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

TL;DR

This paper tests QCD predictions against experimental tau-decay spectral functions using Finite Energy Sum Rules, finding excellent agreement over a wide energy range and constraining vacuum condensate values.

Contribution

It introduces a polynomial kernel in FESR to extend QCD analysis beyond available data, confirming the validity of perturbative QCD and vacuum condensate estimates.

Findings

Excellent data-QCD agreement from 3 to 10 GeV^2

Dimension 4 vacuum condensate consistent with literature

Dimension 2 term in OPE is negligible

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.