The UA(1) problem and the role of correlated q qbar exchange in effective theories of QCD

Abstract

The combined absence of physical realizations of the UA(1) symmetry possessed by the classical QCD action in the chiral limit, and of an isoscalar Goldstone boson associated with its spontaneous breakdown, has been dubbed the UA(1) problem. A formal resolution of this problem proposed by 't Hooft relies on instantons to provide a mass to the would-be Goldstone boson (eta '). An alternate scheme for the generation of an eta ' mass proposed by Kogut and Susskind derives from quark annihilation into gluons and a strong infrared singularity in the gluon propagator associated with confinement. We demonstrate here how such diagrams are generated in quark based effective theories by including a certain class of diagrams which arise from correlated q qbar exchange and are of higher order 1/N_c. A low energy energy expansion of this corrections is of the form discussed by Witten, di Vecchia and Veneziano.