Neutrino Mass Matrix Model with a Bilinear Form

Abstract

A neutrino mass matrix model with a bilinear form $M_\nu = k_\nu (M_D M_R^{-1} M_D^T)^2$ is proposed within the framework of the so-called yukawaon model, which has been proposed for the purpose of a unified description of the lepton mixing matrix $U_{PMNS}$ and the quark mixing matrix $V_{CKM}$. The model has only two adjustable parameters for the PMNS mixing and neutrino mass atios. (Other parameters are fixed from the observed quark and charged lepton mass ratios and the CKM mixing.) The model gives reasonable values $\sin^2 2\theta_{12} \simeq 0.85$ and $\sin^2 2\theta_{23} \sim 1$ and $\sin^2 2\theta_{13} \sim 0.09$ together with $R_\nu \equiv \Delta m^2_{21}/\Delta m^2_{32} \sim 0.03$. Our prediction of the effective neutrino mass $<m>$ in the neutrinoless double beta decay takes a sizable value $< m >\simeq 0.0034$ eV.