Rephasing Invariant Formula for CP Phase in Kobayashi-Maskawa Parametrization and Exact Sum Rule with Unitarity Triangle δ_{\rm PDG} + δ_{\rm KM} = π- α+ γ

2025/08/14 by Yang, Masaki J. S. · 1 citation
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph)

paper · doi:10.48550/arxiv.2508.10249

Abstract

In this letter, we obtain a rephasing invariant formula for the CP phase in the Kobayashi--Maskawa parameterization δ_{\rm KM} = arg [ - V_ud det V_{\rm CKM} / V_us V_ub V_cd V_td ]. General perturbative expansion of the formula and observed value δ_{\rm KM} ≃ π/2 reveal that the phase difference of the 1-2 mixings e^i (ρ₁₂^d - ρ₁₂^u) is close to maximal for sufficiently small 1-3 quark mixings s₁₃^u,d. Moreover, combining this result with another formula for the CP phase δ_{\rm PDG} in the PDG parameterization, we derived an exact sum rule δ_{\rm PDG} + δ_{\rm KM} = π- α+ γ which relating the phases and the angles α, β, γ of the unitarity triangle.

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• New rephasing invariants and CP violation built from the trios of the CKM or PMNS matrix elements

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