The charm-quark contribution to light-by-light scattering in the muon (g − 2) from lattice QCD

Abstract

We compute the hadronic light-by-light scattering contribution to the muon g−2 from the charm quark using lattice QCD. The calculation is performed on ensembles generated with dynamical(u, d,s) quarks at the SU(3)f 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 ηc meson to define the physical charm-mass point and obtain a final value of aHLbL,c μ = (2.8±0.5)×10−11, 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.