Quark Mass Matrix with a Structure of a Rank One Matrix Plus a Unit Matrix

Abstract

A quark mass matrix model $M_q=M_e^{1/2} O_q M_e^{1/2} $ is proposed where $M_e^{1/2}={\rm diag}(\sqrt{m_e},\sqrt{m_μ},\sqrt{m_τ})$ and $O_q$ is a unit matrix plus a rank one matrix. Up- and down-quark mass matrices $M_u$ and $M_d$ are described in terms of charged lepton masses and additional three parameters (one in $M_u$ and two in $M_d$). The model can predict reasonable quark mass ratios (not only $m_u/m_c$, $m_c/m_t$, $m_d/m_s$ and $m_s/m_b$, but also $m_u/m_d$) and Kobayashi-Maskawa matrix elements.