Quark Mass Matrix Model Research Articles

Parameter-independent quark mass relation in the U(3) × U(3)′ model

Recently, we have proposed a quark mass matrix model based on U(3) × U(3)[Formula: see text] family symmetry, in which up- and down-quark mass matrices [Formula: see text] and [Formula: see text] are described only by complex parameters [Formula: see text] and [Formula: see text], respectively. When we use charged lepton masses as additional input values, we can successfully obtain predictions for quark masses and Cabibbo–Kobayashi–Maskawa mixing. Since we have only one complex parameter [Formula: see text] for each mass matrix [Formula: see text], we can obtain a parameter-independent mass relation by using three equations for [Formula: see text], [Formula: see text] and [Formula: see text], where [Formula: see text] ([Formula: see text]). In this paper, we investigate the parameter-independent feature of the quark mass relation in the model.

Quark and lepton mass matrices described by charged lepton masses

Recently, we proposed a unified mass matrix model for quarks and leptons, in which, mass ratios and mixings of the quarks and neutrinos are described by using only the observed charged lepton mass values as family-number-dependent parameters and only six family-number-independent free parameters. In spite of quite few parameters, the model gives remarkable agreement with observed data (i.e. Cabibbo–Kobayashi–Maskawa (CKM) mixing, Pontecorvo–Maki–Nakagawa–Sakata (PMNS) mixing and mass ratios). Taking this phenomenological success seriously, we give a formulation of the so-called Yukawaon model in detail from a theoretical aspect, especially for the construction of superpotentials and R charge assignments of fields. The model is considerably modified from the previous one, while the phenomenological success is kept unchanged.

Quark and lepton mass matrix model with only six family-independent parameters

We propose a unified mass matrix model for quarks and leptons, in which sixteen observables of mass ratios and mixings of the quarks and neutrinos are described by using no family number-dependent parameters except for the charged lepton masses and only six family number-independent free parameters. The model is constructed by extending the so-called "Yukawaon" model to a seesaw type model with the smallest number of possible family number-independent free parameters. As a result, once the six parameters is fixed by the quark mixing and the mass ratios of quarks and neutrinos, no free parameters are left in the lepton mixing matrix. The results are in excellent agreement with the neutrino mixing data. We predict $\delta_{CP}^\ell =-68^\circ$ for the leptonic $CP$ violating phase and $\langle m\rangle\simeq 21$ meV for the effective Majorana neutrino mass.

Abnormal structure of fermion mixings in a seesaw quark mass matrix model

It is pointed out that in a seesaw quark mass matrix model which yields a singular enhancement of the top-quark mass, the right-handed fermion-mixing matrix U_R^u for the up-quark sector has a peculiar structure in contrast to the left-handed one U_L^u. As an example of the explicit structures of U_L^u and U_R^u, a case in which the heavy fermion mass matrix M_F is given by a form [(unit matrix)+(rank-one matrix)] is investigated. As a consequence, one finds observable signatures at projected high energy accelerators like the production of a fourth heavy quark family.

NEUTRINO MIXING IN A DEMOCRATIC SEESAW MASS MATRIX MODEL

On the basis of a seesaw-type mass matrix model for quarks and leptons, [Formula: see text] where mL∝mR are universal for f=u, d, v and e (up-quark, downquark, neutrino and charged lepton sectors respectively), and MF has a form [(unit matrix)+(democratic-type matrix)], neutrino masses and mixings are investigated. We try to understand a large vµ−vτ mixing, i.e. sin2 2θ23~1, with mv1 ≪ mv2~mv3, which has been suggested by the atmospheric neutrino data.

QUARK MASS MATRIX WITH A STRUCTURE OF A RANK-ONE MATRIX PLUS A UNIT MATRIX

A quark mass matrix model [Formula: see text] is proposed where [Formula: see text] and Oq is a unit matrix plus a rank-one matrix. Up- and down-quark mass matrices Mu and Md are described in terms of charged lepton masses and additional three parameters (one in Mu and two in Md). The model can predict reasonable quark mass ratios (not only mu/mc, mc/mt, md/ms and ms/mb, but also mu/md) and Kobayashi–Maskawa matrix elements.

Phenomenological quark mass matrix model with two adjustable parameters.

A phenomenological quark mass matrix model which includes only two adjustable parameters is proposed from the point of view of the unification of quark and lepton mass matrices. The model can provide reasonable values of quark mass ratios and Kobayashi-Maskawa matrix parameters.

How many parameters does a quark mass matrix model need?

An investigation independent of matrix form is made of how many parameters, which characterize the difference between up- and down-quark mass matrices, are, at least, required from the present data on quark masses and mixings. From a general study of the model with hierarchical three-step mass generations described by the three parameters {alpha}{sub {ital q}}, {beta}{sub {ital q}}, and {gamma}{sub {ital q}} ({vert bar}{alpha}{sub {ital q}}{vert bar}{much gt}{vert bar}{beta}{sub {ital q}}{vert bar}{much gt}{vert bar}{gamma}{sub {ital q}}{vert bar}; {ital q}={ital u},{ital d}), it is pointed out that the model with {beta}{sub {ital u}}/{beta}{sub {ital d}}={gamma}{sub {ital u}}/{gamma}{sub {ital d}} (i.e., with two independent parameters {alpha}{sub {ital q}} and {beta}{sub {ital q}}) is ruled out.