The charm-quark contribution to light-by-light scattering in the muon from lattice QCD

We compute the hadronic light-by-light scattering contribution to the muon $$ from the charm quark using lattice QCD. The calculation is performed on ensembles generated with dynamical (u, d, s) quarks at the SU(3) $$ symmetric point with degenerate pion and kaon masses of around 415 MeV. It includes the connected charm contribution, as well as the leading disconnected Wick contraction, involving the correlation between a charm and a light-quark loop. Cutoff effects turn out to be sizeable, which leads us to use lighter-than-physical charm masses, to employ a broad range of lattice spacings reaching down to 0.039 fm and to perform a combined charm-mass and continuum extrapolation. We use the $$ meson to define the physical charm-mass point and obtain a final value of $$ , whose uncertainty is dominated by the systematics of the extrapolation. Our result is consistent with the estimate based on a simple charm-quark loop, whilst being free of any perturbative scheme dependence on the charm mass. The mixed charm-light disconnected contraction contributes a small negative amount to the final value.