Realising fusion systems

We show that every fusion system on a p-group S is equal to the fusion system associated to a discrete group G with the property that every p-subgroup of G is conjugate to a subgroup of S

Realising fusion systems

We show that every fusion system (saturated or not) on a p-group S is equal to the fusion system associated to a discrete group G containing S as a subgroup and such that every finite subgroup of G is conjugate to a subgroup of S

Probabilities in nonorthogonal basis: Four--quark systems

Four-quark states may exist as colorless meson-meson molecules or compact systems with two-body colored components. We derive an analytical procedure to expand an arbitrary four--quark wave function in terms of nonorthogonal color singlet--singlet vectors. Using this expansion we develop the necessary formalism to evaluate the probability of physical components with an arbitrary four-quark wave function. Its application to characterize bound and unbound four--quark states as meson-meson, molecular or compact systems is discussedComment: Accepted for publication in PR

Multiquark Systems in a Constituent Quark Model with Chiral Dynamics

We discuss the stability of multiquark systems within the recent model of Glozman et al. where the chromomagnetic hyperfine interaction is replaced by pseudoscalar-meson exchange. We find that such an interaction binds a heavy tetraquark system $QQ\bar q\bar q$ ($Q=c, b$ and $q=u, d)$ by $0.2-0.4$ GeV. This is at variance with results of previous models where $cc\bar q\bar q$ is unstable.Comment: 6 pages, Plain Latex, Contribution to the Workshop''Quark Confinement and the Hadron Spectrum II'', Como, Italy, June 26--29, 1996, to appear in the Proceedings, ed. Nora Brambilla, World Scientifi

Heavy-Flavour Pentaquarks in a Chiral Constituent Quark Model

Within the chiral constituent quark model of Glozman and Riska, we discuss the stability of heavy pentaquarks, i.e. hadrons containing four light quarks and a heavy antiquark. The spin-dependent part of the Hamiltonian is dominated by the short-range part of the Goldstone-boson-exchange interaction. We find that these systems are not bound, having an energy above the lowest dissociation threshold into a baryon and a meson.Comment: 10 pages + table

On a three-body confinement force in hadron spectroscopy

Recently it has been argued that a three-body colour confinement interaction can affect the stability condition of a three-quark system and the spectrum of a tetraquark described by any constituent quark model. Here we discuss the role of a three-body colour confinement interaction in a simple quark model and present some of its implications for the spectra of baryons, tetraquarks and six-quark systems.Comment: 19 pages (RevTeX), addition of new material regarding the NN interaction, more accurate discussion of the baryonic case, accepted for publication in Phys. Rev.

k-String tensions and the 1/N expansion

We address the question of whether the large-N expansion in pure SU(N) gauge theories requires that k-string tensions must have a power series expansion in 1/N^2, as in the sine law, or whether 1/N contributions are also allowable, as in Casimir scaling. We find that k-string tensions may, in fact, have 1/N corrections, and consistency with the large-N expansion in the open-string sector depends crucially on an exact cancellation, which we will prove, among terms involving odd powers of 1/N in particular combinations of Wilson loops. It is shown how these cancellations are fulfilled, and consistency with the large-N expansion achieved, in a concrete example, namely, strong-coupling lattice gauge theory with the heat-kernel action. This is a model which has both a 1/N^2 expansion and Casimir scaling of the k-string tensions. Analysis of the closed string channel in this model confirms our conclusions, and provides further insights into the large-N dependence of energy eigenstates and eigenvalues.Comment: RevTeX4, 21 pages. Typos corrected, references added, some discussions expanded; conclusions unchanged. Version to appear on PR

New approach to 4^4He charge distribution

We present a study of the $^4$He charge distribution based on realistic nucleonic wave functions and incorporation of the nucleon's quark substructure. The central depression of the proton point density seen in modern four-body calculations is too small by itself to lead to a correct description of the charge distribution. We utilize six-quark structures calculated in the Chromodielectric Model for N-N interactions, and we find a swelling of the proton charge distribution as the internucleon distance decreases. These charge distributions are combined with the $^4$He wave function using the Independent Pair Approximation and two-body distributions generated from Green's Function Monte Carlo calculations. We obtain a reasonably good fit to the experimental charge distribution without including meson exchange currents.Comment: 9 pages, LaTeX, 4 figures (Figures 1 and 2 doesn't exist as postscript files : they are only available on request

On independent sets in purely atomic probability spaces with geometric distribution.

We are interested in constructing concrete independent events in purely atomic probability spaces with geometric distribution. Among other facts we prove that there are uncountable many sequences of independent events