Trajectories of quadratic differentials for Jacobi polynomials with complex parameters

Motivated by the study of the asymptotic behavior of Jacobi polynomials $\left( P_{n}^{(nA,nB)}\right) _{n}$ with $A\in \mathbb C$ and $B>0$ we establish the global structure of trajectories of the related rational quadratic differential on $\mathbb C$. As a consequence, the asymptotic zero distribution (limit of the root-counting measures of $\left( P_{n}^{(nA,nB)}\right) _{n}$) is described. The support of this measure is formed by an open arc in the complex plan (critical trajectory of the aforementioned quadratic differential) that can be characterized by the symmetry property of its equilibrium measure in a certain external field.Comment: 22 pages, 4 figures. To appear in Computational Methods and Function Theor

Z and Z' decays with and without FCNC in 331 models

In the context of the 331 models, we consider constraints on the extra neutral boson $Z^{\prime}$ predicted by the model, where three different quark family assignments are identified. Using the ansatz of Matsuda as an specific texture for the quark mass matrices, we obtain allowed regions associated with the Z-Z' mixing angle, the mass of the $Z^{\prime}$ boson and the parameter $\beta$ which determines different 331 models. The $Z_{1}$ and $Z_{2}$ decays with and without flavor changing are also considered. The flavor changing decays of the $Z_{1}$ boson into quarks at tree level are highly suppressed by the $Z-Z^{\prime}$ mixing angle, obtaining the same order of magnitude as the standard model prediction at one loop level. The $$ decay widths are calculated with and without flavor changing, where oblique radiative corrections at one loop accounts for about $1$ deviations.Comment: 33 pages, 6 figures, LaTeX2

Quadratic differentials and asymptotics of Laguerre polynomials with varying complex parameters

In this paper we study the asymptotics (as $n\to \infty$) of the sequences of Laguerre polynomials with varying complex parameters $\alpha$ depending on the degree $n$. More precisely, we assume that $\alpha_n = n A_n,$ and $\lim_n A_n=A \in \mathbb{C}$. This study has been carried out previously only for $\alpha_n\in \mathbb{R}$, but complex values of $A$ introduce an asymmetry that makes the problem more difficult. The main ingredient of the asymptotic analysis is the right choice of the contour of orthogonality, which requires the analysis of the global structure of trajectories of an associated quadratic differential on the complex plane, which may have an independent interest. While the weak asymptotics is obtained by reduction to the theorem of Gonchar--Rakhmanov--Stahl, the strong asymptotic results are derived via the non-commutative steepest descent analysis based on the Riemann-Hilbert characterization of the Laguerre polynomials.Comment: 40 pages, 11 figures. To appear in J. Math. Anal. Appl. arXiv admin note: text overlap with arXiv:math/0204248 by other authors. text overlap with arXiv:math/0204248 by other author

SU(3)_{c} X SU(3)_{L} X U(1)_{X} models for \beta arbitrary and families with mirror fermions

A detailed and general study of the fermionic structure of the 331 models with \beta arbitrary is carried out based on the criterion of cancellation of anomalies. We consider models with an arbitrary number of lepton and quark generations, but requiring to associate only one lepton and one quark SU(3) _{L} multiplet for each generation, and at most one right-handed singlet per each left-handed fermion. We see that the number of quark left-handed multiplets must be three times the number of leptonic left-handed multiplets. Furthermore, we consider a model with four families and \beta =-1/\sqrt{3} where the additional family corresponds to a mirror fermion of the third generation of the Standard Model. We also show how to generate ansatzs about the mass matrices of the fermions according to the phenomenology. In particular, it is possible to get a natural fit for the neutrino hierarchical masses and mixing angles. Moreover, by means of the mixing between the third quark family and its mirror fermion, a possible solution for the A_{FB}^{b} discrepancy is obtained.Comment: 32 pages, 15 tables, LaTeX2e. A new section added, introduction and conclusions extended. Version to appear in Phys. Rev.

331 vector-like models with mirror fermions as a possible solution for the discrepancy in the b-quark asymmetries, and for the neutrino mass and mixing pattern

A general study of the fermionic structure of the 331 models with \beta arbitrary shows the possibility of obtaining 331 vector-like models with mirror fermions. On one hand, the existence of mirror fermions gives a possible way to fit the discrepancy in the bottom quark asymmetries from the prediction of the standard model. On the other hand, the vector-like nature of the model permits to address the problem of the fermion mass hierarchy, and in particular the problem of the neutrino mass and mixing pattern. Specifically, we consider a model with four families and \beta =-1/\sqrt{3} where the additional family corresponds to a mirror fermion of the third generation of the Standard Model. We also show how to generate ansatzs about the mass matrices of the fermions according to the phenomenology. In particular, it is possible to get a natural fit for the neutrino hierarchical masses and mixing angles. Moreover, by means of the mixing between the third quark family and its mirror fermion, a possible solution for the A_{FB}^{b} discrepancy is obtained.Comment: 12 pages, 6 tables, LaTeX2

Constraints on top quark FCNC from electroweak precision measurements

We study the one-loop contributions of the effective flavor changing neutral couplings (FCNC) tcZ and tcH on the electroweak precision observables Gamma_Z, R_c, R_b, R_l, A_c and A^FB_c. Using the known experimental limits on these observables, we may place 95% CL bounds on these FCNC couplings which in turn translate into the following limits for the branching ratios: BR(t -> cZ) < 6.7 10^-2 and BR(t -> cH) < (0.09 - 2.9) 10^-3 for 114 < m_H < 170 GeV.Comment: 10 pages, 3 figures. References added. Errors corrected. Numerical results for BR have change

The scalar sector of the SU(3)c⊗SU(3)L⊗U(1)XSU(3)_{c}\otimes SU(3)_{L}\otimes U(1)_{X} model

A complete study of the Higgs sector of the $SU(3)_{c}\otimes SU(3)_{L}\otimes U(1)_{X}$ model is carried out, obtaining all possible cases of vacuum expectation values that permit the spontaneous symmetry breaking pattern$SU(3)_{L}\otimes U(1)_{X}\to SU(2)_{L}\otimes U(1)_{Y}\to U(1)_{Q}.$ We find the most general Higgs potentials that contain three triplets of Higgs and one sextet. A detailed study of the scalar sector for different models with three Higgs triplets is done. The models end up in an electroweak two Higgs doublet model after the first symmetry breakdown; we find that the low energy limit depends on a trilinear parameter of the Higgs potential, and that the decoupling limit from the electroweak two Higgs doublet model to the minimal standard model can be obtained quite naturally.Comment: 41 pages, no figures, two subsections added. Version to appear in Phys. Rev.

CP symmetry violation in the scalar sector of 331 models

In order to understand some frameworks for CP Violation scenarios in the scalar sector, a 331 model was considered which its main property is the incorporation of a local group symmetry SU(3) in the electroweak sector. In particular, a 331 model with a particular choice of free parameter. CP Violation scenarios were obtained by introducing a discrete symmetry in the scalar triplets, which exhibit a spontaneous CP Violation frame with just one independent CP phase associated. Mass state rotations were obtained

Blackbody radiation in a nonextensive scenario

An exact analysis of the N-dimensional blackbody radiation process in a nonextensive \`a la Tsallis scenario is performed for values of the nonextensive's index in the range ($0<q<1$). The recently advanced ``Optimal Lagrange Multipliers" (OLM) technique has been employed. The results are consistent with those of the extensive, $q=1$ case. The generalization of the celebrated laws of Planck, Stefan-Boltzmann, and Wien are investigated. PACS: 05.30.-d, 95.35.+d, 05.70.Ce, 75.10.-b Keywords: Tsallis Thermostatistics, Blackbody radiation.Comment: 12 Pages, 5 Figure

SHM method for damage localization based on substructuring and VARX models

A novel damage localization method is proposed, which is based on a substructuring approach and makes use of Vector Auto-Regressive with eXogenous input (VARX) models. The substructuring approach aims to divide the monitored structure into several multi-DOF isolated substructures. Later, each individual substructure is modeled by a VARX model, and the health of each substructure is determined analyzing the variation of the VARX model. The method allows to detect whether the isolated substructure is damaged, and besides allows to locate the damage within the substructure. Only measured displacement data is required to estimate the isolated substructure's VARX model. Moreover, it is not necessary to have a priori knowledge of the structural model. The proposed method is validated by simulations of an eight-storey shear building