Tests of quark-hadron duality in tau-decays
  An exhaustive number of QCD finite energy sum rules for $\tau$-decay together with the latest updated ALEPH data is used to test the assumption of global duality. Typical checks are the absence of the dimension $d=2$ condensate, the equality of the gluon condensate extracted from vector or axial vector spectral functions, the Weinberg sum rules, the chiral condensates of dimensions $d=6$ and $d=8$, as well as the extraction of some low-energy parameters of chiral perturbation theory. Suitable pinched linear integration kernels are introduced in the sum rules in order to suppress potential quark-hadron duality violations and experimental errors. We find no compelling indications of duality violations in hadronic $\tau$-decay in the kinematic region above $s\simeq2.2$ GeV$^{2}$ for these kernels. 
C. A. Dominguez, L. A. Hernandez, K. Schilcher, and H. Spiesberger
hep-ph hep-ex hep-lat