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 ${ϵ}_{ee}$, ${ϵ}_{e\tau }$, ${ϵ}_{\tau \tau }$ and that the tau-tau component satisfies the constraint ${ϵ}_{\tau \tau }=\mathrm{\mid }{ϵ}_{e\tau }{\mathrm{\mid }}^2\mathrm{/}(1+{ϵ}_{ee})$ which is suggested from the high energy behavior for atmospheric neutrino data.