Neural network parametrization of spectral functions from hadronic tau decays and determination of QCD vacuum condensates

The spectral function $\rho_{V-A}(s)$ is determined from ALEPH and OPAL dataon hadronic tau decays using a neural network parametrization trained to retainthe full experimental information on errors, their correlations and chiral sumrules: the DMO sum rule, the first and second Weinberg sum rules and theelectromagnetic mass splitting of the pion sum rule. Nonperturbative QCD vacuumcondensates can then be determined from finite energy sum rules. Our methodminimizes all sources of theoretical uncertainty and bias producing an estimateof the condensates which is independent of the specific finite energy sum ruleused. The results for the central values of the condensates $O_6$ and $O_8$ areboth negative.Comment: 29 pages, 18 ps figure