Bounds on $a_{\mu }^{\mathrm{H}\mathrm{V}\mathrm{P},\mathrm{L}\mathrm{O}}$ using Hölder'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 ($a_{\mu }^{\mathrm{H}\mathrm{V}\mathrm{P},\mathrm{L}\mathrm{O}}$, $a_{\mu }=(g-2{)}_{\mu }\mathrm{/}2$) by using Hölder’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 $(657.0\pm 34.8)\times {10}^{-10}\le a_{\mu }^{\mathrm{H}\mathrm{V}\mathrm{P},\mathrm{L}\mathrm{O}}\le (788.4\pm 41.8)\times {10}^{-10}$.