George W. S. Hou
In this talk we cover two threads regarding the 4th generation: on CP violation, from Earth up to the Heavens, i.e. from accelerator-based experimental studies, towards baryon asymmetry of the Universe; and on direct search bounds on $m_{t'}$ and $m_{b'}$, towards the possibility of electroweak symmetry breaking through large Yukawa couplings. Prospects and discussions are presented.
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It has been shown that the data from the Large Hadron Collider (LHC) does not rule out a chiral sequential fourth generation of fermions that obtain their masses through an identical mechanism as the other three generations do. However, this is possible only if the scalar sector of the Standard Model is suitably enhanced, like embedding it in a type-II two-Higgs doublet model. In this article, we try to show that double Higgs production (DHP) can unveil the existence of such a hidden fourth generation in a very efficient way. While the DHP cross-section in the SM is quite small, it is signific…
In the Standard Model with four generations, the two-loop renormalization group equations for the Higgs quartic and Yukawa couplings have a fixed point structure. If the masses of the fourth family are sufficiently heavy, it will contain a natural scale $Λ_{FP}$ in the range of a few TeV to the order of $10^2$ TeV, above which the Higgs quartic and Yukawa couplings become practically constant. We found that around $Λ_{FP}$ the strong Yukawa couplings make it possible for the fourth generation to form bound states, including composite extra Higgs doublets. In this scenario the fourth generation…
We construct a model where the Yukawa couplings of the Standard Model (SM) fermions arise from the breaking of a $Z_2$ symmetry and through mixing with a fourth family of vector-like fermions. By adding a scalar leptoquark, which is an electroweak triplet and odd under the $Z_2$ symmetry, we obtain an explanation for $R_{K^{(*)}}$ that is linked to the origin of the Yukawa couplings. The coupling of SM fermions to the leptoquark is mediated by the fourth family fermions, and is predicted to be related to CKM entries and mass ratios of SM fermions.
We explore the possibility that the semi-leptonic $B$ decay ratios $R_{K^{(*)}}$ which violate $μ- e$ universality are related to the origin of the fermion Yukawa couplings in the Standard Model. Some time ago, a vector-like fourth family (without a $Z'$) was used to generate fermion mass hierarchies and mixing patterns without introducing any family symmetry. Recently the idea of inducing flavourful $Z'$ couplings via mixing with a vector-like fourth family which carries gauged $U(1)'$ charges has been proposed as a simple way of producing controlled flavour universality violation while elega…
We revisit a scenario with an enhanced top yukawa coupling in vector-like quark (VLQ) models, where the top yukawa coupling is larger than the standard model value and the lightest VLQ has a negative yukawa coupling. We find that the parameter space satisfying the LHC bounds of the Higgs signal strengths consistently with the precision measurements is rather wide. Because the Lagrangian parameters of the yukawa couplings are large, such scenario can be realized in some strongly interacting theories. It also turns out that there is a noticeable relation between the contributions of the triangle…
We review the present status and the future prospects for the measurements of the Higgs Yukawa couplings to light quarks and charm. A special focus is given to novel proposed off-shell probes, which offer promising and complementary opportunities to test light quark Yukawas in triboson final states. Additionally, a new off-shell strategy to test the charm Yukawa coupling in the final state with two bosons plus a charm and a jet is considered. First estimates for the HL-LHC and the FCC-hh sensitivities on the channel are presented, showing encouraging results.
One of the puzzles of the SM is the large hierarchy between the Yukawa couplings of different flavours. Yukawa couplings of the first and the second generation are constrained only very weakly so far. However, one can obtain large deviations in the Yukawa couplings in several New Physics (NP) models, such as e.g. models with new vector-like quarks, or new Higgs bosons that couple naturally to individual fermion families. In this work, we investigate the potential bounds on the NP Higgs Yukawa couplings modification $ κ_f$ for light quarks from double-Higgs at the LHC, starting from a model ind…
Associated production of the Higgs boson with a single top quark proceeds through Feynman diagrams, which are either proportional to the hWW, top-Yukawa, or the bottom-Yukawa couplings. It was shown in literature that the interference between the top-Yukawa and the gauge-Higgs diagrams can be significant, and thus the measurement of the cross sections can help pin down the sign and the size of the top-Yukawa coupling. Here we perform a detailed study with full detector simulations of such a possibility at the LHC-14 within the current allowed range of hWW and top-Yukawa couplings, using h-> b …
We propose a novel idea for probing the Higgs boson couplings through the measurement of hadronic event shape distributions in the decay of the Higgs boson at lepton colliders. The method provides a unique test of the Higgs boson couplings and of QCD effects in the decay of the Higgs boson. It can be used to probe the Yukawa couplings of the light quarks and to further test the mechanism of electroweak symmetry breaking. From a case study for the proposed Circular Electron-Positron Collider, assuming a hypothesis of SM-like theory, light-quark couplings with a strength greater than 9% of the b…
We propose a novel strategy to constrain the bottom and charm Yukawa couplings by exploiting LHC measurements of transverse momentum distributions in Higgs production. Our method does not rely on the reconstruction of exclusive final states or heavy-flavour tagging. Compared to other proposals it leads to an enhanced sensitivity to the Yukawa couplings due to distortions of the differential Higgs spectra from emissions which either probe quark loops or are associated to quark-initiated production. We derive constraints using data from LHC Run I, and we explore the prospects of our method at fu…
The observation of $t\bar th(125)$ production at the Large Hadron Collider (LHC) is the first direct measurement of the top Yukawa coupling. It opens the window on an extra top Yukawa coupling, $ρ_{tt}$, from a second Higgs doublet, without a $Z_2$ symmetry to forbid flavor changing neutral Higgs couplings. We show that $t\bar th$ and Higgs property measurements at the High Luminosity LHC can constrain the ${\rm Re}\,ρ_{tt}$--${\rm Im}\,ρ_{tt}$ parameter space that could drive electroweak baryogenesis, but the $Γ_h$ width measurement must be considerably improved beyond current projections.
To measure the Yukawa couplings of the up and down quarks, Y_{u,d}, seems to be far beyond the capabilities of current and (near) future experiments in particle physics. By performing a general analysis of the potential misalignment between quark masses and Yukawa couplings, we derive predictions for the magnitude of induced flavor-changing neutral currents (FCNCs), depending on the shift in the physical Yukawa coupling of first-generation quarks. We find that a shift of -100% in the down-quark Yukawa Y_d would generically result in ds transitions in conflict with Kaon physics. This could alre…
We study the interplay between a soft muon Yukawa coupling generated radiatively with the trilinear A-terms of the minimal supersymmetric standard model (MSSM) and the anomalous magnetic moment of the muon. In the absence of a tree-level muon Yukawa coupling the lightest smuon mass is predicted to be in the range between 750 GeV and 2700 GeV at 2 sigma, if the bino mass M_1 is below 1 TeV. Therefore, a detection of a smuon (in conjunction with a sub-TeV bino) at the LHC would directly imply a non-zero muon Yukawa coupling in the MSSM superpotential. Inclusion of slepton flavor mixing could in …
For strong enough Yukawa coupling the electroweak standard model fermion finds it energetically advantageous to transform itself into a bound state in the hedgehog background of Higgs field in semiclassical approximation. By considering the bound states give the masses for lepton and quark, we found that all the strongly Yukawa coupling constants tend to an unitary constant. On the other hand, the masses of $W$ and $Z$ produced by the hedgehog Higgs field keep almost no change.
We study the deviation of yukawa coupling in the gauge-Higgs unification scenario from the Standard Model one. Taking into account the brane mass terms necessary for generating the flavor mixing and removing the exotic massless fermions, we derive an analytic formula determining the KK mass spectrum and yukawa coupling. Applying the obtained results to the tau and bottom yukawa couplings, we numerically calculate the ratio of the yukawa couplings in the gauge-Higgs unification and in the Standard Model.
In some extensions of the Standard Model, Yukawa couplings of the physical Higgs boson can be deviated from those in the Standard Model. We study a possibility whether or not such anomalous Yukawa couplings are consistent with the LHC Run 1 data. It is found that sizable deviations of top and bottom (and tau) Yukawa couplings from the Standard Model predictions can nicely fit the data. New physics beyond the Standard Model can be revealed through more precise measurements of such anomalous Yukawa couplings at the LHC Run 2 in the near future. We also discuss a simple setup which can leads to a…
I make a short review of the most recent determinations of the quark masses and run them to the $M_Z$ energy scale.
A sequential fourth generation is known to be excluded because the non-decoupling contribution to $κ_g$, the Higgs coupling modifier with a gluon pair, is unacceptably large. Recently a new way to save the model was suggested in the Type-II two Higgs doublet model: if the Yukawa couplings of down-type fermions have wrong-sign, the contributions from $t'$ and $b'$ to $κ_g$ are cancelled. We study the theoretical and experimental constraints on this model, focusing on the heavy Higgs bosons. Two constraining features are pointed out. First the exact wrong-sign limit does not allow the alignment,…
We study the influence of messenger Yukawa couplings and top, bottom and $τ$ Yukawa couplings on the proton lifetime in SU(5) Supersymmetric GUT with dynamical supersymmetry breaking mechanism due to Dine and Nelson.
We present a method to find the number of real and imaginary observable parameters coming from the Yukawa sector in an arbitrary gauge theory. The method leads naturally to a classification of Yukawa couplings according to their symmetries and suggests a new parametrization of masses and mixings that is useful to study the behaviour of Yukawa couplings under the renormalization group. We apply it to some examples based on the Standard Model with Yukawa couplings obeying various chiral symmetries. We also show how our method of parameter counting can be used in some models with an enlarged lept…
We calculate within the MSSM the one-loop Yukawa coupling corrections to the processes e+ e- \to stops, sbottoms, and staus in order of Yukawa coupling squared. These corrections are due to the exchange of charginos, neutralinos, charged and neutral Higgs bosons, and charged and neutral Higgs ghosts. We give the complete analytical formulae. We also perform a detailed numerical analysis of the Yukawa coupling corrections, including also the SUSY-QCD corrections. It turns out that for stop and sbottom production the Yukawa coupling corrections are typically +/- 10% of the tree-level cross secti…
We propose a measurement of the top Yukawa coupling at a 100 TeV hadron collider, based on boosted Higgs and top decays. We find that the top Yukawa coupling can be measured to 1%, with excellent handles for reducing systematic and theoretical uncertainties, both from side bands and from $t\bar{t}H/t\bar{t}Z$ ratios.
We propose a GUT model in which visible matter and messengers are treated in unified way what unavoidably leads to messenger-matter mixed Yukawa interactions. Influence of this mixing on the fermion masses and the weak mixing angles is discussed.
Among the firm predictions of softly broken supersymmetry is the identity of gauge couplings and the corresponding Yukawa couplings between gauginos, sfermions and fermions. In the event that a SUSY-like spectrum of new particles is discovered at future colliders, a key follow-up will be to test these relations experimentally. In detailed studies it has been found that the SUSY-Yukawa couplings of the electroweak sector can be studied with great precision at the ILC, but a similar analysis for the Yukawa coupling of the SUSY-QCD sector is far more challenging. Here a first phenomenological stu…
There is a convincing experimental evidence that neutrinos are massive. Therefore we investigate the influence of the neutrino masses on the unification of gauge and Yukawa couplings in the framework of the Minimal Supersymmetric Standard Model. We estimate the contribution of the neutrino Yukawa coupling to the gauge and Yukawa coupling unification. We find that in the case of the gauge coupling unification the effect of massive neutrinos is small and can be neglected. It appears to be much more significant, if we explore Y_{b} and Y_{tau} equality at the GUT scale. The neutrino contribution …
We study the deviation of yukawa coupling in the gauge-Higgs unification scenario from the Standard Model one. Applying the obtained results to the tau and bottom yukawa couplings, we numerically calculate the signal strength of $gg \to H \to \bar b b, \bar τ τ$in the gauge-Higgs unification.
Supersymmetry predicts the identity of Yukawa and gauge couplings in the QCD sector: quark-squark-gluino = squark-squark-gluon = quark-quark-gluon. We examine whether the quark-squark-gluino Yukawa coupling can be determined, by methods complementary to LHC, by analyzing squark-gluino final states at a TeV e+e- collider.
In the constrained sequential dominance (CSD), tri-bimaximal mixing (TBM) pattern in the neutrino sector has been explained, by proposing a certain Yukawa coupling structure for the right-handed neutrinos of the model. However, from the current experimental data it is known that the values of neutrino mixing angles are deviated from the TBM values. In order to explain this neutrino mixing, we first propose a phenomenological model where we consider Yukawa couplings which are modified from that of CSD. Essentially, we add small complex parameters to the Yukawa couplings of CSD. Using these modi…
We extend the already existing two-loop calculation of the effective bottom-Yukawa coupling in the MSSM. In addition to the resummation of the dominant corrections for large values of tg$β$, we include the subleading terms related to the trilinear Higgs coupling $A_b$ and contributions induced by the electroweak gauge couplings. This calculation has been extended to the NNLO corrections to the MSSM strange-Yukawa coupling. Our analysis leads to residual theoretical uncertainties of the effective Yukawa couplings at the per-cent level.
We present the extension of our previous results for three-loop Yukawa coupling beta-functions to the case of complex Yukawa matrices describing the flavour structure of the SM. The calculation is carried out in the context of unbroken phase of the SM with the help of the MINCER program in a general linear gauge and cross-checked by means of MATAD/BAMBA codes. In addition, ambiguities in Yukawa matrix beta-functions are studied.
Yukawa couplings of electroweak Goldstone bosons can be inferred from experiment, but the existence of an elementary Higgs boson is not yet an established fact. If a sequential chiral quark generation does exist, it would bring us now into the strong Yukawa coupling regime. Guided by a Bethe--Salpeter equation approach, we postulate that the leading collapse state, the (heavy) isotriplet and color-singlet $π_1$ meson, becomes the Goldstone boson $G$ itself. Viewing it as a deeply bound state, a gap equation is constructed. This "`bootstrap" picture for electroweak symmetry breaking relies on s…
The scaling behavior and fixed points in the evolution of fermion Yukawa couplings and mixing angles are discussed. The relevance of fixed points in determining the top quark mass is described.
We study electroweak baryogenesis driven by the top quark in a general two Higgs doublet model with flavor-changing Yukawa couplings, keeping the Higgs potential $CP$ invariant. With Higgs sector couplings and the additional top Yukawa coupling $ρ_{tt}$ all of $\mathcal{O}$(1), one naturally has sizable $CP$ violation that fuels the cosmic baryon asymmetry. Even if $ρ_{tt}$ vanishes, the favor-changing coupling $ρ_{tc}$ can still lead to successful baryogenesis. Phenomenological consequences such as $t\to ch$, $τ\to μγ$, electron electric dipole moment, $h\toγγ$, and $hhh$ coupling are discuss…
By solving the gap equation in the quenched, ladder approximation for an Abelian gauge model with Yukawa interaction in the presence of a constant magnetic field, we show that the Yukawa interactions enhance the dynamical generation of fermion mass. The theory is then studied at finite temperature, where we prove that the critical magnetic field, required for the mass generation to be important at temperatures comparable to the electroweak critical temperature, can be substantially decreased due to the Yukawa coupling.
We investigate the origin of phenomenologically interesting small Yukawa couplings in Type I string theory. Utilising the framework of intersecting sets of D9 and orthogonal D5 branes we demonstrate the connection between extra dimensional volumes and Yukawa couplings. For example, we show that extra dimensions with inverse lengths of $10^8$ GeV can lead to $10^{-10}$ Yukawa couplings. String selection rules, arising from the D-Brane setup, impose non-trivial constraints on the set of allowed superpotentials. As a phenomenological application of these results we construct a type I string model…
We revisit four generations within the context of supersymmetry. We compute the perturbativity limits for the fourth generation Yukawa couplings and show that if the masses of the fourth generation lie within reasonable limits of their present experimental lower bounds, it is possible to have perturbativity only up to scales around 1000 TeV, i.e. the current experimental bounds and perturbative unification are mutually exclusive. Such low scales are ideally suited to incorporate gauge mediated supersymmetry breaking, where the mediation scale can be as low as 10-20 TeV. The minimal messenger m…
We analysis the constraints of the general two Higgs doublet models via evolving the Yukawa coupling constants to high energy under renormalization group. We consider the appearance of a Landau pole or large off-diagonal Yukawa couplings which cause tree level flavour changing neutral currents. Our study shows the latter condition can be used to answer that how much $Z_2$ symmetry breaking can be allowed in a given 2HDM model.
Extensions of the MSSM generically feature gauge singlet Higgs bosons. These singlet Higgs bosons have tan(beta)-enhanced Yukawa couplings to down-type quarks and leptons at the one-loop level. We present an effective Lagrangian incorporating these Yukawa couplings and use it to study their effect on singlet Higgs boson phenomenology within both the mnSSM and NMSSM. It is found that the loop-induced couplings represent an appreciable effect for the singlet pseudoscalar in particular, and may dominate its decay modes in some regions of parameter space.
We discuss the Yukawa couplings in 6D gauge-Higgs unification models on $T^2/Z_N$ in the presence of magnetic fluxes. We provide general formulae for them, and numerically evaluate their magnitude in a specific model on $T^2/Z_3$. Thanks to the nontrivial profiles of the zero-mode wave functions, the top quark Yukawa coupling can be reproduced without introducing a large representation of the gauge group for matter fields. However, it is difficult to realize small Yukawa couplings only by the magnetic fluxes and the Wilson-line phases because of the complicated structure of the mode functions …
We calculate the one-loop contributions to the MSSM effective potential when the scalar top fields have non-zero vacuum expectation values and study their impact on charge and colour breaking bounds.
We study the charged Higgs couplings to fermions in the "democratic" three-Higgs-doublet model, in which one doublet couples to down-type quarks, one to up-type quarks, and one to charged leptons. Flavor-changing neutral Higgs couplings are absent because the Glashow-Weinberg-Paschos condition for natural flavor conservation is in effect. We show that this model reproduces the coupling structure of the charged Higgs boson in the recently-proposed Yukawa-aligned two-Higgs-doublet model, with two subtle constraints that arise from the unitarity of the charged Higgs mixing matrix. Adding a fourth…
We investigate a model that the Yukawa coupling form is constructed by two kinds of matrix (M_0 and M_1). For example, in the SO(10) GUT model, M_0 and M_1 are Yukawa couplings generated by the 10 and 126 Higgs scalars. We study how this model can give the observed mass and mixings of quarks and leptons. Parameter fitting is fully scanned by assuming all the input data to be normally distributed around the center value.
We study the impacts of matter field Kähler metric on physical Yukawa couplings in string compactifications. Since the Kähler metric is non-trivial in general, the kinetic mixing of matter fields opens a new avenue for realizing a hierarchical structure of physical Yukawa couplings, even when holomorphic Yukawa couplings have the trivial structure. The hierarchical Yukawa couplings are demonstrated by couplings of pure untwisted modes on toroidal orbifolds and their resolutions in the context of heterotic string theory with standard embedding. Also, we study the hierarchical couplings among un…
Future hadron colliders will have the potential to measure some of the most relevant Higgs boson couplings with high precision. In this paper we investigate the potential of a Very Large Hadron Collider (VLHC) to measure the top-quark Yukawa coupling.
We investigate the infra-red stable fixed points of the Yukawa couplings in the minimal version of the supersymmetric standard model with R-parity violation. Retaining only the R-parity violating couplings of higher generations, we analytically study the solutions of the renormalization group equations of these couplings together with the top- and b-quark Yukawa couplings. We show that only the B-violating coupling $λ^{''}_{233}$ approaches a non-trivial infra-red stable fixed point, whereas all other non-trivial fixed point solutions are either unphysical or unstable in the infra-red region. …
We study the minimal supersymmetric standard model derived from $Z_N \times Z_M$ orbifold models. Moduli dependent threshold corrections of the gauge couplings are investigated to explain the measured values of the coupling constants. Also we study Yukawa couplings of the models. We find that the $Z_2 \times Z_6'$, $Z_2\times Z_6$, $Z_3 \times Z_6$ and $Z_6 \times Z_6$ orbifold models have the possibility to derive Yukawa couplings for the second and third generations as well as the measured gauge coupling constants. Allowed models are shown explicitly by combinations of modular weights for th…
Singlet Higgs bosons present in extensions of the MSSM can have sizable Yukawa couplings to the b quark and the tau lepton for large values of tan(beta) at the 1-loop level. We present an effective Lagrangian which incorporates these tan(beta)-enhanced Yukawa couplings and which enables us to study their effect on singlet Higgs-boson phenomenology within the context of both the mnSSM and the NMSSM. In particular, we find that the loop-induced coupling can be a significant effect for the singlet pseudoscalar, and may dominate its decay modes. Further implications of the tan(beta)-enhanced Yukaw…
Realistic heterotic string models require the presence of the Wilson lines. We study the effect of continuous Wilson lines on the heterotic Yukawa couplings and find that the presence of continuous Wilson lines affects the magnitude of the twisted Yukawa couplings resulting in their stronger hierarchy.
The wave functions and Yukawa couplings of the top and bottom quarks in the SO(5) x U(1) gauge-Higgs unification model are determined. The result is summarized in the effective interactions for \hat θ_H(x) = θ_H + H(x)/f_H where θ_H is the Wilson line phase and H(x) is the 4D Higgs field. The Yukawa, WWH and ZZH couplings vanish at θ_H = \onehalf π. There emerges the possibility that the Higgs particle becomes stable.
Yukawa couplings in the Standard Model are introduced in its most general form, that is, completely arbitrary complex numbers. Here we show that their origin could not be general but dictated by a principle.
We investigate the inclusive production of the Higgs boson with a heavy quark pair, $t {\bar t}$ or $b {\bar b}$, in e^+e^- collisions at high energy. The ${\cal O}(α_s)$ QCD corrections are included.
We study how general two Higgs doublet models can be constrained by considering their properties under renormalization group evolution of the Yukawa couplings. We take into account both the appearance of a Landau pole as well as off-diagonal Yukawa couplings leading to flavour changing neutral currents in violation with experimental constraints at the electroweak scale. We find that the latter condition can be used to limit the amount of Z2 symmetry breaking allowed in a given model.
In order to establish supersymmetry (SUSY) at future colliders, the identity of gauge couplings and the corresponding Yukawa couplings between gauginos, sfermions and fermions needs to be verified. Here a first phenomenological study for determining the Yukawa coupling of the SUSY-QCD sector is presented, using a method which combines information from LHC and ILC.
We show that the normalized Higgs production $p_T$ and $y_h$ distributions are sensitive probes of Higgs couplings to light quarks. For up and/or down quark Yukawa couplings comparable to the SM $b$ quark Yukawa the $\bar u u$ or $\bar d d$ fusion production of the Higgs could lead to appreciable softer $p_T$ distribution than in the SM. The rapidity distribution, on the other hand, becomes more forward. We find that, owing partially to a downward fluctuation, one can derive competitive bounds on the two couplings using ATLAS measurements of normalized $p_T$ distribution at 8\,TeV. With 300 fb…
UV origins of CP-violating leptonic Yukawa couplings
本文研究了CP破坏轻子Yukawa耦合的紫外起源，通过标准模型有效场论分析，探讨了紫外模型参数的约束以及电弱精度测试的影响。
The strength of the dynamically generated Yukawa coupling among composite fields is calculated. The system of N=1 supersymmetric SU(2) gauge theory with massive three flavors is considered as an example. We use the techniques of "integrating in" the gluino-gluino bound state in the low energy effective theory and the instanton calculation and Shifman-Vainshtein-Zakharov sum rule (QCD sum rule) in the fundamental theory. The obtained value of the Yukawa coupling is of the order of unity. The method which is developed in this paper can be applied to the other supersymmetric gauge theories.
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 intermediat…
Based on Refs.1 and 2, we study the couplings of the scalar bound state to the fermions and the weak bosons in walking gauge theories.
Unitarity constraints on anomalous top-Higgs couplings are examined. We also compare the unitarity constraints with the constraints from electroweak baryogenesis and electric dipole moments derived earlier.
The structure of Yukawa coupling matrices is investigated in type IIA T^6/(Z_2 x Z_2) orientifold models with intersecting D-branes. Yukawa coupling matrices are difficult to be realistic in the conventional models in which the generation structure emerges by the multiple intersection of D-branes in the factorized T^6 = T^2 x T^2 x T^2. We study the new type of flavor structure, where Yukawa couplings are dynamically generated, and show this type of models lead to nontrivial structures of Yukawa coupling matrices, which can be realistic.
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