Bounds on $a_\mu^{\mathrm{HVP,LO}}$ using H\"older's inequalities and finite-energy QCD sum rules

TL;DR

This paper derives bounds on the leading-order hadronic vacuum polarization contribution to the muon g-2 using H"older's inequalities and finite-energy QCD sum rules, considering light-quark contributions up to five-loop order.

Contribution

It introduces a novel approach combining H"older's inequalities with QCD sum rules to bound $a_^{ ext{HVP,LO}}$, incorporating high-order perturbative and condensate corrections.

Findings

QCD bounds on $a_^{ ext{HVP,LO}}$ are between $(657.0 1 34.8) imes 10^{-10}$ and $(788.4 1 41.8) imes 10^{-10}$.

The bounds include uncertainties from perturbative and non-perturbative QCD contributions.

The method provides a theoretical constraint on the muon g-2 hadronic contribution.

Abstract

This study establishes bounds on the leading-order (LO) hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon ($a_\mu^{\mathrm{HVP,LO}}$, $a_\mu = (g-2)_\mu/2$) 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 $\left(657.0\pm 34.8\right)\times 10^{-10}\leq a_\mu^{\mathrm{HVP,LO}} \leq \left(788.4\pm 41.8\right)\times10^{-10}\,$.