Yukawaon Model with U(3)$\times$O(3) Family Symmetries

Abstract

A quark and lepton mass matrix model with family symmetries U(3)$\times$O(3) is investigated on the basis of the so-called yukawaon model. In the present model, quarks and leptons are assigned to $(\ell ,e^c,u^c)\sim (3,3,3^{\ast })$ of U(3) and $(q,d^c,{\nu }^c)\sim (3,3,3)$ of O(3). Then, the neutrino mass matrix is given by $M_{\nu }=m_D{M}_R^{-1}{m}_D^T$ with $m_D\propto <{\Phi }_e>$, where the charged lepton mass matrix $M_e$ is given by $M_e=k<{\Phi }_e><{\Phi }_e^T>$. A merit in considering U(3)$\times$O(3) lies in that we can lower the cutoff scale $\Lambda$ in the yukawaon model.

Comments: 14 pages, no figure, minor change of model, title changed