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arXiv · 2604.08351

Lattice determination of the higher-order hadronic vacuum polarization contribution to the muon $g-2$

Arnau Beltran·Alessandro Conigli·Simon Kuberski·Harvey B. Meyer·Konstantin Ottnad·Hartmut Wittig
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Abstract

We present the first lattice QCD calculation of the next-to-leading order (NLO) hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment with sub-percent precision. We employ the time-momentum representation combined with the spatially summed vector correlator computed on CLS ensembles with $N_{\mathrm{f}}=2+1$ flavors of $\mathrm{O}(a)$-improved Wilson fermions, spanning six lattice spacings ($0.039$-$0.097\,$fm) and a range of pion masses including the physical value. After accounting for finite-size corrections and isospin-breaking effects, we obtain in the continuum limit $a_\mu^{\mathrm{hvp,\,nlo}} = (-101.57 \pm 0.26_{\rm stat} \pm 0.54_{\rm syst}) \times 10^{-11}$, corresponding to a total relative error of 0.6$\%$. Our result lies 1.4$\sigma$ below the estimate of the 2025 White Paper update and is two times more precise. It also shows a tension of $4.6\sigma$ with data-driven evaluations based on hadronic cross section measurements prior to the CMD-3 result.

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Arnau Beltran, Alessandro Conigli, Simon Kuberski, Harvey B. Meyer, Konstantin Ottnad, Hartmut Wittig. 2026-04-09. Lattice determination of the higher-order hadronic vacuum polarization contribution to the muon $g-2$. https://arxiv.org/abs/2604.08351

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