Update of the hadronic contribution to the QED vacuum polarization

We have updated the evaluation of the hadronic contribution to the running of the QED fine structure constant. It is obtained from a dispersion integral over a parametrization of the measured cross section of e+e− → hadrons. We find this contribution to be 0.0280 ± 0.0007 at s = MZ2 corresponding to α−1(MZ2) = 128.89 ± 0.09. We have also parametrized the corrections to α as a function of energy and discuss the influence on the luminosity measurements at LEP.