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Updated: 2008.02.03
Physics Letters B, Vol.659, p.260-274 (2008).
DOI:10.1016/j.physletb.2007.10.082
New Origin of a Bilinear Mass Matrix Form
Naoyuki Haba and Yoshio Koide
A charged lepton mass formula is explained
when the masses are proportional to the squared
vacuum expectation values (VEVs) of
scalar fields.
We introduce a U(3) flavor symmetry and its nonet scalar field Phi,
whose VEV structure plays an essential role for generating the
fermion mass spectrum.
We can naturally obtain a bilinear form of the Yukawa coupling
Y_{ij} \propto \sum_k \langle\Phi_{ik}\rangle
\langle\Phi_{kj}\rangle without
non-renormalizable interactions, when the flavor
symmetry is broken only through
Yukawa coupling and tadpole terms.
We also speculate a possible
VEV structure of \langle\Phi\rangle.
Contributed paper to Lepton-Photon 2007
Broken SU(3) Flavor Symmetry and Tribimaximal Neutrino Mixing
Recent work on a lepton mass matrix model based on an SU(3) flavor symmetry
which is broken into S_4 is reviewed. The flavor structures of the masses and
mixing are caused by VEVs of SU(2)_L-singlet scalars \phi which are nonets
({\bf 8}+{\bf 1}) of the SU(3) flavor symmetry, and which are broken into {\bf
2}+{\bf 3}+{\bf 3}' and {\bf 1} of S_4. If we require the invariance under the
transformation (\phi^{(8)},\phi^{(1)}) \to (-\phi^{(8)},+\phi^{(1)}) for the
superpotential of the nonet field \phi^{(8+1)}, the model leads to a beautiful
relation for the charged lepton masses. The observed tribimaximal neutrino
mixing is understood by assuming two SU(3) singlet right-handed neutrinos
\nu_R^{(\pm)} and an SU(3) triplet scalar \chi.
Physical Review D Vol.77, p.016006-01 - 016006-07 , (2008).
DOI: 10.1103/PhysRevD.77.016006
Neutrino Mixing based on Mass Matrices
with a 2-3 Symmetry
(Title was changed from "Possible Dirac Mass Matrix Forms
Under the 2-3 Symmetry and GUT Scenarios")
Yoshio Koide and Eiichi Takasugi
Under an assumption that the $2\leftrightarrow 3$ symmetry is broken
only through phases, we give a systematical investigation of possible
lepton mass matrix forms without referring to explicit parameter values.
Two types of the $2\leftrightarrow 3$ symmetry are investigated:
one is that the left- and right-handed fields $(f_L, f_R)$ obey the
symmetry, and another one is that only $f_L$ obeys the symmetry.
In latter case, in spite of no $2\leftrightarrow 3$ symmetry in the
Majorana mass matrix $M_R$ for $\nu_R$, the neutrino seesaw mass
matrix still obey the $2\leftrightarrow 3$ symmetry. Possible
phenomenology is discussed.
Talk at Internationa Workshop on Neutrino Masses and Mixing
--- Toward Unified Understanding of Quark and Lepton Mass Matrices --- ,
at Shizuoka, Japan, December, 17-19, 2006
International Journal of Modern Physics E, Vo.16, p.1417 -- 1426, (2007)
The recent devolopment on the charged lepton mass forumula
m_e+m_{\mu}+m_{\tau}=
\frac{2}{3}\left( \sqrt{m_e}+\sqrt{m_\mu}
+\sqrt{m_{\tau}}\right)^2$ is reviewed.
An S_3 or A_$ model will be promising for the mass
relation.
Journal of High Energy Physics, Vol.08, p.086-1 --086-13 (2007).
S_4 Flavor Symmetry Embedded into SU(3)
and Lepton Masses and Mixing
Under an assumption that an S_4 flavor symmetry is
embedded into SU(3), a lepton mass matrix model is investigated.
A Frogatt-Nielsen type model is assumed, and the
flavor structures of the masses and mixing are caused by VEVs of
SU(2)_L-singlet scalars \phi_u and \phi_d which are nonets
(8+1) of the SU(3) flavor symmetry, and which are broken
into 2+3+3' and 1 of S_4. If we require the invariance under
the transformation (\phi^{(8)},\phi^{(1)}) \rightarrow
(-\phi^{(8)},+\phi^{(1)}) for the superpotential of the nonet field
\phi^{(8+1)}, the model leads to a beautiful relation for
the charged lepton masses.
The observed tribimaximal neutrino mixing is understood by
assuming two SU(3) singlet right-handed neutrinos \nu_R^{(\pm)}
and an SU(3) triplet scalar \chi.
European Physical Journal C, Vol.52,
p.617 -- 623 (2007)
DOI 10.1140/epjc/s10052-007-0433-1
A_4 Symmetry and Lepton Masses and Mixing
Stimulated by Ma's idea which explains the tribimaximal
neutrino mixing by assuming an A_4 flavor symmetry,
a lepton mass matrix model is investigated.
A Frogatt-Nielsen type model is assumed, and the
flavor structures of the masses and mixing are caused by the VEVs of
SU(2)_L-singlet scalars \phi_i^u and \phi_i^d (i=1,2,3),
which are assigned to 3 and (1, 1', 1'')
of A_4, respectively.
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