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

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 $a_{\mu }^{\mathrm{H}\mathrm{V}\mathrm{P},\mathrm{F}\mathrm{L}\mathrm{A}\mathrm{G}}(\mathrm{i}\mathrm{s}\mathrm{o})=(720.0\pm 6.9)\times {10}^{-10}$ and $a_{\mu }^{\mathrm{H}\mathrm{V}\mathrm{P},\mathrm{W}\mathrm{P}25}(\mathrm{i}\mathrm{s}\mathrm{o})=(714.8\pm 7.4)\times {10}^{-10}$. Our results, which have a relative uncertainty of about $1\mathrm{\%}$, agree well with the corresponding determinations by other lattice groups. After adding to our determination of $a_{\mu }^{\mathrm{H}\mathrm{V}\mathrm{P},\mathrm{W}\mathrm{P}25}(\mathrm{i}\mathrm{s}\mathrm{o})$ the leading isospin-breaking corrections provided in the WP25, namely $a_{\mu }^{\mathrm{H}\mathrm{V}\mathrm{P},\mathrm{W}\mathrm{P}25}(\mathrm{I}\mathrm{B})=0.1(3.4)\times {10}^{-10}$, we obtain for the full HVP the value $a_{\mu }^{\mathrm{H}\mathrm{V}\mathrm{P}}=(714.9\pm 8.1)\times {10}^{-10}$. 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.