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Relations between vacuum condensates and low energy parameters from a rational approach

Conventional methods to determine non-perturbative parameters in QCD, such as the different variants of QCD sum rules or the minimal hadronic approximation, combine a certain degree of matching to QCD with inputs from hadronic parameters. The latter introduce systematic errors difficult to quantify. In this paper I will apply a method based on rational approximant theory where matching is maximized and no hadronic inputs are used, thereby leading to simple analytical relations between high and low energy parameters. I will be mostly interested in the phenomenological applications to the Π_{LR} and Π_{VT} correlators, with especial emphasis on quantities like the d=6 and d=8 vacuum condensates in Π_{LR} or the quark condensate magnetic susceptibility χ_0.