon_{e e} and epsilon_{tau tau} are also operative. Our analysis makes use of accurate analytic forms for the nu_e amplitude A(nu_mu --> nu_e) describing neutrino oscillation in constant-density matter in the presence of epsilon_{e tau}, epsilon_{e e} and epsilon_{tau tau} non- standard interactions.
We give a convenient expression for the appearance probability P(nu_mu -> nu_e) describing neutrino oscillations in matter of constant density, derived using textbook quantum mechanics stratagems. Our formulation retains the clarity of an expansion i
n alpha = Delta m_{21}^2/Delta m_{31}^2 exhibited by the popular Cervera et al. formula [Nucl. Phys. B 579, 17 (2000)] while enabling more accurate evaluation of oscillations over terrestrial baselines.
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 baseli
nes through matter of constant density, the non-standard interaction potential $epsilon_{mutau} V_e$ can contribute an additional term to the oscillation phase whose sign differs for $anumu$ versus $ umu$ propagation in matter. Its presence can cause different apparent $Delta m^2$ to be erroneously inferred on the basis of oscillations in vacuum, with values lying above (for $anumu$) or below (for $ umu$) the actual $Delta m^2_{32}$ for the case where $epsilon_{mutau}$ is predominantly real-valued and of sign opposite to $Delta m_{32}^2$. An NSI scenario invoking only $Re(epsilon_{mutau})$ is shown to be capable of accounting for a disparity recently reported between oscillation survival for $anumu$ and $ umu$ fluxes measured at $735~mathrm{km}$ 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 $ umu$ from $anumu$ on an event-by-event basis.
