Two-loop gluon-condensate contributions to heavy-quark current correlators: exact results and approximations

Abstract

The coefficient functions of the gluon condensate 〈 G 2〉, in the correlators of heavy-quark vector, axial, scalar and pseudoscalar currents, are obtained analytically, to two loops, for all values of z = q 2 4m 2 . In the limiting cases z → 0, z → 1, and z → − ∞, comparison are made previous 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 behaviour, gives the two-loop corrections to better than 1% in the next 10 moments. A two-loop fit to vector data yields 〈 α s πG 2〉 ≈ 0.021 GeV 4 .