Rephasing Invariant Formula for CP Phase in Kobayashi–Maskawa Parametrization and Exact Sum Rule with Unitarity Triangle <i>δ</i> PDG+ <i>δ</i> KM = <i>π</i> – <i>α</i> + <i>γ</i>

Abstract In this letter, we obtain a rephasing invariant formula for the CP phase in the Kobayashi–Maskawa parametrization $\delta _{\rm KM} = \arg [ - { V_{ud} \det V_{\rm CKM} / V_{us} V_{ub} V_{cd} V_{td}} ]$. General perturbative expansion of the formula and the observed value $\delta _{\rm KM} \simeq \pi /2$ reveal that the phase difference of the 1-2 quark mixings $e^{i (\rho _{12}^{d} - \rho _{12}^{u})}$ is close to maximal for sufficiently small 1-3 quark mixings $s_{13}^{u,d}$. Moreover, combining this result with another formula for the CP phase $\delta _{\rm PDG}$ in the Particle Data Group (PDG) parametrization, we derive an exact sum rule $\delta _{\rm PDG} + \delta _{\rm KM} = \pi - \alpha + \gamma$ which relates the phases and the angles $\alpha , \beta , \gamma$ of the unitarity triangle.