Analytic Reconstruction of heavy-quark two-point functions at   O(\alpha_s^3)
  Using a method previously developed, based on the Mellin-Barnes transform, we reconstruct the two-point correlators in the vector, axial, scalar and pseudoscalar channels from the Taylor expansion at q^2=0, the threshold expansion at q^2=4m^2 and the OPE at q^2\rightarrow -\infty, where m is the heavy quark mass. The reconstruction is analytic and systematic and is controlled by an error function which becomes smaller as more terms in those expansions are known. 
David Greynat, Pere Masjuan, Santiago Peris
hep-ph hep-lat