2007

(hep-ph/0708.3913)

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

Abstract

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.

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(hep-ph/0707.0899)

Contributed paper to Lepton-Photon 2007

Broken SU(3) Flavor Symmetry and Tribimaximal Neutrino Mixing

Yoshio Koide

Abstract

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.

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(hep-ph/0706.4373)

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

Abstract

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.

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(hep-ph/0706.2534)

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)

Charged Lepton Mass Formula

-- Development and Prospect --

Yoshio Koide

Abstract

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.

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(hep-ph/0705.2275)

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

Yoshio Koide

Abstract

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.

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US-07-01

(hep-ph/0701018)

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

Yoshio Koide

Abstract

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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