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

Using experimental spectral data for hadronic τ decays from the OPAL experiment, supplemented by a phenomenologically successful parametrization 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, a_μ^HLO, 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 a_μ^HLO 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 Padé approximants known to converge to the true vacuum polarization appears to represent a more promising approach.