We derive predictions for the Dirac phase δ present in the 3 × 3 unitary neutrino mixing matrix , where Ue and Uν are 3 × 3 unitary matrices which arise from the diagonalisation, respectively, of the charged lepton and the neutrino mass matrices. We consider forms of Ue and Uν allowing us to express δ as a function of three neutrino mixing angles, present in U, and the angles contained in Uν. We consider several forms of Uν determined by, or associated with, symmetries, tri-bimaximal, bimaximal, etc., for which the angles in Uν are fixed. For each of these forms and forms of Ue allowing one to reproduce the measured values of the neutrino mixing angles, we construct the likelihood function for cosδ, using (i) the latest results of the global fit analysis of neutrino oscillation data, and (ii) the prospective sensitivities on the neutrino mixing angles. Our results, in particular, confirm the conclusion, reached in earlier similar studies, that the measurement of the Dirac phase in the neutrino mixing matrix, together with an improvement of the precision on the mixing angles, can provide unique information as regards the possible existence of symmetry in the lepton sector.
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机译：我们推导3×3单一中微子混合矩阵中存在的狄拉克相δ的预测 U = U e † U ν ，其中Ue和Uν是3×3 ary矩阵，分别由带电的轻子和中微子质量矩阵的对角线化引起。我们考虑Ue和Uν的形式，使我们可以将δ表示为存在于U中的三个中微子混合角和包含在Uν中的角的函数。我们考虑由对称性，三双最大，双最大等确定或与之相关的几种形式的Uν，其中U ν中的角度是固定的。对于每种形式和 U e 形式（允许人们重现中微子混合角的测量值），我们构造cos δ，使用（i）中微子振荡数据的整体拟合分析的最新结果，以及（ii）对中微子混合角的预期灵敏度。我们的结果尤其证实了在早期类似研究中得出的结论，即中微子混合基质中狄拉克相的测量以及混合角精度的提高，可以就可能存在的问题提供独特的信息。轻子领域的对称性。
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