Hadronic τ decay data and a hybrid strategy for the lattice evaluation of the leading order hadronic vacuum polarization contribution to [formula omitted

Abstract

Starting from the dispersion relation for the I=1 vector polarization, we employ hadronic τ decay data to construct a highly physical model of the subtracted polarization and use this to investigate, and quantify, systematic issues in existing lattice determinations of the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. The model is also used to demonstrate that a hybrid strategy, involving direct numerical integration of lattice data for Euclidean Q2 above ∼0.1–0.2GeV2 and the use of three possible reliable low-Q2 representations to cover the region below this, serves to reduce the errors induced by the identified systematic problems to the sub-percent level, making the hybrid approach an attractive option for use in future lattice analyses.