Abstract
Recent experimental data on tau decays are used to reconstruct the difference in hadronic spectral densities with vector and axial-vector quantum numbers. The saturation of Das-Mathur-Okubo and Weinberg sum rules is studied. Two methods of improving convergence and decreasing errors are applied, and good agreement with the predictions of current algebra and chiral perturbation theory is observed. The resulting value of the pion polarisability is (2.64 +/- 0.36) 10^-4 fm^3.
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