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 Δα(5)had(s)=0.02761±0.00036 at s=mZ2 corresponding to 1/α(5)(mZ2)=128.936±0.046. The improved experimental accuracy is mainly due to recent BES measurements. We have also updated and parametrized the hadronic contribution to α as a function of energy.