In the νSM extended by adding an eV-scale sterile state, the (3 + 1) model, the sterile-active level crossing entails the MSW resonance, here referred as the sterile-active (SA) resonance. In this paper, we construct an effective theory of SA resonance which involves only the sterile-active mixing angles and ∆ \( {m}_{41}^2 \) , thanks to the given environment of high matter potential which freezes the νSM oscillations. We give our first attempt at an analytic treatment of the effective theory to illuminate the global picture of the SA resonance at a glance. We formulate a perturbative framework in which the structure of “texture zeros” of the S matrix in the flavor space and the suppression by the small parameters sin θj4 (j = 1, 2, 3) allows us to reveal the flavor–event-type hierarchy of the resonance-effect strength in the probabilities. We have shown that the cascade events dominantly comes from the three paths through P(νe → νe), P( \( {\overline{\nu}}_e \) → \( {\overline{\nu}}_e \) ), and P( \( {\overline{\nu}}_{\mu } \) → \( {\overline{\nu}}_{\tau } \) ), and a three-component fit is suggested to disentangle the SA resonance generation mechanisms.
