Bounding the Muon g-2: A QCD Sum Rule Approach to Hadronic Vacuum Polarization

We present a novel QCD-based methodology to constrain the leading-order hadronic vacuum polarization (HVP) contribution to the muon's anomalous magnetic moment, a_μ^{HVP, LO}​. By applying Hölder inequalities within finite-energy QCD sum rules, we derive rigorous bounds that complement existing lattice QCD and data-driven approaches. Our analysis, incorporating up to five-loop perturbative corrections in the chiral limit, leading-order light-quark mass effects, and next-to-leading order contributions from dimension-four and leading-order dimension-six QCD condensates, yields a constrained range of (657.0±34.8)×10⁻¹⁰ ≤ a_μ^{HVP, LO}≤ (788.4±41.8)×10⁻¹⁰. This range bridges the gap between current lattice and phenomenological estimates, offering an independent, theory-driven perspective on the HVP contribution. Our approach provides a valuable cross-check for ongoing efforts to resolve the persistent discrepancy between experimental measurements and Standard Model predictions of the muon's anomalous magnetic moment.