On the Parameters of the QCD-Motivated Potential in the Relativistic Independent Quark Model

In the framework of the relativistic independent quark model the parameters of the QCD-motivated static potential and the quark masses are calculated on the basis of the $1^{--}$ meson mass spectra. The value of the confining potential coefficient is found to be ($0.197\pm 0.005) GeV${}^2$. for quark- antiquark interaction independently on their flavours. The dependence of the quasi-Coulombic potential strength on the interaction distance are consistent with the QCD-motivated behaviour. The$q\bar q$-separations are evaluated and the$e^+e^-$ decay widths are estimated with the help of relativistic modification of the Van Royen-Weisskopf formula.Comment: 10 pages, LaTex; added references for the beginning, changed the last paragraph at the end, made a few stylistic correction

Bounding the ground-state energy of a many-body system with the differential method

This paper promotes the differential method as a new fruitful strategy for estimating a ground-state energy of a many-body system. The case of an arbitrary number of attractive Coulombian particles is specifically studied and we make some favorable comparison of the differential method to the existing approaches that rely on variational principles. A bird's-eye view of the treatment of more general interactions is also given.Comment: version 1->2 (main revisions): subsection 2.2, equation (18), footnote 6 have been adde

Effective field theory and the quark model

We analyze the connections between the quark model (QM) and the description of hadrons in the low-momentum limit of heavy-baryon effective field theory in QCD. By using a three-flavor-index representation for the effective baryon fields, we show that the ``nonrelativistic'' constituent QM for baryon masses and moments is completely equivalent through O(m_s) to a parametrization of the relativistic field theory in a general spin--flavor basis. The flavor and spin variables can be identified with those of effective valence quarks. Conversely, the spin-flavor description clarifies the structure and dynamical interpretation of the chiral expansion in effective field theory, and provides a direct connection between the field theory and the semirelativistic models for hadrons used in successful dynamical calculations. This allows dynamical information to be incorporated directly into the chiral expansion. We find, for example, that the striking success of the additive QM for baryon magnetic moments is a consequence of the relative smallness of the non-additive spin-dependent corrections.Comment: 25 pages, revtex, no figure

Relativistic Calculation of the Meson Spectrum: a Fully Covariant Treatment Versus Standard Treatments

A large number of treatments of the meson spectrum have been tried that consider mesons as quark - anti quark bound states. Recently, we used relativistic quantum "constraint" mechanics to introduce a fully covariant treatment defined by two coupled Dirac equations. For field-theoretic interactions, this procedure functions as a "quantum mechanical transform of Bethe-Salpeter equation". Here, we test its spectral fits against those provided by an assortment of models: Wisconsin model, Iowa State model, Brayshaw model, and the popular semi-relativistic treatment of Godfrey and Isgur. We find that the fit provided by the two-body Dirac model for the entire meson spectrum competes with the best fits to partial spectra provided by the others and does so with the smallest number of interaction functions without additional cutoff parameters necessary to make other approaches numerically tractable. We discuss the distinguishing features of our model that may account for the relative overall success of its fits. Note especially that in our approach for QCD, the resulting pion mass and associated Goldstone behavior depend sensitively on the preservation of relativistic couplings that are crucial for its success when solved nonperturbatively for the analogous two-body bound-states of QED.Comment: 75 pages, 6 figures, revised content

Perturbative reliability of the Higgs-boson coupling in the standard electroweak model

We apply Pade summation to the \beta(\lambda) function for the quartic Higgs coupling \lambda in the standard electroweak model. We use the \beta function calculated to five loops in the minimal subtraction scheme to demonstrate the improvement resulting from the summation, and then apply the method to the more physical on-mass-shell renormalization scheme where \beta is known to three loops. We conclude that the OMS \beta function and the running coupling \lambda(\mu) are reliably known over the range of energies and Higgs-boson masses of current interest.Comment: 14 pages, RevTeX, 6 figure