Universal form for quark and lepton mass matrices

Abstract

We propose a universal form for quark and lepton mass matrices, which applies in a “leading order” approximation where CP-violating phases are ignored. Down-quark mass ratios are successfully predicted in our scheme using the measured Cabibbo-Kobayashi-Maskawa mixing angles as input. Assuming an additional discrete symmetry in the neutrino sector, we obtain the “golden ratio” pattern in the leading-order Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix; in addition we predict an inverted neutrino mass hierarchy with m_1-≃-m_2 ≃ 74  meV, m_3 ≃ 55  meV, and neutrinoless double beta decay mass parameter m_(0νββ) ≃ 33  meV. When CP-violating phases are included, our scheme suggests a residual  ℤ_2 antiunitary symmetry of the neutrino mass matrix, in which the interchange of μ and τ neutrinos is accompanied by a time reversal transformation, thus predicting that the CP-violating angle in the neutrino sector is close to the maximal value δ = ± π/2, and that the diagonal phases in the PMNS matrix are α_ 1 ≃ 0, α_2 ≃ π.