Implications of the ALEPHτ-Lepton Decay Data for Perturbative and Nonperturbative QCD

Thomas Schäfer, Edward V. Shuryak
2001 Physical Review Letters  
We use ALEPH data on hadronic τ 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 α_s. We also analyze the range of validity of
more » ... e Operator Product Expansion (OPE). In the V-A channel we find a dimension d=6 contribution which is comparable to the original SVZ estimate, but the instanton model provides a different non-singular term of the same magnitude. In the V+A case both the OPE and the instanton model predict the same d=4 power correction induced by the gluon condensate, but it is masked by much larger perturbative contributions. We conclude that the range of validity of the OPE is limited to x0.3 fm, whereas the instanton model describes the data over the entire range.
doi:10.1103/physrevlett.86.3973 pmid:11328073 fatcat:l2mdnal3kbckzhn5op5b5j5zvu