Bounds on a_μHVP,LO using H\"older's inequalities and finite-energy QCD sum rules

This study establishes 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) by using H\"older's inequality and related inequalities in Finite-Energy QCD sum rules. Considering contributions from light quarks ($u,d,s$) up to five-loop order in perturbation theory within the chiral limit, leading-order light-quark mass corrections, next-to-leading order for dimension-four QCD condensates, and leading-order for dimension-six QCD condensates, the study finds QCD lower and upper bounds as (657.0± 34.8)× 10⁻¹⁰≤ a_μHVP,LO ≤ (788.4± 41.8)×10⁻¹⁰\,.