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The measurement of the anomalous magnetic moment of the muon and itsprediction allow for a high-precision test of the Standard Model (SM). In thisproceedings article we present ongoing work combining lattice QCD and continuumQED in order to determine an important SM contribution to the magnetic moment,the hadronic light-by-light contribution. We compute the quark-connectedcontribution in the Mainz position-space approach and investigate thelong-distance part of our data using calculations of the $\pi^0$-pole andcharged pion loop contributions.

Developments in the position-space approach to the HLbL contribution to the muon $g-2$ on the lattice