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

CP violation in neutrino interactions is described by three phases contained in Pontecorvo–Maki–Nakagawa–Sakata mixing matrix (UPMNS). We argue that the phenomenologically consistent result of the Dirac CP violation can be obtained if UPMNS 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 UPMNS. As a result, the solar, atmospheric and reactor neutrino mixing angles θ12, θ23 and θ13, respectively, are correlated to satisfy cos 2θ12 = sin2 θ23 - tan2 θ13 (case 1) or cos 2θ12 = cos2 θ23 - tan2 θ13 (case 2). Furthermore, if Dirac CP violation is observed to be maximal, θ23 is determined by θ13 to be: ${\rm sin}^2\theta_{23} \approx \big(\sqrt2-1\big)\big({\rm cos}^2\theta_{13}+\sqrt2\, {\rm sin}^2\theta_{13}\big)$ (case 1) or ${\rm cos}^2\, \theta_{23} \approx\big(\sqrt2-1\big)\big({\rm cos}^2\theta_{13}+\sqrt2\, {\rm sin}^2\theta_{13}\big)$ (case 2)...