We present the first lattice QCD calculation of the next-to-leading order hadronic vacuum polarization contribution to the muon anomalous magnetic moment with sub-percent precision. We employ the time-momentum representation for the space-like kernel, which is combined with the spatially summed vector correlator computed on CLS ensembles with Nf=2+1 flavors of O(a)-improved Wilson fermions, covering six lattice spacings between 0.039 and 0.097fm and a range of pion masses including the physical value. After accounting for finite-size corrections and isospin-breaking effects, we obtain as our final, continuum-extrapolated result aμhvp,nlo=−101.57(26)stat(54)syst×10−11. It lies below the estimate provided by the 2025 White Paper of the Muon (g−2) Theory Initiative by 1.4σ but is two times more precise. It also exhibits a strong tension of 4.6σ with data-driven evaluations based on hadronic cross section measurements excluding the recent result by CMD-3.
@article{arxiv.2603.06806,
title = {Higher-order hadronic vacuum polarization contribution to the muon $g-2$ from lattice QCD},
author = {Arnau Beltran and Alessandro Conigli and Simon Kuberski and Harvey B. Meyer and Konstantin Ottnad and Hartmut Wittig},
journal= {arXiv preprint arXiv:2603.06806},
year = {2026}
}