A derivative-based approach for the leading order hadronic contribution to $g_\mu-2$

We describe a lattice approach to calculating the leading-order hadronic contribution to the anomalous magnetic moment of the muon. We employ lattice momentum derivatives, in both the spatial and temporal directions, to determine the hadronic vacuum polarization scalar at low momenta and construct a smooth, intregrable function in this momentum region. The method is tested on one hex-smeared Wilson-quark lattice ensemble with physical pion masses.