Charged Lepton Mass Relations in a SUSY Scenario

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 $K=(\mathrm{Tr}[\Phi \Phi ])/(\mathrm{Tr}[\Phi ]{)}^2$ and $\kappa =\det \Phi /(\mathrm{Tr}[\Phi ]{)}^3$ 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.

8 pages, no figures: Versio accepted PLB

References in corpus (4)

• Spectroscopy of Family Gauge Bosons
• Muon-Electron Conversion in a Family Gauge Boson Model
• Family Gauge Boson Production at the LHC
• Another Formula for the Charged Lepton Masses

Cited by in corpus (2)

• New Physics Search at the CEPC: a General Perspective
• A modified version of the Koide formula from flavor nonets in a scalar potential model and in a Yukawaon model