| Summary: | This work consists of two themes. First, we work with Finite Energy QCD Sum Rules (FESR) approach in the vacuum. We tackle the problem of quark-hadron duality violation (DV), using the vector and axial-vector hadronic spectral function from tau-decay. A pinched integration kernel is introduce in the FESR in order to quench potential duality violations on the real axis in the complex squared energy plane and effectively extend the analysis well beyond the kinematical Ƭ-decay end-point. As the sum rules are well satisfied, we conclude that possible DV must be buried under the experimental uncertainties. Also, using the latest updated ALEPH data on hadron decays, we use FESR to determine the vacuum condensates of dimension d = 2 and d = 4, to check the validity of the Weinberg sum rules, and to determine the chiral condensates of dimension d = 6 and d = 8, and values of the chiral perturbation theory L10 and C87.
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