QCD bounds on leading-order hadronic vacuum polarization contributions to the muon anomalous magnetic moment

Abstract

QCD bounds on the leading-order (LO) hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon (\(a_\mu^{\mathrm{HVP,LO}}\), \(a_\mu=\left(g-2\right)_\mu/2\)) are determined by imposing Hölder inequalities and related inequality constraints on systems of Finite-Energy QCD sum-rules. This novel methodology is complementary to lattice QCD and data-driven approaches to determining \(a_\mu^{\mathrm{HVP,LO}}\). For the light-quark (\(u,d,s\)) contributions up to five-loop order in perturbation theory in the chiral limit, LO in light-quark mass corrections, next-to-leading order in dimension-four QCD condensates, and to LO in dimension-six QCD condensates, we find that \(\left(657.0\pm 34.8\right)\times 10^{-10}\leq a_\mu^{\mathrm{HVP,LO}} \leq \left(788.4\pm 41.8\right)\times10^{-10}\,\), bridging the range between lattice QCD and data-driven values.