The charmonium model, formulated in detail in an earlier publication, is compared in a comprehensive fashion with the data on the $\ensuremath{\psi}$ family. The parameters of the "naive" model, in which the system is described as a $c\overline{c}$ pair, are determined from the observed positions of $\ensuremath{\psi}$, ${\ensuremath{\psi}}^{\ensuremath{'}}$, and the $P$ states. The model then yields a successful description of the spectrum of spin-triplet states above the charm threshold. It also accounts for the ratio of the leptonic widths of ${\ensuremath{\psi}}^{\ensuremath{'}}$ and $\ensuremath{\psi}$. When the $c\overline{c}$ potential is applied to the $\ensuremath{\Upsilon}$ family, it accounts, without any readjustment of parameters, for the positions of the $2S$ and $3S$ levels and for the leptonic widths of $\ensuremath{\Upsilon}$ and ${\ensuremath{\Upsilon}}^{\ensuremath{'}}$ relative to that of $\ensuremath{\psi}$. The model does not give acceptable values of the absolute leptonic widths, a shortcoming which is ascribed to large quantum-chromodynamic corrections to the van Royen-Weisskopf formula. The calculated $E1$ rates are about twice the values observed in the $\ensuremath{\psi}$ family. This naive model is also extended with considerable success to mesons composed of one heavy and one light quark. A significant extension of the model is achieved by incorporating coupling to charmed-meson decay channels. This gives a satisfactory understanding of $\ensuremath{\psi}(3772)$ as the $1^{3}D_{1}$ $c\overline{c}$ state, mixed via open and closed decay channels to $2^{3}S$. The model has decay amplitudes that are oscillatory functions of the decay momentum; these oscillations are a direct consequence of the radial nodes in the $c\overline{c}$ parent states. These amplitudes provide a qualitative understanding of the observed peculiar branching ratios into various charmed-meson channels near the resonance at 4.03 GeV, which is assigned to $3^{3}S$. The coupling of the $c\overline{c}$ states below the charm threshold to closed decay channels modifies the bound states and leads to reduction of about 20% in $E1$ rates in comparison to those of the naive model.

Charmonium: Comparison with Experiment

If we assume that the strong interactions of baryons
and mesons are correctly described in terms of
the broken "eightfold way", we are tempted to
look for some fundamental explanation of the situation.
A highly promised approach is the purely dynamical
"bootstrap" model for all the strongly interacting
particles within which one may try to derive
isotopic spin and strangeness conservation and
broken eightfold symmetry from self-consistency
alone. Of course, with only strong interactions,
the orientation of the asymmetry in the unitary
space cannot be specified; one hopes that in some
way the selection of specific components of the F-spin
by electromagnetism and the weak interactions
determines the choice of isotopic spin and hypercharge
directions.

A Schematic Model of Baryons and Mesons

Strong decays of ψdblac; (4.028) as a radial excitation of charmonium

Why is ψ(4.414) so narrow

The classification and decays of resonant particles

The mesons as a relativistic fermi-quark-antiquark system with strong binding

The dynamics of strong binding of heavy scalar particles (quarks) are discussed with the help of the Bethe-Salpeter equation with a smooth ladder-type kernel. For this purpose, the Bethe-Salpeter amplitudes are expanded intoO4 spherical functions and the remaining « hyper-radial » equation is solved by a variational method. These calculations are considered as a model of mesons as bound states of heavy quarks. The low-lying mesons form linear trajectories with a slope of 1 (GeV)−2. The modification of the vector-meson dominance form factor by the bound-state wave functions is calculated and found to be in good agreement with experiment.

Relativistic scalar quark model with strong binding

Quark dynamics and strong meson decays

In our lectures we deal with the specific dynamical problems arising in the formulation of the relativistic quark model in the framework of field theory1. After the discussion of some basic questions occurring in this particular attempt towards a foundation of hadron dynamics, we develop extensively the methods for the description of mesons as quark-antiquark bound-states and give some illuminating phenomenological applications. In order to outline the spirit of our approach, let us first answer some general questions.

H. Joos

Papers

The mesons as a relativistic fermi-quark-antiquark system with strong binding

Relativistic scalar quark model with strong binding

Quark dynamics and strong meson decays

Dynamical Problems of the Relativistic Quark Model