\section{Conclusion}

The final results of the fast rotation analysis of the \runo\ \sixty\ data set is:

\begin{align*}
x_e & = 6.35\pm 0.01 ~(\text{stat}) \pm 0.38 ~\text{(syst) mm},\\
\sigma & = 9.19\pm 0.01 ~(\text{stat}) \pm 0.34 ~\text{(syst) mm},\\
C_E & = -519 \pm 1 ~(\text{stat}) \pm 36 ~\text{(syst) ppb}.
\end{align*}

The level of uncertainty is satisfying for the \runo. There is room, however, to improve the uncertainty by bettering the understanding of
the analysis performance and impacts from beam dynamics and detector effects.
It will rely on thorough studies with toy Monte Carlo, {\tt BMAD} and {\tt GM2RINGSIM}.
The main uncertainty to be tackled are related to the start and end time scans, as well as 
the positron energy threshold and background definition. 
It is possible that additional systematic uncertainties will be estimated in the future: time-momentum
correlation of the incoming bunch, muon loss, etc. (see~\cite{tmcperf} Sec. 5).
The correlations between the various systematic uncertainties need to be estimated for a more accurate estimation of the total systematic uncertainty\footnote{It means
the current total uncertainty budget might be over- or under-estimated depending on what the correlations actually are.}.
The approach of estimating a systematic uncertainty by taking half the maximum variation in the results for a given systematic scan could also be revisited, 
taking the spread in the results is an alternate approach.

This will not happen for \runo\ but will hopefully happen for the \runt\ analysis. Improvements for \runt\ are
expected using the information proided by the IBMS3 detector. The IBMS3 detector can measure the beam profile
for the first $\mu s$ after injection starting from injection itself. It will likely prove useful.

\textbf{Important:} the uncertainties above are associated with the fast rotation analysis itself. It needs to be added
the uncertainty associated with the simulation efforts led by David Rubin. The work aims at estimating the uncertainty
on the electric correction due to the uncertainty on the electrostatic quadrupoles plate alignment, voltages etc.
The final number on the electric field correction is currently:

\begin{align*}
C_E = -519 \pm 36 ~(\text{fast rotation analysis}) \pm \textbf{??} ~\text{(simulation) ppb}.
\end{align*}
