A phenomenological analysis of the Weinberg sum rules and of the π+ − π0 mass difference

Abstract

We use recent data on τ-lepton hadronic decays to extract the q2 dependent vector and axial-vector spectral functions. Even though our results are necessarily restricted kinematically, we make use of these experimentally determined spectral functions to check to what extent the Weinberg sum rules are satisfied and to compute the pion electromagnetic mass difference. Although the results we obtain are satisfactory, the agreement with theoretical expectations appears to be somewhat fortuitous. A much more relevant and reliable theoretical comparison is provided by a Laplace transform version of the sum rules, which is more convergent and for which the QCD corrections are under better control.