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

Abstract

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, aHLOμ, 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 aHLOμ 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.