  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.
