Corrections to quark asymmetries at LEP

Abstract.

The most precise measurement of the weak mixing angle $\sin^2 \theta_{\mathrm{eff}}^l$ at LEP is from the forward-backward asymmetry $e^ + e^- \rightarrow b \overline{b}$ at the Z-pole. In this note the QED and electroweak radiative corrections to obtain the pole asymmetry from the measured asymmetry for b- and c-quarks have been calculated using ZFITTER, which has been amended to allow a consistent treatment of partial two-loop corrections for the b-quark final asymmetries. A total correction of $\delta A_{\mathrm{FB}}^{{b}} = 0.0019 \pm 0.0002$ and $\delta A_{\mathrm{FB}}^{{c}} = 0.0064 \pm 0.0001$ has been found, where the remaining theoretical uncertainty is much too small to explain the apparent discrepancy between $\sin^2 \theta_{\mathrm{eff}}^l$ obtained from A _FB ^b and from the left-right asymmetry at SLD.