  Central exclusive production (CEP) processes in high-energy proton --
(anti)proton collisions offer a very promising framework within which to study
both novel aspects of QCD and new physics signals. Among the many interesting
processes that can be studied in this way, those involving the production of
heavy (c,b) quarkonia and gamma gamma states have sufficiently well understood
theoretical properties and sufficiently large cross sections that they can
serve as `standard candle' processes with which we can benchmark predictions
for new physics CEP at the CERN Large Hadron Collider. Motivated by the broad
agreement with theoretical predictions of recent CEP measurements at the
Fermilab Tevatron, we perform a detailed quantitative study of heavy quarkonia
(chi and eta) and gamma gamma production at the Tevatron, RHIC and LHC, paying
particular attention to the various uncertainties in the calculations. Our
results confirm the rich phenomenology that these production processes offer at
present and future high-energy colliders.
