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

Abstract

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 $a_{\mu }^{\mathrm{LD},\mathrm{iso},\mathrm{conn},\mathrm{ud}}=411.4(4.3)(2.4)\times 10^{-10}$. We also provide the currently most precise calculation of the total isospin symmetric light-quark connected contribution, $a_{\mu }^{\mathrm{iso},\mathrm{conn},\mathrm{ud}}=666.2(4.3)(2.5)\times 10^{-10}$, 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.

12 pages, 9 figures