Sterile-active resonance: A global qualitative picture

A bstract In the ν SM 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 ∆ $$ {m}_{41}^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mn>41</mml:mn> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> , thanks to the given environment of high matter potential which freezes the ν SM 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 θ j 4 ( 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 ( ν e → ν e ), P ( $$ {\overline{\nu}}_e $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>e</mml:mi> </mml:msub> </mml:math> → $$ {\overline{\nu}}_e $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>e</mml:mi> </mml:msub> </mml:math> ), and P ( $$ {\overline{\nu}}_{\mu } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>μ</mml:mi> </mml:msub> </mml:math> → $$ {\overline{\nu}}_{\tau } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>τ</mml:mi> </mml:msub> </mml:math> ), and a three-component fit is suggested to disentangle the SA resonance generation mechanisms.