Another Formula for the Charged Lepton Masses

TL;DR

The paper explores a new potential relation among charged lepton masses, extending known formulas, and proposes a scalar potential model to support this conjecture.

Contribution

It introduces a novel mass relation for charged leptons and suggests a scalar potential framework to explain it.

Findings

Proposes a new mass relation involving geometric means of lepton masses.

Suggests a scalar potential model as a theoretical basis for the relation.

Extends the understanding of lepton mass formulas.

Abstract

A charged lepton mass formula $(m_e +m_\mu + m_\tau)/(\sqrt{m_e}+\sqrt{m_\mu} + \sqrt{m_\tau})^2 =2/3$ is well-known. Since we can, in general, have two relations for three quantities, we may also expect another relation for the charged lepton masses. Then, the relation will be expressed by a form of $\sqrt{m_e m_\mu m_\tau}/(\sqrt{m_e}+\sqrt{m_\mu} + \sqrt{m_\tau})^3$. According to this conjecture, a scalar potential model is speculated.