Phenomenological Analysis of a Dimension-Two Operator in QCD and its Impact on $\alpha_{s}(M_{\tau})$

Abstract

Fits to the ARGUS data on hadronic decays of the tau-lepton, which determine the vector and axial-vector spectral functions, are used in order to determine the size of a dimension $d=2$ term in the Operator Product Expansion. Constraints from the first Weinberg sum rule (in the chiral limit) are enforced in order to reduce the uncertainty of this determination. Results for the $d=2$ operator are consistent with a quadratic dependence on $\Lambda_{QCD}$. The impact of this term on the extraction of $\alpha_{s}(M_{\tau})$ is assessed.