On the Charm Contribution to the Muon $g-2$ Light-by-Light

We combine existing perturbative results to show that a precise analytic determination of the charm-quark contribution to the hadronic light-by-light (HLbL) part of the muon anomalous magnetic moment is possible. Working in the $\overline{\mathrm{M}\mathrm{S}}$ scheme, we include the NLO $\mathcal{O}({\alpha }_s)$ correction, which significantly reduces the residual renormalization-scale dependence and the perturbative uncertainty. Our final result is $a_{\mu }^{\mathrm{H}\mathrm{L}\mathrm{b}\mathrm{L}\mathrm{c}}=3.65(25)\times {10}^{-11}$, in good agreement with recent lattice determinations.