Nt1310 Unit 1 Exercise 1

The low yield for the $\omega\to\pi^0\gamma$ final state at 1.45~GeV is discussed in Section~\ref{stat} and hence the underestimated branching ratio for 1.45~GeV data set is discussed in Section~\ref{brlumS} might have influence from the systematic effect from the final state selection criteria.
The energy-momentum conservation constraint is one of the key conditions playing an important role to select the $\omega\to\pi^0\gamma$ final state.
The quantitative effect of the energy-momentum conservation constraint is already seen in Table~\ref{Deff}, where almost 3.91$\%$ of the events for 1.45~GeV (3.24$\%$ for 1.5~GeV) is thrown away by this cut.
The variation of the cut might make a considerable difference over the yield of the
$\omega\to\pi^0\gamma$

The systematic check is done by fixing the all other analysis conditions to same as explained in
Section~\ref{pi0gfinalstate} and using different energy-momentum constraints. The different energy-momentum constraints are illustrated on the $\delta$E vs $\delta$P plot in Appendix~\ref{Fdedpsys}.
The description about each constraint is given in Appendix~\ref{Adedpsys}. In an overall picture, the constraints are varied from subset of the final cut in Figure~\ref{dedp} to the superset.
As this cut is almost rejecting all the background coming from charged multi-pion a well as pion based
$\omega$ decays. It is expected if a super set would go too far from the final cut, the in-peak background contributions might be selected as a signal. This will add up to the exclusive numbers and hence the branching ratio. The missing mass for each cut is fitted with the method established in Section~\ref{ch4mmfitinclu}. Only converging fits are taken into

& { 2872(25$\%$)} & { 2499(22$\%$)} & { 5795(26$\%$)} & { 5100(23$\%$)}\\ $N_{\omega\to\pi^0\gamma}^{\circ}$ & { 4487(15$\%$)} & { 3590(12$\%$)}
& { 1978(6$\%$)} & { 1721(5$\%$)} & { 5846(9$\%$)} & { 5145(8$\%$)} \\ \hline $BR^{measured}_{\omega\to\pi^0\gamma}$ & \textcolor{red}{ 1.07} & \textcolor{red}{ 0.78} & \textcolor{red}{ 0.52} & \textcolor{red}{ 0.43} & \textcolor{red}{ 0.73} & \textcolor{red}{ 0.61} \\

($\%$) & \textcolor{red}{ (15$\%$)} & \textcolor{red}{ (11$\%$)} & \textcolor{red}{ (6$\%$)} & \textcolor{red}{ (5$\%$)} & \textcolor{red}{ (9$\%$)} & \textcolor{red}{ (8$\%$)} \\ \hline
&
\multicolumn{6}{c|} {\bf $\sigma_{dedp-sys}=\sigma^{av}_{rms}\times(1-\sigma_{fit-sys}^{rel})$ } \\ \hline
\end{tabular}
\caption[The standard deviation $\sigma^{av}_{rms}$ in ${N_{\omega\to\pi^0\gamma}}^{rec}$,
${N_{\omega\to\pi^0\gamma}}^{\circ}$ and
$BR^{measured}_{\omega\to\pi^0\gamma}$ for the different energy-momentum conservation constraint are presented]
{
The standard deviation $\sigma^{av}_{rms}$ in ${N_{\omega\to\pi^0\gamma}}^{rec}$ and
$BR^{measured}_{\omega\to\pi^0\gamma}$ for the different energy-momentum conservation