Heavy-quark-antiquark potential in the MIT bag model

Abstract

The MIT bag model for a meson composed of a heavy quark and a heavy antiquark is solved using the Born-Oppenheimer approximation. For fixed $q\overline{q}$ separations the color-electric fields and bag shapes are determined by solving numerically the Yang-Mills equations with bag boundary conditions to lowest order in the quark-gluon coupling constant. Spin effects are not included. The resulting bag energy is used as a potential energy in the Schrödinger equation for the relative motion of the quarks. Good agreement with the experimental $\psi$ and $\Upsilon$ spectra and leptonic decay widths is found. When the same potential is applied to strange-quark systems, a consistent picture of the masses of the $\phi$ and $F^{*}$ mesons emerges. The relation between spectroscopy and the variation of the coupling constant with distance is explored.