Confronting QCD with the experimental hadronic spectral functions from tau-decay

Abstract

The (non-strange) vector and axial-vector spectral functions extracted from $\tau$-decay by the ALEPH collaboration are confronted with QCD in the framework of a Finite Energy QCD sum rule (FESR) involving a polynomial kernel tuned to suppress the region beyond the kinematical end point where there is no longer data. This effectively allows for a QCD FESR analysis to be performed beyond the region of the existing data. Results show excellent agreement between data and perturbative QCD in the remarkably wide energy range $s=3-10{GeV}^2$, leaving room for a dimension $d$ =4 vacuum condensate consistent with values in the literature. A hypothetical dimension $d$=2 term in the Operator Product Expansion is found to be extremely small, consistent with zero. Fixed Order and Contour Improved perturbation theory are used, with both leading to similar results within errors. Full consistency is found between vector and axial-vector channel results.

Additional remarks have been added. There is no change in the results, conclusions, etc

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• Chiral sum rules and vacuum condensates from tau-lepton decay data
• The rho meson in a scenario of pure chiral restoration
• Charm-quark mass from weighted finite energy QCD sum rules
• Quark masses in QCD: a progress report
• Analytical determination of the QCD quark masses
• Hadronic Contribution to the muon $g-2$ factor
• Introduction to QCD sum rules
• Contribution from Duality Violations to the theoretical error on alpha_s
• Quark-hadron duality: pinched kernel approch