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

Abstract

We construct a physically motivated model for the isospin-one non-strange vacuum polarization function Pi(Q^2) based on a spectral function given by vector-channel OPAL data from hadronic tau decays for energies below the tau mass and a successful parametrization, employing perturbation theory and a model for quark-hadron duality violations, for higher energies. Using a covariance matrix and Q^2 values from a recent lattice simulation, we then generate fake data for Pi(Q^2) and use it to test fitting methods currently employed on the lattice for extracting the hadronic vacuum polarization contribution to the muon anomalous magnetic moment. This comparison reveals a systematic error much larger than the few-percent total error sometimes claimed for such extractions in the literature. In particular, we find that errors deduced from fits using a Vector Meson Dominance ansatz are misleading, typically turning out to be much smaller than the actual discrepancy between the fit and exact model results. The use of a sequence of Padé approximants, recently advocated in the literature, appears to provide a safer fitting strategy.

Comments: 7 pages, 4 figures. Presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, Germany