Democracy of Families and Neutrino Mass Matrix
Abstract
Description
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 $f=u,d,ν$ 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 $b_ν=-1/2$, the model can provide a large $ν_μ$-$ν_τ$ mixing, $\sin^2 2θ_{23}\simeq 1$, with $m_{ν1} \ll m_{ν2} \simeq m_{ν3}$, which is favorable to the atmospheric and solar neutrino data.
10 pages, a LaTex file without figures. A hard copy with figures is available upon request
10 pages, a LaTex file without figures. A hard copy with figures is available upon request