Charmonium: The model

Abstract

A comprehensive treatment of the charmonium model of the $\ensuremath{\psi}$ family is presented. The model's basic assumption is a flavor-symmetric instantaneous effective interaction between quark color densities. This interaction describes both quark-antiquark binding and pair creation, and thereby provides a unified approach for energies below and above the threshold for charmed-meson production. If coupling to decay channels is ignored, one obtains the "naive" model wherein the dynamics is completely described by a single charmed-quark pair. A detailed description of this "naive" model is presented for the case where the instantaneous potential is a superposition of a linear and Coulombic term. A far more realistic picture is attained by incorporating those terms in the interaction that couple charmed quarks to light quarks. The coupled-channel formalism needed for this purpose is fully described. Formulas are given for the inclusive ${e}^{+}{e}^{\ensuremath{-}}$ cross section and for ${e}^{+}{e}^{\ensuremath{-}}$ annihilation into specific charmed-meson pairs. The influence of closed decay channels on $\ensuremath{\psi}$ states below charm threshold is investigated, with particular attention to leptonic and radiative widths.