Yukawa Coupling Matrices Research Articles

Generations of Quarks and Leptons from Noncompact Horizontal Symmetry

The three chiral generations of quarks and leptons may be generated through a spontaneous breakdown of the noncompact horizontal gauge symmetry $G_{H}$ which governs, together with the standard gauge symmetry ${SU(3) \times SU(2) \times U(1)}$, the world in a vectorlike manner. In a framework of supersymmetric theory, the simplest choice ${G_{H}=SU(1,1)}$ works quite well for this scenario in which quarks, leptons and Higgses belong to infinite dimensional unitary representation of $SU(1,1)$. The relevance of the scenario to the hierarchical structure of their Yukawa coupling matrices are discussed.

Third-generation effects on fermion mass predictions in supersymmetric grand unified theories.

Relations among fermion masses and mixing angles at the scale of grand unification are modified at lower energies by renormalization group running induced by gauge and Yukawa couplings. In supersymmetric theories, the $b$ quark and $\tau$ lepton Yukawa couplings, as well as the $t$ quark coupling, may cause significant running if $\tan \beta$, the ratio of Higgs field expectation values, is large. We present approximate analytic expressions for the scaling factors for fermion masses and CKM matrix elements induced by all three third generation Yukawa couplings. We then determine how running caused by the third generation of fermions affects the predictions arising from three possible forms for the Yukawa coupling matrices at the GUT scale: the Georgi-Jarlskog, Giudice, and Fritzsch textures.

Comment on "Flavor-changing processes and CP violation in the S3 x Z3 model"

Deshpande, Gupta, and Pal neglected the presence of a complex phase in the mass matrix and in the Yukawa coupling matrices of the down-type quarks. I argue that that phase should not be neglected, because it can explain the observed CP violation. Though its effects are negligible in the mass matrix, they are not negligible in the Yukawa coupling matrices. The mechanism of CP violation considered by those authors may certainly be present, but for simplicity one may want to eliminate it by restricting the soft-breaking sector of the Higgs potential in such a way that complex Higgs-boson propagators do not occur. Then, CP violation originates in the exchange of scalar and pseudoscalar Higgs bosons, which have complex Yukawa couplings, but the scalars do not mix with the pseudoscalars.

Heavy top quark and scale dependence of quark mixing

One-loop renormalization group equations for the quark mixing elements | V ij | and for the ratios h i h j of the eigenvalues of the Yukawa coupling matrices are derived in analytic form for a large class of theories and solved in the presence of large third generation Yukawa couplings. Comparison of scale dependence of the elements | V ij | and of the ratios h i h j is also given. The possible relevance of the evolution effects for understanding the pattern of quark masses and mixing is discussed.

Nonlinear evolution of Yukawa couplings in the double Higgs and supersymmetric extensions of the standard model

The nonlinear evolution equations for Yukawa coupling matrices are discussed in the context of the standard, double Higgs and supersymmetric model of electroweak interactions. In each case, even in the presence of a very heavy top quark the approximate analytical solutions for the nonlinear evolution of masses and mixing angles are found. Comparison of the analytical approach with numerical solutions confirm the excellent validity of the approximation. Some possible further applications of the developed method are suggested.

Mass-matrix ansatz and flavor nonconservation in models with multiple Higgs doublets.

Motivated by the existence of three fermion generations, we consider models with three Higgs doublets (for each hypercharge). It is shown that, if the basic Yukawa coupling matrices are of the Fritzsch form or some generalizations thereof (two such examples are presented), then the neutral flavor-changing couplings have a hierarchical structure given by ${\ensuremath{\Delta}}_{\mathrm{ij}}$ \ensuremath{\surd}${m}_{i}$${m}_{j}$ , where ${\ensuremath{\Delta}}_{\mathrm{ij}}$ is a combination of mixing angles and the ${m}_{i}$'s are the relevant fermion masses. These couplings give a lower bound of the order of ${\ensuremath{\Delta}}_{\mathrm{ds}}$ times 1 TeV on the mass of the exchanged scalar from the neutral-kaon mass difference. If the Higgs-boson mass is not significantly greater than this limit, one expects DD\ifmmode\bar\else\textasciimacron\fi{} mixing comparable to the present experimental bound.

Inverted hierarchy and asymptotic freedom in grand unified supersymmetric theories

The interrelation between an inverted hierarchy mechanism and asymptotic freedom in supersymmetric theories is analyzed in two models for which we performed a detailed analysis of the effective potentials and effective couplings. We find it difficult to accomodate an inverted hierarchy together with asymptotic freedom for the matter-Yukawa couplings.