Democracy of Families and Neutrino Mass Matrix

Abstract

On the basis of a seesaw-type mass matrix model for quarks and leptons, $M_f \simeq m_L M_F^{-1} m_R$, where $m_L\propto m_R$ are universal for $f=u,d,\nu$ and $e$ (up-quark-, down-quark-, neutrino- and charged lepton-sectors), and $M_F$ is given by $M_F=K ({\bf 1} + 3 b_f X)$ ({\bf 1} is a $3\times 3$ unit matrix, $X$ is a democratic-type matrix and $b_f$ is a complex parameter which depends on $f$, neutrino mass spectrum and mixings are discussed. The model can provide an explanation why $m_t \gg m_b$, while $m_u\sim m_d$ by taking $b_u=-1/3$, at which the detarminant of $M_F$ becomes zero. At $b_\nu=-1/2$, the model can provide a large $\nu_\mu$-$\nu_\tau$ mixing, $\sin^2 2\theta_{23}\simeq 1$, with $m_{\nu 1} \ll m_{\nu 2} \simeq m_{\nu 3}$, which is favorable to the atmospheric and solar neutrino data.