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The well-known discrepancy in the muon $g-2$ between experiment and theorydemands further theory investigations in view of the upcoming new experiments.One of the leading uncertainties lies in the hadronic light-by-light scatteringcontribution (HLbL), that we address with our position-space approach. We focuson exploratory studies of the pion-pole contribution in a simple model and thefermion loop without gluon exchanges in the continuum and in infinite volume.These studies provide us with useful information for our planned computation ofHLbL in the muon $g-2$ using full QCD.

Exploratory studies for the position-space approach to hadronic light-by-light scattering in the muon $g-2$