Position-space approach to hadronic light-by-light scattering in the muon $g-2$ on the lattice

Understand

The anomalous magnetic moment of the muon currently exhibits a discrepancy of about three standard deviations between the experimental value and recent Standard Model predictions.

• The theoretical uncertainty is dominated by the hadronic vacuum polarization and the hadronic light-by-light (HLbL) scattering contributions, where the latter has so far only been fully evaluated using different models.
• To pave the way for a lattice calculation of HLbL, we present an expression for the HLbL contribution to $g-2$ that involves a multidimensional integral over a position-space QED kernel function in the continuum and a lattice QCD four-point correlator.
• We describe our semi-analytic calculation of the kernel and test the approach by evaluating the $\pi^0$-pole contribution in the continuum.