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

Understand

The measurement of the anomalous magnetic moment of the muon and its prediction allow for a high-precision test of the Standard Model (SM).

• In this proceedings article we present ongoing work combining lattice QCD and continuum QED in order to determine an important SM contribution to the magnetic moment, the hadronic light-by-light contribution.
• We compute the quark-connected contribution in the Mainz position-space approach and investigate the long-distance part of our data using calculations of the $\pi^0$-pole and charged pion loop contributions.