Charged Lepton Mass Formula -- Development and Prospect --

The recent devolopment on the charged lepton mass forumula m_e+m_{\mu}+m_{\tau}={2/3}(\sqrt{m_e}+\sqrt{m_\mu}+\sqrt{m_{\tau}})^2 is reviewed. An S_3 or A_4 model will be promising for the mass relation.Comment: Latex, 11 pages, no figure, Talk at Internationa Workshop on Neutrino Masses and Mixing, at Shizuoka, Japan, December, 17-19, 200

Permutation Symmetry S_3 and VEV Structure of Flavor-Triplet Higgs Scalars

A model with flavor-triplet Higgs scalars \phi_i (i=1,2,3)is investigated under a permutation symmetry S_3 and its symmetry breaking. A possible S_3 breaking form of the Higgs potential whose vacuum expectation values v_i=< \phi_i> satisfy a relation v_1^2 +v_2^2 +v_3^2 ={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 = {2/3} (\sqrt{m_e}+\sqrt{m_\mu} +\sqrt{m_\tau})^2.Comment: 7 pages, 1 figure, final version to appear in PR

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 eptons, 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.Comment: version accepted by EPJ

S_4 Flavor Symmetry Embedded into SU(3) and Lepton Masses and Mixing

Based on 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)}) \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.Comment: 12 pages, no figure, to appear on JHE

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 {\bf 3} and ({\bf 1}, {\bf 1}',{\bf 1}'') of A_4, respectively.Comment: 13 pages including 1 table, errors in Sec.7 correcte

A Unified Description of Quark and Lepton Mass Matrices in a Universal Seesaw Model

In the democratic universal seesaw model, the mass matrices are given by \bar{f}_L m_L F_R + \bar{F}_L m_R f_R + \bar{F}_L M_F F_R (f: quarks and leptons; F: hypothetical heavy fermions), m_L and m_R are universal for up- and down-fermions, and M_F has a structure ({\bf 1}+ b_f X) (b_f is a flavour-dependent parameter, and X is a democratic matrix). The model can successfully explain the quark masses and CKM mixing parameters in terms of the charged lepton masses by adjusting only one parameter, b_f. However, so far, the model has not been able to give the observed bimaximal mixing for the neutrino sector. In the present paper, we consider that M_F in the quark sectors are still "fully" democratic, while M_F in the lepton sectors are partially democratic. Then, the revised model can reasonably give a nearly bimaximal mixing without spoiling the previous success in the quark sectors.Comment: 7 pages, no figur

Quark Mass Matrix with a Structure of a Rank One Matrix Plus a Unit Matrix

A quark mass matrix model $M_q=M_e^{1/2} O_q M_e^{1/2}$ is proposed where $M_e^{1/2}={\rm diag}(\sqrt{m_e},\sqrt{m_\mu},\sqrt{m_\tau})$ and $O_q$ is a unit matrix plus a rank one matrix. Up- and down-quark mass matrices $M_u$ and $M_d$ are described in terms of charged lepton masses and additional three parameters (one in $M_u$ and two in $M_d$). The model can predict reasonable quark mass ratios (not only $m_u/m_c$, $m_c/m_t$, $m_d/m_s$ and $m_s/m_b$, but also $m_u/m_d$) and Kobayashi-Maskawa matrix elements.Comment: 8 pages, Latex, no figure

Universal Seesaw Mass Matrix Model with an S_3 Symmetry

Stimulated by the phenomenological success of the universal seesaw mass matrix model, where the mass terms for quarks and leptons f_i (i=1,2,3) and hypothetical super-heavy fermions F_i are given by \bar{f}_L m_L F_R +\bar{F}_L m_R f_R + \bar{F}_L M_F F_R + h.c. and the form of M_F is democratic on the bases on which m_L and m_R are diagonal, the following model is discussed: The mass terms M_F are invariant under the permutation symmetry S_3, and the mass terms m_L and m_R are generated by breaking the S_3 symmetry spontaneously. The model leads to an interesting relation for the charged lepton masses.Comment: 8 pages + 1 table, latex, no figures, references adde

Top Quark Mass Enhancement in a Seesaw-Type Quark Mass Matrix

We investigate the implications of a seesaw type mass matrix, i.e., $M_f\simeq m_L M_F^{-1} m_R$, for quarks and leptons $f$ under the assumption that the matrices $m_L$ and $m_R$ are common to all flavors (up-/down- and quark-/lepton- sectors) and the matrices $M_F$ characterizing the heavy fermion sectors have the form [(unit matrix) + $b_f$ (a democratic matrix)] where $b_f$ is a flavor parameter. We find that by adjusting the complex parameter $b_f$, the model can provide that $m_t\gg m_b$ while at the same time keeping $m_u\sim m_d$ without assuming any parameter with hierarchically different values between $M_U$ and $M_D$. The model with three adjustable parameters under the ``maximal" top quark mass enhancement can give reasonable values of five quark mass ratios and four KM matrix parameters.Comment: 22 pages, Latex, 5 postscript figures available upon reques

Evolution of the Yukawa coupling constants and seesaw operators in the universal seesaw model

The general features of the evolution of the Yukawa coupling constants and seesaw operators in the universal seesaw model with det M_F=0 are investigated. Especially, it is checked whether the model causes bursts of Yukawa coupling constants, because in the model not only the magnitude of the Yukawa coupling constant (Y_L^u)_{33} in the up-quark sector but also that of (Y_L^d)_{33} in the down-quark sector is of the order of one, i.e., (Y_L^u)_{33} \sim (Y_L^d)_{33} \sim 1. The requirement that the model should be calculable perturbatively puts some constraints on the values of the intermediate mass scales and tan\beta (in the SUSY model).Comment: 21 pages, RevTex, 10 figure