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_μHVP,LO, a_μ=(g-2)_μ/2) are determined by imposing H\"older 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_μHVP,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 (673.0± 40.0)× 10⁻¹⁰≤ a_μHVP,LO ≤ (807.5± 48.0)×10⁻¹⁰\,, bridging the range between lattice QCD and data-driven values.