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A highly physical model of the subtracted $I=1$ vector polarization, obtainedusing a dispersive representation with precise hadronic $\tau$ decay data asinput, is used to investigate systematic issues in the lattice evaluation ofthe leading order hadronic vacuum polarization contribution to the anomalousmagnetic moment of the muon. The model is also employed to study possibleresolutions of these problems. A hybrid approach to analyzing lattice data,involving low-order Pad\'e, low-degree conformal-variable polynomial, orsupplemented NNLO ChPT fits for $Q^2$ below $\sim 0.1-0.2$ GeV$^2$ and directnumerical integration of lattice data above this point, is shown to bring thesystematic issues identified under control at the sub-$1\%$ level.

A new strategy for evaluating the LO HVP contribution to $(g-2)_\mu$ on the lattice