Constraints on the flavor-dependent non-standard interaction in propagation from atmospheric neutrinos

The sensitivity of the atmospheric neutrino experiments to the non-standard flavor-dependent interaction in neutrino propagation is studied under the assumption that the only nonvanishing components of the non-standard matter effect are the electron and tau neutrino components $\epsilon_{ee}$, $\epsilon_{e\tau}$, $\epsilon_{\tau\tau}$ and that the tau-tau component satisfies the constraint $\epsilon_{\tau\tau}=|\epsilon_{e\tau}|^2/(1+\epsilon_{ee})$ which is suggested from the high energy behavior for atmospheric neutrino data.