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

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CP violation in neutrino interactions is described by three phases contained in Pontecorvo-Maki-Nakagawa-Sakata mixing matrix (UPMNS). We argue that the phenomenologocally 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 results, the solar, atmospheric and reactor neutrino mixing angles θ₁₂, θ₂₃ and θ₁₃, respectively, are correlated to satisfy 2θ₁₂ = ²θ₂₃ - ²θ₁₃ (case 1) or 2θ₁₂ = ²θ₂₃ - ²θ₁₃ (case 2). Furthermore, if Dirac CP violation is observed to be maximal, θ₂₃ is determined by θ₁₃ to be: ²θ₂₃ ≈ (√ 2 - 1)(²θ₁₃ + √ 2 ²θ₁₃) (case 1) or ²θ₂₃ ≈ (√ 2 - 1)(²θ₁₃ + √ 2 ²θ₁₃) (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.