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

Abstract

Abstract We compute the hadronic light-by-light scattering contribution to the muon $$g-2$$ 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) $$_\mathrm{f}$$ 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 $$\eta _c$$ η c meson to define the physical charm-mass point and obtain a final value of $$a_\mu ^\mathrm{HLbL,c}= (2.8\pm 0.5) \times 10^{-11}$$ a μ HLbL , c = ( 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.