Determination of the gluon condensate from data in the charm-quark region

Abstract

The gluon condensate, $⟨\frac{{\alpha }_s}{\pi }{G}^2⟩$, i.e. the leading order power correction in the operator product expansion of current correlators in QCD at short distances, is determined from $e^{+}{e}^{-}$ annihilation data in the charm-quark region. This determination is based on finite energy QCD sum rules, weighted by a suitable integration kernel to (i) account for potential quark-hadron duality violations, (ii) enhance the contribution of the well known first two narrow resonances, the $J/\psi$ and the $\psi (2S)$, while quenching substantially the data region beyond, and (iii) reinforce the role of the gluon condensate in the sum rules. By using a kernel exhibiting a singularity at the origin, the gluon condensate enters the Cauchy residue at the pole through the low energy QCD expansion of the vector current correlator. These features allow for a reasonably precise determination of the condensate, i.e. $⟨\frac{{\alpha }_s}{\pi }{G}^2⟩=0.037\pm 0.015{\text{mbox}GeV}^4$.

Comments: Revised version with improved error analysis, more detailed discussions, and additional references