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

QCD bounds on the leading-order (LO) hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon ($a_{\mu }^{\mathrm{H}\mathrm{V}\mathrm{P},\mathrm{L}\mathrm{O}}$, $a_{\mu }={(g-2)}_{\mu }\mathrm{/}2$) 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 $a_{\mu }^{\mathrm{H}\mathrm{V}\mathrm{P},\mathrm{L}\mathrm{O}}$. 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 $(657.0\pm 34.8)\times {10}^{-10}\le a_{\mu }^{\mathrm{H}\mathrm{V}\mathrm{P},\mathrm{L}\mathrm{O}}\le (788.4\pm 41.8)\times {10}^{-10}$, bridging the range between lattice QCD and data-driven values.