Relativistic wave equation and heavy quarkonium spectra

Abstract

We solve an equal-time relativistic wave equation with a confinement potential for heavy-quark-antiquark systems. A new pair of coupled equations, which are appropriate in the presence of a linear confinement potential, are introduced for the ${J}^{\mathrm{PC}}={1}^{\ensuremath{-}\ensuremath{-}}$ trajectory. With a set of standard potential parameters, we obtain a fit to the charmonium and the $\ensuremath{\Upsilon}$ spectra, which is as satisfactory as the nonrelativistic one, to the extent of neglecting magnetic interactions. In contrast to the nonrelativistic treatment, we obtain the absolute mass values of the quark-antiquark systems. Furthermore, the quark masses are found to be much smaller than the corresponding nonrelativistic values, which we show cannot be identified with the physical quark mass.