Production of bound quark-antiquark systems

We use the technique of averaging low-order quantum-chromodynamics diagrams over the range from quark threshold to meson threshold to compute the photoproduction of $\psi$ and $\Upsilon$ vector mesons and the hadroproduction of $\Upsilon$. We find that the energy dependence of $\psi$ photoproduction is reproduced quite well. The model then implies a very rapid energy variation for $\Upsilon$ photoproduction at Fermilab energies. Calculations for hadroproduction of $\Upsilon$ show that at Fermilab energies the Drell-Yan mechanism is much more important for the production of $b$ quarks than it is for the production of charmed quarks. We compute rates for the production of $\Upsilon$ at Fermilab and CERN ISR energies and compare with experiment. Because the model has well defined dependence on the mass of the quark involved, we can compute the expected rates for hadroproduction of higher-mass bound systems. The variation of these rates with mass is comparable to that observed for experimental ${\mu }^{+}{\mu }^{-}$ pair production in this mass region, leading us to conclude that the signal/noise ratio for production of higher vector mesons should be roughly comparable to that for the $\Upsilon$.