Parametrization of Pontecorvo–Maki–Nakagawa–Sakata mixing matrix based on CP-violating bipair neutrino mixing

Abstract

CP violation in neutrino interactions is described by three phases contained in Pontecorvo–Maki–Nakagawa–Sakata mixing matrix (U PMNS ). We argue that the phenomenologically consistent result of the Dirac CP violation can be obtained if U PMNS is constructed along bipair neutrino mixing scheme, namely, requiring that |U12| = |U32| and |U22| = |U23| (case 1) and |U12| = |U22| and |U32| = |U33| (case 2), where Uij stands for the i × j matrix element of U PMNS . As a result, the solar, atmospheric and reactor neutrino mixing angles θ12, θ23 and θ13, respectively, are correlated to satisfy cos 2θ12 = sin 2 θ23 - tan 2 θ13 (case 1) or cos 2θ12 = cos 2 θ23 - tan 2 θ13 (case 2). Furthermore, if Dirac CP violation is observed to be maximal, θ23 is determined by θ13 to be: [Formula: see text] (case 1) or [Formula: see text] (case 2). For the case of non-maximal Dirac CP violation, we perform numerical computation to show relations between the CP-violating Dirac phase and the mixing angles.