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 $m_1\simeq m_2\simeq 74meV$, $m_3\simeq 55meV$, and neutrinoless double beta decay mass parameter $m_{0\nu \beta \beta }\simeq 33meV$. 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 ${\alpha }_1\simeq 0$, ${\alpha }_2\simeq \pi$.

Comments: 4.5 pages, 2 figures, added references, added more discussions for ${\theta }_{13}$ angle