PLANE-WAVE, COORDINATE-SPACE, AND MOMENT TECHNIQUES IN THE OPERATOR-PRODUCT EXPANSION - EQUIVALENCE, IMPROVED METHODS, AND THE HEAVY-QUARK EXPANSION

We compare plane-wave, coordinate-space and moment methods for evaluat ing operator-product expansion (OPE) coefficients of the light-quark a nd gluon condensates. Equivalence of these methods for quark condensat e contributions is proven to all orders in the quark mass parameter m. The three methods are also shown to yield equivalent gluon condensate contributions to two-current correlation functions, regardless of the gauge chosen for external gluon fields in the coordinate space approa ch. An improved method for evaluating quark-condensate OPE coefficient s is presented for several (two-current) correlation functions. Gauge- dependent Green functions are also discussed. It is shown that contrad ictory expressions for the gluon-condensate contribution to the quark propagator occurring from the plane-wave and coordinate-space approach es yield identical relations between the heavy-quark and gluon condens ates, as anticipated from the gauge invariance of the heavy-quark expa nsion.