SOME THEORETICAL CONSIDERATIONS ON HEAVY QUARKONIUM SYSTEMS

There is a recent revival of experimental and theoretical interest in the heavy quarkonia systems with the experimental hint of a P-1(1) sta te in the charmonium system. In the future, CLEO II will run on the Up silon(3S) resonance and accumulate as much as 2.1 x 10(6) Upsilon(3S) decays. We discuss here the theoretical implications for these systems . Topics consider are the kappa parameter and S-D mixing in heavy quar konia, Upsilon(3S) --> Upsilon(P-1(1))pi pi decay rate and spectrum, t he predicted rate for Upsilon(1D) --> Upsilon(1S)pi pi, the problem of the production of spin-singlet states from hadronic transitions of ch armonia and the puzzle of the missing psi(P-1(1)) --> J/psi pi(+)pi(-) decay.