New approach to the parametrization of the quark and neutrino mixing matrices

Abstract

The quark and neutrino mixing matrices, V and Vv, are written as a linear combination of the unit matrix I and a hermitian unitary matrix (U and Uv). Thus, V = cosθI + isinθU and Vv = cosθvI + isinθvUv. In general, the matrix V (Vv) depends on only 3 real parameters including θ (θv). Our ansatz gives a good fit of the available data on the CKM‐matrix (V) for θ = π/4. The neutrino oscillation data requires θv = π/4 for maximal vμ and vτ mixing with Uv depending on only one small parameter. Even though V and Vv are very different, in our approach the remarkable equality θ = θv = π/4 emerges which suggests an underlying quark‐lepton symmetry in the mixing matrices.