Bounds on $a_{\hat{I}}{¼}^{\mathrm{HVP},\mathrm{LO}}$ using Hölder's inequalities and finite-energy QCD sum rules

Abstract

This study establishes bounds on the leading-order (LO) hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon ($a_{\hat{I}}{¼}^{\mathrm{HVP},\mathrm{LO}}$, $a_{\hat{I}}¼=(g-2{)}_{\hat{I}}¼/2$) 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 $\left(657.0\pm 34.8\right)\times 10^{-10}\le a_{\hat{I}}{¼}^{\mathrm{HVP},\mathrm{LO}}\le \left(788.4\pm 41.8\right)\times 10^{-10}$.

7 pages, 2 figures, 3 tables. Proceedings article for QCD24: 27th High-Energy Physics International Conference in Quantum Chromodynamis