Quark mass matrices inspired by a numerical relation

Abstract

In 1981, Yoshio Koide noticed that the square root values of the charged lepton masses satisfy the relation \[ Q=\frac{m_e+m_μ+m_τ}{(\sqrt{m_e}+\sqrt{m_μ}+\sqrt{m_τ})^2} \approx \frac{2}{3} \] Inspired by this relation, we introduce tentative mass matrices, using numerical values, and find matrices that display an underlying democratic texture.