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Yang","submitted_at":"2026-05-31T03:28:41Z","abstract_excerpt":"We show that the CP phases $\\phi_{1,2}$ appearing in the TM$_{1,2}$ mixing are directly identified with rephasing invariants $\\phi _{1} = - \\arg \\left[ { U_{e2} U_{e3} U_{\\mu 1} U_{\\tau 1} / U_{e 1} \\det U } \\right]$, $\\phi_{2} = - \\arg \\left[ { U_{e1} U_{e3} U_{\\mu 2} U_{\\tau 2} / U_{e 2} \\det U} \\right]$. Furthermore, we demonstrate relations $\\phi_{i} = \\delta - \\arg [ U_{\\mu i}^{0} U_{\\tau i}^{0} ]$ among $\\phi_{1,2}$, the Dirac CP phase $\\delta$ and matrix elements in the PDG parametrization $U^{0}$. 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S. Yang","submitted_at":"2026-05-31T03:28:41Z","abstract_excerpt":"We show that the CP phases $\\phi_{1,2}$ appearing in the TM$_{1,2}$ mixing are directly identified with rephasing invariants $\\phi _{1} = - \\arg \\left[ { U_{e2} U_{e3} U_{\\mu 1} U_{\\tau 1} / U_{e 1} \\det U } \\right]$, $\\phi_{2} = - \\arg \\left[ { U_{e1} U_{e3} U_{\\mu 2} U_{\\tau 2} / U_{e 2} \\det U} \\right]$. Furthermore, we demonstrate relations $\\phi_{i} = \\delta - \\arg [ U_{\\mu i}^{0} U_{\\tau i}^{0} ]$ among $\\phi_{1,2}$, the Dirac CP phase $\\delta$ and matrix elements in the PDG parametrization $U^{0}$. 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