Pattern of Texture Zeroes in Quark Mass Matrices With a Divergent Top-Yukawa Coupling at the GUT Scale

In a SUSY GUT model responsible for generating symmetric quark mass matrices at the GUT scale (mu = Lamda) we assume that the top-Yukawa coupling, lamda_t, becomes infinite at that scale. As a consequence, the MSSM renormalization group equations for quark Yukawa couplings exhibit hierarchical solutions which lead to a pattern of texture zeroes in quark mass matrices at mu = Lamda similar to one of the solutions of Ramond, Roberts, and Ross. The evolution in energy scale to low energies shows excellent agreement between the measured quantities involving the scale-independent ratios of CKM matrix elements and their predicted values in terms of quark mass ratios. It is noted that the tt-bar condensate model of Bardeen, et al. predicts an infinite lamda_t at mu = Lamda implying, for our model, that at mu = Lamda, both the symmetry of Yukawa matrices and condensate dynamics may have a common origin.Comment: 29 pages, added PS version, fixed PS fil

Kurt Symanzik - a stable fixed point beyond triviality

In 1970 Kurt Symanzik proposed a "precarious" phi**4-theory with a negative quartic coupling constant as a valid candidate for an asymptotically free theory of strong interactions. Symanzik's deep insight in the non-trivial properties of this theory has been overruled since then by the Hermitian intuition of generations of scientists, who considered or consider this actually non-Hermitian highly important theory to be unstable. This short - certainly controversial - communication tries to shed some light on the historical and formalistic context of Symanzik's theory in order to sharpen our (quantum) intuition about non-perturbative theoretical physics between (non)triviality and asymptotic freedom.Comment: 6 pages, no figures, new style files, revised for typos, improved discussion, new references adde

Minimal See-Saw Model for Atmospheric and Solar Neutrino Oscillations

We present a minimal see-saw model based on an extension of the standard model (SM) which includes an additional U(1), with gauge charge $B - \frac{3}{2} (L_\mu + L_\tau)$. Requirement of anomaly cancellation implies the existence of two right-handed singlet neutrinos, carrying this gauge charge, which have normal Dirac couplings to $\nu_\mu$ and $\nu_\tau$ but suppressed ones to $\nu_e$. Assuming the U(1) symmetry breaking scale to be 10$^{12-16}$~GeV, this model can naturally account for the large (small) mixing solutions to the atmospheric (solar) neutrino oscillations.Comment: 14 pages, latex, no figure

Perturbative QCD Calculations of Total Cross Sections and Decay Widths in Hard Inclusive Processes

A summary of the current understanding of methods of analytical higher order perturbative computations of total cross sections and decay widths in Quantum Chromodynamics is presented. As examples, the total cross section in electron positron annihilation, the hadronic decay rates of the tau lepton and Higgs boson up to O(\alpha_s^2) and O(\alpha_s^3) are considered. The evaluation of the four-loop QED \beta - function at an intermediate step of the calculation is briefly described. The problem of renormalization group ambiguity of perturbative results is considered and some of the existing prescriptions are discussed. The problem of estimation of theoretical uncertainty in perturbative calculations is briefly discussed.Comment: 83 pages, LaTeX, Reviews of Modern Physics style, 14 figures plus figural equations (not included). Hard copy available upon request at [email protected]. To be published in Reviews of Modern Physic