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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


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.