Charmonium in the instantaneous approximation

Abstract

The charmonium system is studied in a Salpeter model with a vector plus scalar potential. We use a kinematical formalism based on the one developed by Suttorp, and present general eigenvalue equations and expressions for decay observables in an onium system for such a potential both in the Feynman and Coulomb gauges. Special attention is paid to the problem with renormalization of the lepton pair decays, and we argue that they must be defined relative to one of the experimental decay widths because renormalization of the vertex function is not possible. The parameters of the model are determined by a fit to the mass spectrum and the lepton pair decay rates. Two gamma decays and E1 and M1 transitions are then calculated and found to be well accounted for. No significant differences in the results in Feynman or Coulomb gauge are found. A comparison is made, regarding the electromagnetic transitions, between the full and reduced Salpeter equation. A large difference is found showing the importance of using the full Salpeter equation.