Implications of the ALEPH tau-lepton decay data for perturbative and nonperturbative QCD

We use ALEPH data on hadronic tau decays in order to calculate Euclidean coordinate space correlation functions in the vector and axial-vector channels. The linear combination V-A receives no perturbative contribution and is quantitatively reproduced by the instanton liquid model. In the case of V+A the instanton calculation is in good agreement with the data once perturbative corrections are included. These corrections clearly show the evolution of alpha(s). We also analyze the range of validity of the operator product expansion (OPE). We conclude that the range of validity of the OPE is limited to x less, similar 0.3 fm, whereas the instanton model describes the data over the entire range.