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arXiv:1805.09533 (hep-ph)
Physics Letters B vol. 787 (2018) 171 (Elsevier)
DOI./10.1016/j.physletb.2018.10.053
Charged Lepton Mass Relations in a SUSY Scenario
Yoshio Koide and Toshifumi Yamashita
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.
arXiv:1805.07334 (hep-ph)
Parameter-Independent Quark Mass Relation in the U(3)$\times$U(3)$'$
Model
Yoshio Koide and Hiroyuki Nishiura
Recently, we have proposed a quark mass matrix model based on
U(3)$\times$U(3)$'$ family symmetry, in which up- and down-quark mass matrices
$M_u$ and $M_d$ are described only by complex parameters $a_u $ and $a_d $,
respectively. When we use charged lepton masses as additional input values, we
can successfully obtain predictions for quark masses and
Cabibbo-Kobayashi-Maskawa mixing. Since we have only one complex parameter
$a_q$ for each mass matrix $M_q$, we can obtain a parameter-independent mass
relation by using three equations for ${\rm Tr}[H_q]$, ${\rm Tr}[H_q H_q]$ and
${\rm det}H_q$, where $H_q \equiv M_q M_q^\dagger$ ($q=u, d$). In this paper,
we investigate its parameter-independent feature of the quark mass relation in
the model.
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