Yukawaon Approach to the Sumino Relation for Charged Lepton Masses

Abstract

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.

Comments: 14 pages, 3 figures, version accepted by PLB