{\bf Theory uncertainties}

As mentioned in the previous section, the dominant systematic error on these numbers is the theoretical uncertainty on the predicted event rate. It is difficult to say today what this uncertainty will be at the time of the FCC-ee startup. To evaluate its effects, the likelihood in Eq.~\ref{eq:likelihood} was enhanced with the corresponding Gaussian nuisance factor, and the form factor uncertainties were determined for any value of the assumed cross-section theoretical error. The result is displayed in Fig.~\ref{fig:crosserr} for a theoretical error between 0.01\% and 100\%. The uncertainties on the first four form factors stay below a few per mil if the total cross section can be predicted with a precision of 2\% or better. The uncertainty on $F_{1A}^Z$ remains essentially unaffected as long as the theoretical precision is below 10\%.