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Implications of the ALEPH tau-Lepton Decay Data for Perturbative and Non-Perturbative QCD

Thomas Schaefer·Edward Shuryak
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Abstract

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 the 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 $x\lsim0.3$ fm, whereas the instanton model describes the data over the entire range.

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Thomas Schaefer, Edward Shuryak. 2000-10-11. Implications of the ALEPH tau-Lepton Decay Data for Perturbative and Non-Perturbative QCD. https://doi.org/10.1103/physrevlett.86.3973

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