  In this work we push the matching between the QCD operator product expansion
(OPE) and resonance chiral theory (RchiT) to order alpha_s. To this end we
compute two- and three-point QCD Green functions (GFs) in both theories and
compare the results. GFs which are order parameters of chiral symmetry breaking
make this matching more transparent and thus we concentrate on those. On the
OPE side one needs to calculate the hard-gluon virtual corrections to the quark
condensate, and in particular for three-point GFs this computation was hitherto
missing. We also discuss the need for including the infinite tower of hadronic
states in the hadronic representation of the GF when non-analytic terms such as
logarithms are present in the OPE Wilson coefficients.
