A universal form for quark and neutrino 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 CKM mixing angles as input. Assuming an additional discrete symmetry in the neutrino sector, we obtain the ``golden ratio'' pattern in the leading-order PMNS mixing matrix; in addition we predict an inverted neutrino mass hierarchy with $m_1\simeq m_2 \simeq74 meV$, $m_3\simeq 55 meV$, and neutrinoless double beta decay mass parameter $m_{0\nu\beta\beta}\simeq 33~ meV$. We also predict that the $CP$-violating angle in the neutrino sector is close to the maximal value $\delta=\pm\pi/2$, and that the diagonal phases in the PMNS matrix are $\alpha_1\simeq 0$, $\alpha_2\simeq\pi$.