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

*N. Asmussen, J. Green, H.B. Meyer, A. Nyffeler*

in 34th annual International Symposium on Lattice Field Theory

Contribution: pdf

**Abstract**

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.