Parametrization of the quark mixing matrix involving its Eigenvalues

Abstract

A parametrization of the 3 × 3 Cabibbo-Kobayashi-Maskawa matrix, V , is presented in which the parameters are the eigenvalues and the components of its eigenvectors. In this parametrization, the small departure of the experimentally determined V from being moduli symmetric (i.e. |V_ij | = |V_ji|) is controlled by the small difference between two of the eigenvalues. In case, any two eigenvalues are equal, one obtains a moduli symmetric V depending on only three parameters. Our parametrization gives very good fits to the available data including CP-violation. Our value of sin 2β ≈ 0.7 and other parameters associated with the 'unitarity triangle' V₁₁V * ₁₃ +V₂₁V *₂₃V₃₁V *₃₃ = 0 are in good agreement with data and other analyses.