Tests of hadronic vacuum polarization fits for the muon anomalous magnetic moment

Original · EN

Using experimental spectral data for hadronic tau decays from the OPAL experiment, supplemented by a phenomenologically successful parameterization for the high-s region not covered by the data, we construct a physically constrained model of the isospin-one vector-channel polarization function. Having such a model as a function of Euclidean momentum Q² allows us to explore the systematic error associated with fits to the Q² dependence of lattice data for the hadronic electromagnetic current polarization function which have been used in attempts to compute the leading order hadronic contribution, aμʰLO, to the muon anomalous magnetic moment. In contrast to recent claims made in the literature, we find that a final error in this quantity of the order of a few percent does not appear possible with current lattice data, given the present lack of precision in the determination of the vacuum polarization at low Q². We also find that fits to the vacuum polarization using fit functions based on Vector Meson Dominance are unreliable, in that the fit error on aμʰLO is typically much smaller than the difference between the value obtained from the fit and the exact model value. The use of a sequence of Pade approximants known to converge to the true vacuum polarization appears to represent a more promising approach.