狄拉克型左右对称理论中的强CP与PMNS相位
Strong CP and the PMNS Phase in Dirac Left-Right Symmetry
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中文总结 AI 辅助
该研究在狄拉克型左右对称理论中，通过对狄拉克轻子 Yukawa 矩阵施加 sectorial 实条件，将轻子CP破坏转化为分支依赖的预言，建立了轻子CP破坏、中微子质量与强CP之间的关联。
中文摘要 AI 辅助
具有广义宇称的左右对称理论将QCD裸角限制为CP守恒值，并将物理强CP相位\\(\bar\theta\\)与CP奇的宇称破缺参数\\(\eps\\)关联起来。我们证明，在狄拉克中微子实现中，对狄拉克轻子 Yukawa 矩阵施加 sectorial 实条件，可将可观测的轻子CP破坏从独立输入转化为分支依赖的预言。宇称重构右手轻子混合矩阵，而轻子实条件要求其与左手混合矩阵的复共轭在重定相下等价。对于一般三代 Yukawa 矩阵，兼容性等价于单个 Jarlskog 型 CP 奇不变量的消失。在物理狄拉克质量序中，固定振荡数据、质量排序和离散轻子分支后，兼容性将 PMNS Jarlskog 不变量确定为最轻中微子质量和\\(\eps\\)的函数。我们推导其主导解析行为并数值得到非线性兼容性分支。在压缩混合符号狄拉克中微子谱中，小的带符号质量和可将微小的宇称变形放大为归一化 PMNS Jarlskog 不变量的量级为1的值，包括最大 CP 破坏。对应的夸克重构独立提供\\(\eps\\)与\\(\bar\theta\\)之间可计算的分支依赖转换。轻子和夸克关系共同定义了轻子CP破坏、绝对中微子质量标度与强CP之间的一系列关联。
英文摘要
Left--right symmetric theories with generalized parity restrict the bare QCD angle to a CP-conserving value and relate the physical strong-CP phase \(\barθ\) to a CP-odd parity-breaking parameter \(\eps\). We show that, in the Dirac-neutrino realization, imposing a sectorial reality condition on the Dirac lepton Yukawa matrices turns observable leptonic CP violation from an independent input into a branch-dependent prediction. Parity reconstructs the right-handed leptonic mixing matrix, whereas leptonic reality requires it to be rephasing-equivalent to the complex conjugate of the left-handed one. For generic three-generation Yukawas, compatibility is equivalent to the vanishing of a single Jarlskog-type CP-odd invariant. In the physical Dirac hierarchy, for fixed oscillation data, mass ordering, and discrete leptonic branch, compatibility determines the PMNS Jarlskog invariant as a function of the lightest neutrino mass and \(\eps\). We derive its leading analytic behavior and obtain the nonlinear compatibility branches numerically. In compressed mixed-sign Dirac-neutrino spectra, small signed mass sums can amplify a tiny parity deformation into order-one values of the normalized PMNS Jarlskog invariant, including maximal CP violation. The corresponding quark reconstruction independently provides a calculable, branch-dependent conversion between \(\eps\) and \(\barθ\). Together, the leptonic and quark relations define a family of correlations among leptonic CP violation, the absolute neutrino mass scale, and strong CP.
