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

TL;DR

This paper constructs a physically constrained model of the hadronic vacuum polarization function using experimental tau decay data and assesses the systematic errors in lattice QCD calculations of the muon g-2, highlighting the limitations of current data and fit methods.

Contribution

It introduces a model based on experimental data and phenomenological parameterization to evaluate systematic errors in lattice QCD calculations of the muon anomalous magnetic moment.

Findings

Current lattice data lack sufficient precision at low Q^2 to achieve a few percent error in a_μ^HLO.

Vector Meson Dominance based fits are unreliable for this purpose.

Pade approximants show promise as a more accurate fitting method.

Abstract

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 Q^2 allows us to explore the systematic error associated with fits to the Q^2 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_\mu^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 Q^2. 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_\mu^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 Pade approximants known to converge to the true vacuum polarization appears to represent a more promising approach.