Issues in QCD and properties of the Upsilon system.

Abstract

Recent results from lattice gauge theory and Gromes's consistency condition are used to determine the long-range (nonperturbative) spin-orbit potential. An important characteristic of this potential is that its sign is opposite to that of the leading perturbative contribution from one-gluon exchange. Moreover, this sign can be established without additional assumptions about the nature of the confining potential. Experimental support for this claim is garnered from the ratios of the fine-structure splittings of the \ensuremath{\Upsilon} system. Results for the energies, splittings, leptonic widths, and dipole transition rates are presented from a calculation based on full one-loop perturbative potentials supplemented by a linear confining potential and the long-range spin-orbit potential. Some of the assumptions about the nature of the renormalization scale and strong coupling constant are explored, and a procedure for finding the optimum values of these parameters is developed. The value of the strong coupling constant obtained in this manner is found to agree remarkably well with that obtained from gluon annihilation rates. Frequent comparison with the results and viewpoints of Gupta, Radford, and Repko, and Kwong and Rosner are carried out.