Testing quantum chromodynamics with moment sum rules

We investigate the consistency of $e^{+}{e}^{-}$ annihilation data with QCD. The gluon-condensate matrix element is determined independent of the value of the strong coupling constant or possible mass-renormalization ambiguities. Our method employs finite-contour sum rules which explicitly consider continuum data. For $c$-quark production the condensate parameter is ${\phi }_c=(2.5\mathrm{}\pm 0.4)\times {10}^{-3\mathrm{}}$, while for $b$-quark production we find ${\phi }_b=(0.4\mathrm{}\pm 1.0)\times {10}^{-3\mathrm{}}$, consistent with zero. The concept of duality of moments is proved and its applicability discussed.