We introduce a model independent method for the determination of the hadronic contribution to the QED running coupling, $\Delta {\alpha }_{\mathrm{HAD}}(M_Z^2)$, requiring no $e^{+}{e}^{-}$ annihilation data as input. This is achieved by calculating the heavy-quark contributions entirely in perturbative QCD, while 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 $\Delta {\alpha }_{\mathrm{HAD}}(M_Z^2)$ can be improved by some 20% by computing the heavy-quark pieces in perturbative QCD, while using $e^{+}{e}^{-}$ data only for the low-energy light-quark sector. We obtain in this case $\Delta {\alpha }_{\mathrm{HAD}}(M_Z^2)=275.7(0.8)\times {10}^{-4}$, which currently is the most precise value of $\Delta {\alpha }_{\mathrm{HAD}}(M_Z^2)$.

• Received 21 September 2012

DOI:https://doi.org/10.1103/PhysRevD.86.093013