Hadronic contribution to the QED running coupling $\alpha(M_{Z}^2)$

TL;DR

This paper presents a model-independent method to determine the hadronic contribution to the QED running coupling at the Z boson mass, combining perturbative QCD for heavy quarks and lattice QCD for light-quark resonances, improving precision without relying on $e^+e^-$ data.

Contribution

The novel approach eliminates the need for $e^+e^-$ annihilation data by using perturbative QCD and lattice QCD, enhancing the precision of $ riangle ext{α}_{ ext{HAD}}(M_Z^2)$ determination.

Findings

Heavy-quark contributions computed in PQCD improve precision.

Light-quark resonance contributions derived from lattice QCD.

Current best estimate: $ riangle ext{α}_{ ext{HAD}}(M_Z^2)=275.7(0.8) imes 10^{-4}$.

Abstract

We introduce a model independent method for the determination of the hadronic contribution to the QED running coupling, $\Delta\alpha_{\text{HAD}}(M_{Z}^{2})$, requiring no $e^+e^-$ annihilation data as input. This is achieved by calculating the heavy-quark contributions entirely in perturbative QCD, whilst the light-quark resonance piece is determined using available lattice QCD results. Future reduction in the current uncertainties in the latter shall turn this method into a valuable alternative to the standard approach. Subsequently, we find that the precision of current determinations of $\Delta\alpha_{\text{HAD}}(M_{Z}^{2})$ can be improved by some 20% by computing the heavy-quark pieces in PQCD, whilst using $e^+e^-$ data only for the low-energy light-quark sector. We obtain in this case $\Delta\alpha_{\text{HAD}}(M_{Z}^{2})=275.7(0.8) \times 10^{-4}$, which currently is the most precise value of $\Delta\alpha_{\text{HAD}}(M_{Z}^{2})$.