Is there evidence for dimension-two corrections in QCD two-point functions?

TL;DR

This paper investigates the presence of dimension-two corrections in QCD two-point functions using tau decay data and Finite Energy Sum Rules, finding results consistent with zero within current uncertainties.

Contribution

It provides a novel analysis of ALEPH tau decay data to search for dimension-two contributions in the Operator Product Expansion, a topic not conclusively addressed before.

Findings

$C_2$ is consistent with zero within uncertainties.

$C_2$ depends strongly on $\Lambda_{QCD}$.

Results are stable against continuum threshold variations.

Abstract

The ALEPH data on the (non-strange) vector and axial-vector spectral functions, extracted from tau-lepton decays, is used in order to search for evidence for a dimension-two contribution, $C_{2 V,A}$, to the Operator Product Expansion (other than $d=2$ quark mass terms). This is done by means of a dimension-two Finite Energy Sum Rule, which relates QCD to the experimental hadronic information. The average $C_{2} \equiv (C_{2V} + C_{2A})/2$ is remarkably stable against variations in the continuum threshold, but depends rather strongly on $\Lambda_{QCD}$. Given the current wide spread in the values of $\Lambda_{QCD}$, as extracted from different experiments, we would conservatively conclude from our analysis that $C_{2}$ is consistent with zero.