Rephasing invariant CP phases and sum rules in TM$_{1,2}$ mixing
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866916070849249280 |
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| author | Yang, Masaki J. S. |
| author_facet | Yang, Masaki J. S. |
| contents | We show that the CP phases $ϕ_{1,2}$ appearing in the TM$_{1,2}$ mixing are directly identified with rephasing invariants $ϕ_{1} = - \arg \left[ { U_{e2} U_{e3} U_{μ1} U_{τ1} / U_{e 1} \det U } \right]$, $ϕ_{2} = - \arg \left[ { U_{e1} U_{e3} U_{μ2} U_{τ2} / U_{e 2} \det U} \right]$. Furthermore, we demonstrate relations $ϕ_{i} = δ- \arg [ U_{μi}^{0} U_{τi}^{0} ]$ among $ϕ_{1,2}$, the Dirac CP phase $δ$ and matrix elements in the PDG parametrization $U^{0}$. These relations of CP phases are interpreted as specific elements of general sum rules among physical quantities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00980 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rephasing invariant CP phases and sum rules in TM$_{1,2}$ mixing Yang, Masaki J. S. High Energy Physics - Phenomenology We show that the CP phases $ϕ_{1,2}$ appearing in the TM$_{1,2}$ mixing are directly identified with rephasing invariants $ϕ_{1} = - \arg \left[ { U_{e2} U_{e3} U_{μ1} U_{τ1} / U_{e 1} \det U } \right]$, $ϕ_{2} = - \arg \left[ { U_{e1} U_{e3} U_{μ2} U_{τ2} / U_{e 2} \det U} \right]$. Furthermore, we demonstrate relations $ϕ_{i} = δ- \arg [ U_{μi}^{0} U_{τi}^{0} ]$ among $ϕ_{1,2}$, the Dirac CP phase $δ$ and matrix elements in the PDG parametrization $U^{0}$. These relations of CP phases are interpreted as specific elements of general sum rules among physical quantities. |
| title | Rephasing invariant CP phases and sum rules in TM$_{1,2}$ mixing |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2606.00980 |