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

Abstract

We introduce a model independent method for the determination of the hadronic contribution to the QED running coupling, $Δα_{\text{HAD}}(M_{Z}^{2})$, 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 $Δα_{\text{HAD}}(M_{Z}^{2})$ 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 $Δα_{\text{HAD}}(M_{Z}^{2})=275.7(0.8) \times 10^{-4}$, which currently is the most precise value of $Δα_{\text{HAD}}(M_{Z}^{2})$.

A misprint in Eq. (6) has been corrected