The hadronic-vacuum-polarization contribution to the muon anomalous magnetic moment in isospin-symmetric lattice QCD with twisted-mass fermions

Abstract

We present a lattice-QCD calculation of the leading-order hadronic-vacuum-polarization (HVP) contribution to the anomalous magnetic moment of the muon in isospin-symmetric QCD. We employ the gauge configurations generated by the Extended Twisted Mass Collaboration (ETMC) with $N_f = 2 + 1 + 1$ flavors of Wilson-clover twisted-mass quarks at four lattice spacings and at values of the quark-mass parameters matching the definition of isospin-symmetric QCD given in the FLAG review 2024 and in the 2025 edition of the Muon $g-2$ Theory Initiative White Paper (WP25). After retuning the simulation parameters to precisely match these two definitions of isospin-symmetric QCD, and after carrying out an extrapolation to the continuum limit based on the data at lattice spacings $a \simeq 0.049, 0.057, 0.068$ and $0.079$~fm, and spatial lattice sizes up to $L \simeq 7.7$~fm, we obtain $a_μ^{\rm HVP, FLAG}(\rm{iso}) = (720.0 \pm 6.9) \times 10^{-10}$ and $a_μ^{\rm HVP, WP25}(\rm{iso}) = (714.8 \pm 7.4) \times 10^{-10}$. Our results, which have a relative uncertainty of about $1 \%$, agree well with the corresponding determinations by other lattice groups. After adding to our determination of $a_μ^{\rm HVP, WP25}(\rm{iso})$ the leading isospin-breaking corrections provided in the WP25, namely $a_μ^{\rm HVP, WP25}({\rm IB}) = 0.1(3.4)\times 10^{-10}$, we obtain for the full HVP the value $a_μ^{\rm HVP}= (714.9 \pm 8.1)\times 10^{-10}$. This result translates into a Standard Model prediction for the muon anomalous magnetic moment that is fully consistent with the latest result by the Fermilab Muon $g-2$ experiment and strengthens the tension between lattice QCD and data-driven (pre-CMD3) dispersive determinations.