Yukawaon Approach to the Sumino Relation for Charged Lepton Masses

On the basis of a supersymmetric yukawaon model, Sumino's relation for charged lepton masses is re-derived. A relation between values of $K(\mu) \equiv (m_e +m_\mu + m_\tau)/(\sqrt{m_e} + \sqrt{m_\mu} + \sqrt{m_\tau})^2$ and $\kappa(\mu) \equiv \sqrt{m_e m_\mu m_\tau}/ (\sqrt{m_e} + \sqrt{m_\mu}+ \sqrt{m_\tau})^3$ is investigated without using a relation $K=2/3$. Predicted value of $\kappa(\mu)$ is compared with the observed value of $\kappa(\mu)$, and it is concluded that the value $\xi(\mu)\equiv (3/2)K(\mu) -1$ is of the order of $10^{-3}$ or less.