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 𝑎LD,iso,conn,ud𝜇=411.4⁢(4.3)⁢(2.4)×10−10. We also provide the currently most precise calculation of the total isospin-symmetric light-quark connected contribution, 𝑎iso,conn,ud𝜇=666.2⁢(4.3)⁢(2.5)×10−10 in the BMW20 world, which is more than 4⁢𝜎 larger compared to the data-driven estimates of Boito et al. [Phys. Rev. D 107, 074001 (2023)] and 1.7⁢𝜎 larger compared to the lattice QCD result of BMW20.