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arXiv · 2204.08844

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

En-Hung Chao·Renwick J. Hudspith·Antoine Gérardin·Jeremy R. Green·Harvey B. Meyer
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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)$_{\rm f}$ 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 $\eta_c$ meson to define the physical charm-mass point and obtain a final value of $a_\mu^{\rm HLbL,c} = (2.8\pm 0.5) \times 10^{-11}$, 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.

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En-Hung Chao, Renwick J. Hudspith, Antoine Gérardin, Jeremy R. Green, Harvey B. Meyer. 2022-04-19. The charm-quark contribution to light-by-light scattering in the muon $(g-2)$ from lattice QCD. https://doi.org/10.1140/epjc/s10052-022-10589-2

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