{"paper":{"title":"Rephasing invariant structure of CP phase for simplified mixing matrices in Fritzsch--Xing parametrization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"An explicit rephasing transformation converts any unitary mixing matrix to the Fritzsch-Xing parametrization, and under the approximations U13^e=0 and U23^e=0 the FX phase simplifies to the sum of the neutrino-intrinsic phase and the 1-2 re","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Masaki J. S. Yang","submitted_at":"2026-02-16T06:51:23Z","abstract_excerpt":"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 $\\delta_{\\rm FX}$ 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 neutr"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We construct an explicit rephasing transformation that converts an arbitrary unitary mixing matrix into the Fritzsch--Xing (FX) parametrization... 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_FX and the contribution from the relative phase ρ'_1 - ρ'_2.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The approximations U_{13}^e = 0 and U_{23}^e = 0, where the 1-3 and 2-3 elements of the charged-lepton diagonalization matrix are neglected; these are invoked to obtain the compact expression for δ_FX.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Under the approximations U13^e = 0 and U23^e = 0, the Fritzsch-Xing CP phase equals the sum of the neutrino-intrinsic phase and the relative phase between the first two generations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"An explicit rephasing transformation converts any unitary mixing matrix to the Fritzsch-Xing parametrization, and under the approximations U13^e=0 and U23^e=0 the FX phase simplifies to the sum of the neutrino-intrinsic phase and the 1-2 re","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8d6e5371e54e3fb580b17fc0ecff15a1ca76dbc17b17bf50a8c2c40077ab173e"},"source":{"id":"2602.14513","kind":"arxiv","version":2},"verdict":{"id":"3515b6a3-4ff1-45c6-b244-9cf0101f5eb9","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T22:18:27.345544Z","strongest_claim":"We construct an explicit rephasing transformation that converts an arbitrary unitary mixing matrix into the Fritzsch--Xing (FX) parametrization... 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_FX and the contribution from the relative phase ρ'_1 - ρ'_2.","one_line_summary":"Under the approximations U13^e = 0 and U23^e = 0, the Fritzsch-Xing CP phase equals the sum of the neutrino-intrinsic phase and the relative phase between the first two generations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The approximations U_{13}^e = 0 and U_{23}^e = 0, where the 1-3 and 2-3 elements of the charged-lepton diagonalization matrix are neglected; these are invoked to obtain the compact expression for δ_FX.","pith_extraction_headline":"An explicit rephasing transformation converts any unitary mixing matrix to the Fritzsch-Xing parametrization, and under the approximations U13^e=0 and U23^e=0 the FX phase simplifies to the sum of the neutrino-intrinsic phase and the 1-2 re"},"references":{"count":56,"sample":[{"doi":"","year":null,"title":"Before proceeding to the general situation, let us consider another simplified scenario, in whichU e 23 = 0 is imposed by sacrificing the conditionU ν 13 = 0. The mixing matrix is then given by U=  ","work_id":"f959d001-fcf6-44c7-8582-490130b1d111","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"If|U e 23|is sufficiently small, we can perturbatively expand the expression ofδ FX","work_id":"61274656-9421-49bc-86d9-9c48c6a3b904","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1985,"title":"C. Jarlskog, Phys. Rev. Lett.55, 1039 (1985)","work_id":"fa2960e7-f3fd-4f85-b7cb-fccf53c4c622","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1986,"title":"D.-d. Wu, Phys. Rev. D33, 860 (1986)","work_id":"5cba8f22-e1ff-4450-94ad-8264ed5061c8","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1986,"title":"J. Bernabeu, G. C. Branco, and M. Gronau, Phys. Lett. B169, 243 (1986)","work_id":"aa87f074-e5d4-49f4-8074-830255cce60f","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":56,"snapshot_sha256":"136efe7be1e022adc39d6b9e9f5f1c881d4c0ba8221c706b7ef55d063f20dbf5","internal_anchors":26},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}