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日大理工・益川塾連携 素粒子物理学シンポジュウム： 2011.10.31, 東京
「世代 (generation)」派の対極に位置する「家族 (families)」派の
立場から，クォーク・レプトンの質量スペクトルと混合の問題が
論じられる．ユカワオン模型についての解説がなされる．
(4) OU-HET-730/2011; MISC-2011-16
arXiv:1110.5413 [hep-ph]: Oct. 26, 2011
SU(5)-Compatible Yukawaon Model With Two Family Symmetries U(3)$\times$O(3)
A yukawaon model which is compatible
with an SU(5) GUT model is investigated.
In a previous SU(5) compatible yukawaon model
with a U(3) family gauge symmetry,
we could not build a model with a lower energy scale of
the family gauge symmetry breaking scale $\Lambda_{fam}$
than $10^{13}$ GeV, so the family gauge boson effects in the
previous model were invisible.
In the present model, we consider two family symmetries
U(3)$\times$O(3), and we assume that the conventional quarks
and leptons $(\bar{\bf 5}+{\bf 10}+{\bf 1})$ of SU(5)
are described as
$(\bar{\bf 5}_i+{\bf 10}_\alpha+{\bf 1}_\alpha)$
($ i=1,2,3$ and $\alpha=1,2,3$ are indices of U(3) and
O(3), respectively).
As a result, we build a model with $\Lambda_{O3}
\sim 10^{16}$ GeV and $\Lambda_{U3}
\sim 10^{3}$ GeV.
The lightest U(3) family gauge boson $A_1^1$
will be observed with a mass of the order of 1 TeV.
(3) OU-HET-711/2011; MISC-2011-11
arXiv:1106.5202 [hep-ph]: June 28, 2011 ;
Revised: Dec. 29, 2011
For revised version, see (1) in 2012.
Neutrino Mass Matrix in a U(3) Yukawaon Model
with a New Fundamental VEV Matrix
Yoshio Koide and Hiroyuki Nishiura
In the so-called ``yukawaon" model, it is assumed that Yukawa coupling
constants originate in
vacuum expectation values (VEVs) $\langle Y_f\rangle$ of scalars
$Y_f$. In the previous yukawaon model based on an O(3) family symmetry,
the VEV matrices
$\langle Y_f\rangle$ have been given in terms of a fundamental
VEV matrix $\langle \Phi_e \rangle \propto {\rm diag}(\sqrt{m_e},
\sqrt{m_\mu}, \sqrt{m_\tau})$.
We propose a new model based on a U(3) family symmetry, in which
all quark and lepton mass matrices are described
in terms of a new fundamental VEV matrix $\langle \Phi_0 \rangle$
(not $\langle \Phi_e \rangle$ as in the previous model).
The new model has only four parameters in the up-quark and lepton sectors
for 12 observable quantities (2 up-quark mass ratios, 4 lepton mass ratios,
and 4+2 lepton mixing parameters).
By using observed values of up-quark mass ratios, charged lepton mass ratios,
and $\sin^2 \theta_{solar}$ as input values, we predict
$\sin^2 2\theta_{atm} \simeq 0.99$, $\sin^2 2\theta_{13} \simeq 0.015$,
$\Delta m^2_{21}/\Delta m^2_{32} \simeq 0.030$,
$\langle m_{ee}\rangle \simeq 0.0039$ eV, and so on.
(2) OU-HET-709/2011; MISC-2011-09
arXiv:1106.0971 [hep-ph]: June 6, 2011
International Journal of Modern Physics A, Vol. 27,
pp.1250028-1 -- 1250028-14 (2012)
DOI: 10.1142/S0217751X12500285
SU(5)-Compatible Yukawaon Model
A yukawaon model which is compatible
with an SU(5) GUT model is investigated.
In previous yukawaon models, the effective Yukawa
coupling constants $Y_f^{eff}$ are given by vacuum
expectation values of fields $Y_f$ (``yukawaons") as
$(Y_f^{eff})_{ij}= (y_f/\Lambda)\langle (Y_f)_{ij} \rangle$.
In order to build a model without a cutoff scale $\Lambda$,
vector-like fields $(\bar{\bf 5}+{\bf 10}+{\bf 5}+\bar{\bf 10})$
are introduced in addition to the conventional quarks
and leptons $(\bar{\bf 5}+{\bf 10}+{\bf 1})$.
The model naturally leads to a model in which a yukawaon $Y_e$
in the charged lepton sector plays a role of a substitute
for a yukawaon $Y_\nu$ in the neutrino Dirac mass sector.
Stimulated by Sumino's model, U(3)$\times$O(3) are
assumed as family symmetries.
The U(3) symmetry is broken at
$\langle Y_f\rangle \sim 10^{13}$ GeV.
Revised version of (7) in 2010
arXiv:1011.1064 [hep-ph]:
Revised version June 3, 2011
Title was changed together with a major change of the text.
Journal of Physics G: Nuclear and Particle Physics,
Vol.38, p.085004(12pp) (2011)
DOI:10.1088/0954-3899/38/8/085004
Yukawaon Model with U(3)$\times$O(3) Family Symmetries
A quark and lepton mass matrix model with family symmetries
U(3)$\times$O(3) is investigated on the basis of the
so-called yukawaon model.
In the present model, quarks and leptons are assigned
to $(\ell, e^c, u^c) \sim ({\bf 3}, {\bf 3}, {\bf 3}^*)$ of U(3) and
$(q, d^c, \nu^c) \sim ({\bf 3}, {\bf 3}, {\bf 3})$ of O(3).
Then, the neutrino mass matrix is given by
$M_\nu = m_D M_R^{-1} m_D^T$ with
$m_D \propto \langle \Phi_e \rangle$,
where the charged lepton mass matrix $M_e$ is given by
$M_e = k \langle \Phi_e \rangle \langle \Phi_e^T \rangle$.
A merit in considering U(3)$\times$O(3) lies in that
we can lower the cutoff scale $\Lambda$ in the yukawaon
model.
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