The long-distance window of the hadronic vacuum polarization for the muon g-2

We provide the first ab-initio calculation of the Euclidean long-distance window of the isospin symmetric light-quark connected contribution to the hadronic vacuum polarization for the muon $g-2$ and find $a_{\mu }^{\mathrm{L}\mathrm{D},\mathrm{i}\mathrm{s}\mathrm{o},\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{n},\mathrm{u}\mathrm{d}}=411.4(4.3)(2.4)\times {10}^{-10}$. We also provide the currently most precise calculation of the total isospin symmetric light-quark connected contribution, $a_{\mu }^{\mathrm{i}\mathrm{s}\mathrm{o},\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{n},\mathrm{u}\mathrm{d}}=666.2(4.3)(2.5)\times {10}^{-10}$, which is more than 4$\sigma$ larger compared to the data-driven estimates of Boito et al. 2022 and 1.7$\sigma$ larger compared to the lattice QCD result of BMW20.