Quark Mass Matrices Research Articles

Linking leptonic CP violation to quark unitarity triangle

We study the linking between the CP violating phase of the lepton sectors and the unitarity triangle of the B0 meson system. Antusch, King, Malinsky and Spinrath have shown that the quark mass matrices with the negligible 1-3 mixing give an interesting relation between the phase of the quark mixing matrices and CP violating measure phi_2(alpha). This approach is extended by considering the SO(10) GUT including the Pati-Salam symmetry, which links the Yukawa matrices of the quark sector to the one of the lepton sector. We discuss the relation of the CP violating phases between both quark and lepton sectors as well as the mixing angles. Then, the leptonic CP violating phase is predicted in terms of the angle of the unitarity triangle of the B0 meson system. The leptonic CP violating phase deltaPMNS is predicted in the region -74 to -89, which is the consistent with the recent T2K results. Our predicted phase is sensitive to phi_2(alpha) and phi_3(gamma). These predictions will be clearly tested in the future neutrino experiments as well as the Belle-II experiment.

A complete survey of texture zeros in general and symmetric quark mass matrices

We perform a systematic analysis of all possible texture zeros in general and symmetric quark mass matrices. Using the values of masses and mixing parameters at the electroweak scale, we identify for both cases the maximally restrictive viable textures. Furthermore, we investigate the predictive power of these textures by applying a numerical predictivity measure recently defined by us. With this measure we find no predictive textures among the viable general quark mass matrices, while in the case of symmetric quark mass matrices most of the 15 maximally restrictive textures are predictive with respect to one or more light quark masses.

Finding a unique texture for quark mass matrices

Within the Standard Model, starting with the most general mass matrices, we have used the facility of making weak basis transformations and have imposed the condition of ``naturalness'' to carry out their analysis within the texture-zero approach. Interestingly, our analysis reveals that a particular set of texture-4 zero quark mass matrices can be considered to be a unique viable option for the description of quark mixing data.

Reply to “Comment on ‘Texture zeros and weak basis transformations in the quark sector of the standard model”’

We respond to the comments on my recent paper, Y. Giraldo [Phys. Rev. D 86, 093021 (2012)]. In their comments, they begin discussing a particular class of five-zero texture non-Fritzsch-like quark mass matrix, which was proposed by me, and question its validity. Then, they put in doubt the phases included in the unitary matrices used for diagonalizing the quark mass matrices, from which they claim that the $CP$ violating parameter ${\ensuremath{\epsilon}}_{k}$ obtained does not agree with the experimental value. Because of these comments, finally, they recommend being careful while analyzing the implications of weak basis transformations on textures. Other minor points are also discussed by them. In the following, I will show that the mentioned five-zero texture non-Fritzsch-like quark mass matrices are completely valid and generate all the physical quantities involved, including the $CP$ violating parameter ${\ensuremath{\epsilon}}_{k}$, for which is required the inclusion of phases in the unitary matrices used for diagonalizing the quark mass matrices in order to put the Cabibbo-Kobayashi-Maskawa matrix in standard form. These phases can be rotated away so they do not have any physical meaning. Finally, the relevance of the weak basis transformation is appreciated: it is complete and facilitates calculations, especially of texture zeros.

Comment on “Texture zeros and weak basis transformations in the quark sector of the standard model”

Recently, using specific weak basis transformations, Y. Giraldo [Phys. Rev. D 86, 093021 (2012)] constructed some texture 5 and 4 zero quark mass matrices and examined their compatibility with the quark mixing data. In this comment, we have reanalyzed these to bring forth certain important issues regarding their viability which need to be taken note of.

Nucleon decay via dimension-6 operators in the E6 x SU(2)F x U(1)A SUSY GUT model

In the previous paper, we have shown that $R_1\equiv\frac{\Gamma_{n \rightarrow \pi^0 + \nu^c}}{\Gamma_{p \rightarrow \pi^0 + e^c}}$ and $R_2\equiv\frac{\Gamma_{p \rightarrow K^0 + \mu^c}}{\Gamma_{p \rightarrow \pi^0 + e^c}}$ can identify the grand unification group $SU(5)$, $SO(10)$, or $E_6$ in typical anomalous $U(1)_A$ supersymmetric (SUSY) grand unified theory (GUT) in which nucleon decay via dimension-6 operators becomes dominant. When $R_1 > 0.4$ the grand unification group is not $SU(5)$, while when $R_1 > 1$ the grand unification group is $E_6$. Moreover, when $R_2 > 0.3$, $E_6$ is implied. Main ambiguities come from the diagonalizing matrices for quark and lepton mass matrices in this calculation once we fix the vacuum expectation values of GUT Higgs bosons. In this paper, we calculate $R_1$ and $R_2$ in $E_6\times SU(2)_F$ SUSY GUT with anomalous $U(1)_A$ gauge symmetry, in which realistic quark and lepton masses and mixings can be obtained though the flavor symmetry $SU(2)_F$ constrains Yukawa couplings at the GUT scale. The ambiguities of Yukawa couplings are expected to be reduced. We show that the predicted region for $R_1$ and $R_2$ is more restricted than in the $E_6$ model without $SU(2)_F$ as expected. Moreover, we re-examine the previous claim for the identification of grand unification group with $100$ times more model points ($10^6$ model points), including $E_6 \times SU(2)_F$ model.

Flavour models with three Higgs generations

We construct models with a spontaneously broken $SU(3)_F$ flavour symmetry where three generations of Higgs multiplets transform in a flavour-triplet representation. The models are embedded in a supersymmetric Pati-Salam GUT framework, which includes left-right symmetry. We study the possible flavon representations and show that a model with flavons in the decuplet representation is able to reproduce the hierarchy structure of the quark and lepton mass and mixing matrices. This result requires no additional structure or fine-tunings except for an extra $Z_4$ discrete symmetry in the superpotential.

Endowing the Standard Model with a new r-symmetry

In the Standard Model, there is the single Higgs field, ϕ, which gives rise to constituent quark and lepton masses. The Yukawa coupling is a highly complex set of 3 × 3 matrices, resulting in many textures of quark and lepton masses. In this talk, we propose to transfer the complexity of the Yukawa coupling matrices to a family of Higgs fields, so that the Yukawa coupling itself becomes a simple interaction. In the context of an Enriched Standard Model, we introduce a new r-symmetry in the extended SU(2)L × U(1)Y × U(1)R model and show how a particularly simple scenario results in a near degeneracy of masses in the 126 GeV region, with a hierarchy of heavier masses suggested by the quark and lepton texture mass matrices.

Light vectorlike fermions in a minimalSU(5)setup

The Standard Model fermion sector is enlarged by either one light singlet vectorlike down-type quark or one light vectorlike lepton doublet, which might be accommodated within a five-dimensional representation of $SU(5)$. At low energies the inclusion of these states affects precisely measured observables in flavor physics, as well as electroweak precision measurements. These experimental results strongly constrain couplings of vectorlike states to the Standard Model particles. Having these bounds, we investigate the impact of vectorlike fermions on the mass matrices for down-type quarks and charged leptons in an $SU(5)$ setting. We find that unitary transformations relating an arbitrary flavor basis to the mass eigenstate basis depend only on three free parameters. Then we discuss the parameter space constrained by low-energy data, assuming vectorlike quark and vectorlike lepton masses to be 800 GeV and 400 GeV, respectively. We demonstrate that these two scenarios generate unique patterns for relevant proton decay widths. A further improvement of experimental bounds on proton decay modes would thus differentiate the allowed parameter space. We finally present two full-fledged $SU(5)$ models that allow for gauge coupling unification with light vectorlike fermions under consideration and discuss their viability.

UV completions of partial compositeness: the case for a SU(4) gauge group

We present a model of partial compositeness arising as the IR limit of a SU(4) gauge theory with only fermionic matter. This group is one of the most promising ones among a handful of possible choices allowing a symmetry breaking pattern incorporating custodial symmetry and a top partner candidate, while retaining asymptotic freedom. It is favored for not giving rise to lepto-quarks or Landau poles in the SM gauge couplings. The minimal UV theory consists of five hyperfermions in the anti-symmetric representation and three in the fundamental and anti-fundamental. The IR theory is centered around the coset SU(5)/SO(5), with top partners in the fundamental of SO(5), giving rise to one composite fermion of electric charge 5/3, three of charge 2/3 and one of charge −1/3. Electro-Weak symmetry breaking occurs via top-quark-driven vacuum misalignment. The top quark mass is generated via the mechanism of partial compositeness, while the remaining fermions acquire a mass via a standard quadratic coupling to the Higgs. We compute the top and bottom quark mass matrix and the Electro-Weak currents of the composite fermions. The model does not give rise to unacceptably large deviations from the SM Z → $$ b\overline{b} $$ decay width.

Solving the strong CP problem with discrete symmetries and the right unitarity triangle

We present a solution to the strong CP problem based on spontaneous CP violation and discrete family symmetries. The model predicts in a natural way the almost right-angled quark unitarity triangle angle (α≃90°) by making the entries of the quark mass matrices either real or imaginary. By this choice the determinants of the mass matrices are rendered real and hence the strong CP phase vanishes. We present a toy model for the quark sector that demonstrates the viability of our approach.

Neutrino mixing and masses from a minimum principle

Abstract We analyze the structure of quark and lepton mass matrices under the hypothesis that they are determined from a minimum principle applied to a generic potential invariant under the [SU(3)]5 ⊗ $ \mathcal{O} $ (3) flavor symmetry, acting on Standard Model fermions and right-handed neutrinos. Unlike the quark case, we show that hierarchical masses for charged leptons are naturally accompanied by degenerate Majorana neutrinos with one mixing angle close to maximal, a second potentially large, a third one necessarily small, and one maximal relative Majorana phase. Adding small perturbations the predicted structure for the neutrino mass matrix is in excellent agreement with present observations and could be tested in the near future via neutrino-less double beta decay and cosmological measurements. The generalization of these results to arbitrary sew-saw models is also discussed.

Minimal weak basis textures and quark mixing data

The phenomenology of the most general quark mass matrices with a minimum of three texture zeros obtained through weak basis (WB) transformations has been discussed within the framework of the standard model. The relationship between the textures, naturalness and WB transformations has also been studied. Adopting a ‘hierarchical’ parameterization for the quark mass matrix, we have detailed exact relations for the various elements of the quark mixing matrix along with the CP asymmetry angle β, illustrating the explicit relationship between the observed hierarchies among the WB quark mass matrices and the quark mixing matrix. Besides exploring the complete parameter space available to the (Mq)11, (q = u, d) elements in these mass matrices, their implications for quark mixing data and CP violation asymmetries have also been explored.

HIERARCHICAL MASSES AND UNIVERSAL MIXING IN QUARK–LEPTON MASS MATRICES

The universality hypothesis for quark and lepton mixing matrices (CKM and MNS) is further developed. This hypothesis explains why the CKM is almost diagonal whereas the MNS is almost maximally mixed. If this hypothesis is true, the Dirac CP violating phase of the MNS mixing matrix is bounded around π or 0. Quark–lepton mass matrices which realize this hypothesis are constructed, showing simple power law relations among mass matrices for up-type, down-type quarks and neutrinos.

Non-degenerate squarks from flavored gauge mediation

Abstract We study the squark spectra of Flavored Gauge Mediation Models, in which messenger-matter uperpotential couplings generate new, generation-dependent contributions to the squark masses. The new couplings are controlled by the same flavor symmetry that explains the fermion masses, leading to excellent alignment of the quark and squark mass matrices. This allows for large squark mass splittings consistent with all flavor bounds. In particular, second-generation squarks are often significantly lighter than the first-generation squarks. As squark production at the LHC is dominated by the up- and down-squarks and the efficiencies for squark searches increase with their masses, the charm and/or strange squark masses can be well below the current LHC bounds. At the same time, even with a single set of messengers, the models can generate large stop mixings which result in large loop contributions to the Higgs mass.

Quark sectorCPviolation of the universal seesaw model

We study the CP violation of universal seesaw model, especially its quark sector. The model is based on SU(2)_L \times SU(2)_R \times U(1)_{Y^\prime}. In order to count the number of parameters in quark sector, we use the degree of freedom of weak basis transformation. For N(3)-generation model, the number of CP violating phase in quark sector is identified as 3N^2-3N+1 (19). We also construct nineteen CP violating weak basis invariants of Yukawa coupling matrices and SU(2) singlet quark mass matrices in the three-generation universal seesaw model. The quark interaction terms induced by neutral currents are given as an exact formula. Both of the charged current and the neutral current are expressed in terms of the mass basis by finding the transformations from weak basis to mass basis. Finally, we calculate the mixing matrix element approximately assuming that the SU(2)_R breaking scale v_R is much larger than the electro-weak breaking scale v_L.

Five texture zeros andCPviolation for the standard model quark mass matrices

The phenomenology of the five independent sets of $3\ifmmode\times\else\texttimes\fi{}3$ quark mass matrices with five texture zeros is carried through in full detail, including predictions for the $CP$-violation asymmetries. Our study is done without any approximation, first analytically and then numerically.

Heptagonic symmetry for quarks and leptons

The non-Abelian discrete symmetry D(7) of the heptagon is successfully applied to both quark and lepton mass matrices, including CP violation.

Role of Current Quark Mass Dependent Multi-quark Interactions in Low Lying Meson Mass Spectra

We call attention to a class of current-quark mass dependent multi-quark interaction terms which break explicitly the chiral $SU(3)_L\times SU(3)_R$ and $U_A(1)$ symmetries. They complete the set of effective quark interactions that contribute at the same order in $N_c$ as the 't Hooft flavor determinant interaction and the eight quark interactions in the phase of spontaneously broken chiral symmetry. The $N_c$ classification scheme matches the counting rules based on arguments set by the scale of spontaneous chiral symmetry breaking. Together with the leading in $N_c$ four quark Nambu-Jona-Lasinio Lagrangian and current quark mass matrix, the model is apt to account for the correct empirical ordering and magnitude of the splitting of states in the low lying mass spectra of spin zero mesons. The new terms turn out to be essential for the ordering $m_K < m_\eta$ in the pseudoscalar sector and $m_{\kappa_0} < m_{a_0}\sim m_{f0}$ for the scalars.

Texture zeros and weak basis transformations in the quark sector of the standard model

Stimulated by the recent attention given to the texture zeros found in the quark mass matrices sector of the Standard Model, an analytical method for identifying (or to exclude) texture zeros models will be implemented here, starting from arbitrary quark mass matrices and making a suitable weak basis transformation, we are be able to find equivalent quark mass matrix. It is shown that the number of non-equivalent quark mass matrix representations is finite. We give exact numerical results for parallel and non-parallel four-texture zeros models. We find that some five-texture zeros Ans$\ddot{\textrm{a}}$tze are in agreement with all present experimental data. And we confirm definitely that six-texture zeros of Hermitian quark mass matrices are not viable models anymore.