Charmonium: Comparison with experiment

Abstract

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.