2-LOOP GLUON-CONDENSATE CONTRIBUTIONS TO HEAVY-QUARK CURRENT CORRELATORS - EXACT RESULTS AND APPROXIMATIONS

The coefficient functions of the gluon condensate [G2], in the correlators of heavy-quark vector, axial, scalar and pseudoscalar currents, are obtained analytically, to two loops, for all values of z = q2/4m2. In the limiting cases z --> 0, z --> 1, and z --> -infinity, comparisons are made with previous partial results. Approximation methods, based on these limiting cases, are critically assessed, with a view to three-loop work. High accuracy is achieved using a few moments as input. A single moment, combined with only the leading threshold and asymptotic behaviours, gives the two-loop corrections to better than 1% in the next 10 moments. A two-loop fit to vector data yields [alpha(s)/piG2] almost-equal-to 0.021 GeV4.