Rephasing invariant structure of CP phase for simplified mixing matrices in Fritzsch--Xing parametrization
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911682858582016 |
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| author | Yang, Masaki J. S. |
| author_facet | Yang, Masaki J. S. |
| contents | In this paper, we construct an explicit rephasing transformation that converts an arbitrary unitary mixing matrix into the Fritzsch--Xing (FX) parametrization, which is obtained by trivializing arguments of the matrix elements in the third row and third column. We further analyze rephasing invariant structure of the FX phase $δ_{\rm FX}$ under an approximation $U_{13}^{e} = 0$, where the 1-3 element of the diagonalization matrix of charged leptons $U^{e}$ is neglected. With an additional approximation $U_{23}^{e} = 0$, the FX phase becomes highly simplified, reducing to a sum of the neutrino-intrinsic FX phase $δ^ν_{\rm FX}$ and the contribution from the relative phase $ρ'_{1}- ρ'_{2}$ between the lighter 1-2 generations. The phase $δ_{\rm FX}$ for finite $U_{23}^{e}$ is understood as a generalization of the compact expression. This result covers almost all perturbative calculations of CP phases for the CKM and MNS matrices with hierarchical charged fermions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_14513 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rephasing invariant structure of CP phase for simplified mixing matrices in Fritzsch--Xing parametrization Yang, Masaki J. S. High Energy Physics - Phenomenology In this paper, we construct an explicit rephasing transformation that converts an arbitrary unitary mixing matrix into the Fritzsch--Xing (FX) parametrization, which is obtained by trivializing arguments of the matrix elements in the third row and third column. We further analyze rephasing invariant structure of the FX phase $δ_{\rm FX}$ under an approximation $U_{13}^{e} = 0$, where the 1-3 element of the diagonalization matrix of charged leptons $U^{e}$ is neglected. With an additional approximation $U_{23}^{e} = 0$, the FX phase becomes highly simplified, reducing to a sum of the neutrino-intrinsic FX phase $δ^ν_{\rm FX}$ and the contribution from the relative phase $ρ'_{1}- ρ'_{2}$ between the lighter 1-2 generations. The phase $δ_{\rm FX}$ for finite $U_{23}^{e}$ is understood as a generalization of the compact expression. This result covers almost all perturbative calculations of CP phases for the CKM and MNS matrices with hierarchical charged fermions. |
| title | Rephasing invariant structure of CP phase for simplified mixing matrices in Fritzsch--Xing parametrization |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2602.14513 |