LONG-RANGE SPIN-ORBIT POTENTIAL, GROMES CONSISTENCY CONDITION, RICHARDSON POTENTIAL, AND PROPERTIES OF HEAVY QUARKONIUM SYSTEMS

The energies, fine-structure splittings, leptonic widths, and dipole electromagnetic transition rates are calculated for the and charmonium systems using a potential model based on Richardson's interpolating form for the running coupling constant. Using the definitions of the spin-dependent potentials of Eichten and Feinberg and arguments based on lattice pauge calculations, we have determined the long-range spin-orbit potential from Gromes's consistency condition. It is also shown that the sign difference between the long-range spin-orbit potential and the perturbative spin-orbit potential is important in explaining the measured values of the fine-structure ratio in both the and charmonium P states. The question of whether the parameter of Richardson's potential is supposed to play the role of the universal QCD scale is addressed. It is argued that the agreement of the and charmonium leptonic widths with experiment is convincing support for Richardson's form for the running coupling constant since these numbers reflect directly the values of the various S state wave functions at the origin. Certain problems with the magnitudes of the hyperfine splittings and dipole transition rates of charmonium are discussed. © 1990 The American Physical Society.