Yukawaon Approach to the Sumino Relation for Charged Lepton Masses

TL;DR

This paper re-derives Sumino's relation for charged lepton masses within a supersymmetric yukawaon model, exploring relations between mass parameters and comparing predictions with observed values to understand their small deviations.

Contribution

It introduces a novel derivation of Sumino's relation using a yukawaon model without assuming K=2/3, and investigates the relation between key mass parameters.

Findings

Predicted ppa(5) closely matches observed values.

The parameter (5) is of order 10^{-3} or less.

The model successfully reproduces charged lepton mass relations.

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.