A determination of the QED coupling at the $Z$ pole

Abstract

We critically examine the evaluation of the hadronic contribution to the running of the QED coupling, $\hat{I}\pm$, from $Q^2=0$ to $Q^2=M_Z^2$. Using data for $e^{+}{e}^{-}\to$hadrons we find that $\hat{I}\pm (M_Z^2{)}^{-1}=128.99\pm 0.06$, as compared to the existing value of $128.87\pm 0.12$.

We have made refinements to the calculation of the contribution to $\hat{I}\pm (M_Z^2)$ from the $\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ production, and from the region just above the $\ddot{I}ˆ$ resonances, including, in particular, a study of the implications of the Crystal Ball data for $R$. These refinements slightly reduce the value of $\hat{I}\pm (M_Z^2{)}^{-1}$ from $129.10\pm 0.06$ to $128.99\pm 0.06$. Standard Latex, 12 pages. Four uufiled postscript files included. Compressed postscript version with figures available via anonymous ftp at ftp://phenom.physics.wisc.edu/pub/preprints/current/