Some constraints on new physics by atmospheric neutrinos

From the analytic oscillation probability for high energy atmospheric neutrinos in the presence of new physics in propagation, it is argued that the components $\mathrm{\mid }{ϵ}_{e\mu }\mathrm{\mid }$ and $\mathrm{\mid }{ϵ}_{\mu \tau }\mathrm{\mid }$ as well as the quantity $\mathrm{\mid }{ϵ}_{\tau \tau }-\mathrm{\mid }{ϵ}_{e\tau }{\mathrm{\mid }}^2\mathrm{/}(1+{ϵ}_{ee})\mathrm{\mid }$ should be small.