QCD bounds on leading-order hadronic vacuum polarization contributions to the muon anomalous magnetic moment

Abstract

QCD bounds on the leading-order (LO) hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon ($a_{\mu }^{\mathrm{HVP},\mathrm{LO}}$, $a_{\mu }={\left(g-2\right)}_{\mu }/2$) are determined by imposing Hölder 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 $a_{\mu }^{\mathrm{HVP},\mathrm{LO}}$. 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 $\left(657.0\pm 34.8\right)\times 10^{-10}\le a_{\mu }^{\mathrm{HVP},\mathrm{LO}}\le \left(788.4\pm 41.8\right)\times 10^{-10}$, bridging the range between lattice QCD and data-driven values.

Comments: 17 pages, 4 figures. v2 contains extended analysis and discussion