Couplings of low-lying glueballs to light quarks, gluons, and hadrons

Abstract

We derive a set of QCD sum rules for the operator ..integral..dx G/sub ..mu..//sup ..nu../G/sub ..nu..//sup ..mu../, which is in a sense a generalization of the trace anomaly. Combining these with plausible phenomenology, we arrive at a semiquantitative picture of the couplings between the two lowest-lying glueballs (called S for J/sup P/C = 0/sup + +/ and P for 0/sup - +/) and light quarks, gluons, and hadrons. These couplings suggest the existence of an approximate chiral/dilatation symmetry carried by the glueball interactions, with large and calculable symmetry-breaking terms arising primarily from the glueball masses. The couplings are of typical hadronic size, even though suppressed in the large-N limit. The QCD sum rules mentioned above are closely related to the one-loop effective action, although derived quite differently; we believe the sum rules partially justify use of the effective action for small field strengths. A somewhat speculative generalization of sum rules to axial-anomaly densities gives an approximate evaluation of the Witten sum rule for the theta dependence of the vacuum energy. The S-P chiral symmetry is related to the quark U/sub A/(1) symmetry through the Peccei-Quinn mechanism; this symmetry is badly broken by the P mass.