Physical Review D73, 073002-1 -- 073002-7 (2006)
Shape of the Unitary Triangle and Phase
Conventions of the CKM Matrix
A shape of the unitary triangle versus a CP violating parameter
\delta depends on the phase conventions of the CKM matrix,
although relations among observable quantities are
independent of the phase conventions.
In order to seek for a clue to the quark mass matrix structure
and the origin of the CP violation, the dependence of the
unitary triangle shape on the parameter \delta is
systematically investigated.
Physical Review D73, 057901-1 -- 057901-4 (2006)
Permutation Symmetry S_3 and
VEV Structure of Flavor-Triplet Higgs Scalars
Vacuum expectation values v_i=\langle \phi_i\rangle
of flavor-triplet Higgs scalars \phi_i (i=1,2,3)
in a Higgs potential with a permutation symmetry
S_3 and its small violation are investigated.
Especially, a possible form of the Higgs potential which
gives a relation v_1^2 +v_2^2 +v_3^2 =\frac{2}{3}
(v_1 +v_2 +v_3)^2$ is investigated, because if we suppose
a seesaw-like mass matrix model M_e = m M^{-1} m
with m_{ij} \propto \delta_{ij} v_i and
M_{ij} \propto \delta_{ij}, such a model can lead
to the well-known charged lepton mass relation
m_e +m_\mu +m_\tau = \frac{2}{3} (\sqrt{m_e}+\sqrt{m_\mu}
+\sqrt{m_\tau})^2.
European Physical Journal C48, 223-228, (2006)
Seesaw Mass Matrix Model of Quarks and Leptons
with Flavor-Triplet Higgs Scalars
In a seesaw mass matrix model $M_f = m_L M_F^{-1} m_R^\dagger$
with a universal structure of $m_L \propto m_R$, as the origin
of $m_L$ ($m_R$) for quarks and leptons,
flavor-triplet Higgs scalars whose vacuum expectation values $v_i$
are proportional to the square roots of the charged lepton masses
$m_{ei}$, i.e. $v_i \propto \sqrt{m_{ei}}$, are assumed.
Then, it is investigated whether such a model can explain the
observed neutrino masses and mixings (and also quark masses and
mixings) or not.
Challenge to the Mystery of
the Charged Lepton Mass Formula
Contribution Paper to Lepton-Photon 2005
Why the charged lepton mass formula
m_e +m_\mu +m_\tau = \frac{2}{3} (\sqrt{m_e}+\sqrt{m_\mu}
+\sqrt{m_\tau})^2 is mysterious is reviewed, and guiding
principles to solve the mystery are presented. According
to the principles, an example of such a mass generation
mechanism is proposed, where the origin of the mass spectrum
is attributed not to the structure of the Yukawa coupling
constants, but to a structure of vacuum expectation
values of flavor-triplet scalars under Z_4 \times S_3
symmetries.
Radiative Neutrino Masses and Quark and Lepton Unification Model
This review article was written as an official report on the
research project "Radiative Neutrino Mass Hypothesis and
Quark and Lepton Unification Model", which was supported
by Grand-in-Aid for Scientific Research, Ministry of Education,
Scientific Research, the Ministry of Education, Science and
Culture, Japan (Grant No.~15540283), during the 2003 and 2004
fiscal years.
Against to the conventional point of view that
the radiative mass generation mechanism
cannot be embedded into the framework of a
SUSY GUT model, we conclude that
the difficulty is not an inevitable trouble in the theory,
and we demonstrate that model-building of such a SUSY GUT model
without proton decay is, indeed, possible.
We will give a general mass matrix form
for the radiatively-induced neutrino masses.
And also, some related topics on the mass matrix models are reviewed.
Quark and Lepton Mass Matrix Structures
Suggested by the Observed Unitary Triangle Shape
Under the hypothesis that the CP violating phase parameter
\delta in the CKM matrix V takes own value so that the radius
R(\delta) of the circle circumscribed about the unitary
triangle takes its minimum value, possible phase conventions
of the CKM matrix are investigated. We find that two of the
9 phase conventions can give favorable predictions for
the observed shape of the unitary triangle. One of the
successful two suggests phenomenologically interesting structures
of the quark and lepton mass matrices, which lead to
|V_{us}|\simeq \sqrt{m_d/m_s}=0.22, |V_{ub}|\simeq \sqrt{m_u/m_t}
=0.0036 and |V_{cb}|\simeq \sqrt{m_c/2m_t}=0.043 for the CKM
matrix V, and to \sin^2 2\theta_{atm}=1, \tan^2 \theta_{solar}
\simeq |m_{\nu 1}/m_{\nu 2}| and |U_{13}|\simeq \sqrt{m_e/2 m_\tau}
for the lepton mixing matrix U under simple requirements for the
textures.