Charged Lepton Mass Relations in a SUSY Scenario

TL;DR

This paper investigates charged lepton mass relations within a supersymmetric framework, demonstrating their stability against renormalization effects and proposing simple superpotential forms to realize these relations.

Contribution

It introduces a supersymmetric scenario that stabilizes charged lepton mass relations against renormalization effects and suggests explicit superpotential forms for these relations.

Findings

Mass relations are stable under RG effects in SUSY scenarios.

Proposed superpotential forms realize the charged lepton mass relations.

Stability achieved despite superpotential corrections.

Abstract

The observed charged lepton masses satisfy the relations $K \equiv (m_e +m_\mu+m_\tau)/(\sqrt{m_e} +\sqrt{m_\mu} +\sqrt{m_\tau})^2 =2/3$ and $\kappa \equiv \sqrt{m_e m_\mu m_\tau}/(\sqrt{m_e} +\sqrt{m_\mu} +\sqrt{m_\tau})^3 =1/486$ with great accuracy. These parameters are given as $K=( {\rm Tr}[\Phi \Phi])/ ({\rm Tr}[\Phi ])^2$ and $\kappa = {\rm det} \Phi/({\rm Tr}[\Phi ])^3$ if the charged lepton masses $m_{ei}$ are given by $m_{ei} \propto \sum_k \Phi_i^{\ k} \Phi_k^{\ i}$ where $\Phi$ is a U(3)-family nonet scalar. Simple scalar potential forms to realize the relations have been already proposed in non-supersymmetric scenarios, but the potential forms are not stable against the renormalization group effects. In this paper, we examine supersymmetric scenarios and find that the parameters $K$ and $\kappa$ are made stable against the effects in a very nontrivial way, even though the superpotential itself (in the canonical basis) suffers the usual corrections. We also show possible simple superpotential forms for the relations.