Neutrino Mass Matrix Model with a Bilinear Form

TL;DR

This paper proposes a neutrino mass matrix model with a bilinear form within the yukawaon framework, successfully explaining lepton and quark mixing parameters with minimal adjustable parameters.

Contribution

It introduces a novel bilinear form for the neutrino mass matrix in the yukawaon model, linking lepton and quark mixing with only two free parameters.

Findings

Predicted neutrino mixing angles are consistent with observations.

Estimated effective neutrino mass for neutrinoless double beta decay is around 0.0034 eV.

Model achieves reasonable mass ratio and mixing predictions with minimal parameters.

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.