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

TL;DR

This paper determines the gluon condensate in QCD using finite energy sum rules and $e^+ e^-$ data in the charm-quark region, achieving a reasonably precise value by employing a specialized integration kernel.

Contribution

It introduces a novel sum rule approach with a singular kernel to accurately extract the gluon condensate from experimental data, accounting for duality violations and resonance contributions.

Findings

Gluon condensate value: 0.037 ± 0.015 GeV^4

Enhanced resonance contribution in sum rules

Reduced uncertainties in condensate determination

Abstract

The gluon condensate, $\langle \frac{\alpha_s}{\pi} G^2 \rangle$, 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. $\langle \frac{\alpha_s}{\pi} G^2 \rangle =0.037 \,\pm\, 0.015 \;{\mbox{GeV}}^4$.