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

• Published in: arXiv.org 2014-11
• Main Authors: Iizuka, Jun, Kitabayashi, Teruyuki, Minagawa, Yuki, Masaki Yasue
• Format: Article
• Language: English
• Subjects: CP violation; Matter & antimatter; Neutrinos; Numerical analysis; Parameterization
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1405.4045

CP violation in neutrino interactions is described by three phases contained in Pontecorvo-Maki-Nakagawa-Sakata mixing matrix (\(U_{PMNS}\)). We argue that the phenomenologocally consistent result of the Dirac CP violation can be obtained if \(U_{PMNS}\) is constructed along bipair neutrino mixing scheme, namely, requiring that \( | U_{12} | = | U_{32} | {\rm and} | U_{22} | = | U_{23} | (\rm case 1)\) and \( | U_{12} | = | U_{22} | {\rm and} | U_{32} | = | U_{33}| (\rm case 2)\), where \(U_{ij}\) stands for the \(i\)-\(j\) matrix element of \(U_{PMNS}\). As a results, the solar, atmospheric and reactor neutrino mixing angles \(\theta_{12}\), \(\theta_{23}\) and \(\theta_{13}\), respectively, are correlated to satisfy \(\cos 2{\theta_{12}} = \sin^2\theta_{23} - \tan^2\theta_{13}\) (case 1) or \(\cos 2{\theta_{12}} = \cos^2\theta_{23} - \tan^2\theta_{13}\) (case 2). Furthermore, if Dirac CP violation is observed to be maximal, \(\theta_{23}\) is determined by \(\theta_{13}\) to be: \(\sin^2\theta_{23} \approx ({\sqrt 2 - 1})({\cos^2\theta_{13} + \sqrt 2 \sin^2\theta_{13}})\) (case 1) or \(\cos^2\theta_{23} \approx ({\sqrt 2 - 1})({\cos^2\theta_{13} + \sqrt 2 \sin^2\theta_{13}})\) (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.