TheA 1-and the ?-meson in QCD

Recently we used a method of stable analytic extrapolation to test whether strictly local duality between the asymptotic and the resonance region, which is believed to be valid in QCD, appears already at the present stage of QCD calculations. Probing the QCD ?-amplitude, we found a prominent bump structure in the resonance region, i.e. a rather direct evidence for the validity of local duality. In the present paper we confirm and extend this result by giving two further applications, theA ₁-meson and the ?-meson. While we do not meet theA ₁, as was to be expected since other sum rules can not separate it from the continuum, too, the extrapolation of the ?-amplitude leads to an enormous bump. Comparing this ?-bump with our ?-bump, we recover at least qualitatively the real proportions.