Pattern Of Quark Mass Matrices Research Articles

Quark mass matrices, textures and CKM precision measurements

In the light of several recent analyses pointing toward texture 4-zero Fritzsch-like quark mass matrices as the only viable structures for quark mass matrices, this work adopts a model independent approach to reconstruct an alternate and simplified structure of texture specific quark mass matrices in a generalized “[Formula: see text]-diagonal” basis within the Standard Model framework using the unitarity of CKM matrix and the observed hierarchies in quark mass spectra and mixing angles. It is observed that the measured [Formula: see text] values of the three physical parameters namely [Formula: see text], [Formula: see text] and [Formula: see text] naturally lead to the vanishing of (11) element in the down type quark mass matrix and that the single measurable CP violating phase [Formula: see text] in the CKM matrix is sufficient enough in [Formula: see text] to explain the observed mixing pattern in a suitable basis. The leading order as well as exact analytic phenomenological solutions are addressed for the modest pattern of quark mass matrices derived from CKM matrix and precision measurements of mixing parameters.

FERMION MASSES AND MIXING IN FOUR AND MORE DIMENSIONS

We give an overview of recent progress in the study of fermion mass and flavor mixing phenomena. Mass matrix ansatze are considered within the Standard Model (SM) and SUSY GUT's where some predictive frameworks based on SU(5) and SO(10) are reviewed. We describe a variety of schemes to construct quark mass matrices in extra dimensions focusing on four major classes: models with the SM residing on 3-brane, models with universal extra dimensions, models with split fermions and models with warped extra dimensions. We outline how realistic patterns of quark mass matrices could be derived from orbifold models in heterotic superstring theory. Finally, we address the fermion mass problem in intersecting D-branes scenarios, and present models with D6-branes able to give a good quantitatively description of quark masses and mixing. The role of flavor/CP violation problem as a probe of new physics is emphasized.

Complete parameter space of quark mass matrices with four texture zeros

The full parameter space of Hermitian quark mass matrices with four texture zeros is explored by using current experimental data. We find that all ten free parameters of the four-zero quark mass matrices can be well constrained. In particular, only one of the two phase parameters plays an important role in CP violation. The structural features of this specific pattern of quark mass matrices are also discussed in detail.

Textures of quark mass matrices and renormalization effects

Two natural patterns of quark mass matrices are constructed at the electroweak scale, and their corresponding Yukawa coupling matrices are obtained at very high energy scales by use of the renormalization-group equations in the minimal supersymmetric standard model. It is found that the structural features of both patterns are essentially stable against renormalization effects. Some comments are also given on other possible ways to construct the stable textures of quark mass matrices.

QUARK MASS MATRICES IN SUPERSTRING MODELS

Four simple but realistic patterns of quark mass matrices are derived from orbifold models of superstring theory in the absence of gauge symmetries. Two of them correspond to the Ramond–Roberts–Ross types, which have five texture zeros in up and down quark sectors. The other two, with four texture zeros, preserve the structural parallelism between up and down sectors. The phenomenological consequences of these mass matrices on flavor mixing and CP violation are analyzed at the weak scale. With the same input values of quark mass ratios, we find that only one or two of the four patterns can be in good agreement with current experimental data.

A String-Inspired Ansatz for Quark Masses and Mixing

We propose a simple but realistic pattern of quark mass matrices at the string scale, which can be derived from orbifold models of superstring theory with no use of gauge symmetries. This pattern is left–right symmetric and preserves the structural parallelism between up and down quark sectors. Its phenomenological consequences on flavor mixing and CP-violation are confronted with current experiments at the weak scale by using the renormalization group equations in the framework of minimal supersymmetric standard model. We find that good agreement is achievable without fine-tuning.

Scale dependence of quark mass matrices in models with flavor symmetries.

Numerical correlations between fermion masses and mixings could indicate the presence of a flavor symmetry at high energies. In general, the search for these correlations using low-energy data requires an estimate of leading-log radiative corrections. We present a complete analysis of the evolution between the electroweak and the grand unification scales of quark mass parameters in minimal supersymmetric models. We take $M_t=180$ GeV and consider all possible values of $\tan \beta$. We also analize the possibility that the {\it top} and/or the {\it bottom} Yukawa couplings result from an intermediate quasifixed point (QFP) of the equations. We show that the quark mixings of the third family do {\it not} have a QFP behaviour (in contrast to the masses, the renormalization of all the mixings is linear), and we evaluate the low-energy value of $V_{ub}$ which corresponds to $V_{ub}(M_X)=0$. Then we focus on the renormalization-group corrections to {\it (i)} typical relations obtained in models with flavor symmetries at the unification scale and {\it (ii)} a superstring-motivated pattern of quark mass matrices. We show that in most of the models the numerical prediction for $V_{ub}$ can be {\it corrected} in both directions (by varying $\tan\beta$) due to {\it top} or {\it bottom} radiative corrections.

Patterns of quark mass matrices in a class of Calabi-Yau models

We study a class of superstring models compactified in the 3-generation Calabi-Yau manifold of Tian and Yau. Our analysis includes the complete E 6-singlet sector, which has been recently evaluated using techniques of spectral and exact sequences. We use the discrete symmetries of the models to find flat directions of symmetry breaking that leave unbroken a low energy matter parity and make all leptoquarks heavy while preserving light Higgs fields. Then we classify the patterns of ordinary quark mass matrices and show that (without invoking effects due to nonrenormalizable terms) only one structure can accommodate the observed value of fermion masses and mixing angles. The model, which unifies perturbatively and predicts a realistic structure of quark mass matrices with texture zeros, is one of the many possible string vacua. However, in contrast with what is often assumed in the search for realistic unified scenarios, it is highly nonminimal near the unification scale, and the predicted mass matrices have no simple symmetry properties.

The pattern of lepton and quark masses

The observed hierarchy of the lepton-quark masses and the emerging hierachical pattern of the weak interaction mixing matrix is discussed, as well as an underlying theoretical framework based on a step-wise breaking of chiral symmetries. The flavor mixing angles are functions of quark mass ratios and must vanish if the associated generation is massless. A specific pattern of quark mass matrices emerges, which can be used to extrapolate to higher energies and to deduce the properties of ultra-heavy quarks.

Pattern of quark mass matrices and the mixing-angle hierarchy.

By expressing the quark masses, as well as the quark-mixing angles, in powers of the Cabibbo angle (\ensuremath{\lambda}) we show that the up- and down-quark mass matrices are proportional to each other up to terms of order ${\ensuremath{\lambda}}^{2}$. This implies that the mass ratio of these two types of quarks should be roughly the same in each generation except for the lightest quarks. We then demonstrate that this is the key ingredient that enables the Fritzsch ansatz for quark mass matrices to reproduce the observed pattern of Kobayashi-Maskawa (KM) mixings and predict that the KM angle ${\mathrm{theta}}_{3}$=O(${\ensuremath{\lambda}}^{3}$). Some of the phenomelogical implications, including that for the kaon CP-violation parameter \ensuremath{\epsilon}, are worked out.