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

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, $C_{2V,A}$, 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.

Comments: A misprint in Eq. (14) has been corrected. No other changes. Paper to appear in Phys. Rev. D