| 77 |
|
$Z+jets$ will be determine using the method described |
| 78 |
|
in~\ref{sec:D0Matrix}. |
| 79 |
|
|
| 80 |
< |
From the fit, we will consider a systematics error of 10\%. |
| 80 |
> |
From the fit, we will consider a systematics error of XXX. %10\%. |
| 81 |
|
|
| 82 |
< |
If we consider an error of 5\% on the fake rate and an error of 2\% |
| 82 |
> |
If we consider an error of XXX % 5\% |
| 83 |
> |
on the fake rate and an error of XXX % 2\% |
| 84 |
|
on the efficiency on signal to go from loose to tight criteria, we can |
| 85 |
|
calculate the error on the estimated background as follow: |
| 86 |
|
\begin{equation} |
| 87 |
< |
\Delta N_j ^{t} = \sqrt{(\frac{(p[N_{t} - p(N_{l}+N_{t})])}{(\epsilon -p)^2})^2 \times \Delta \epsilon^2 |
| 88 |
< |
+(\frac{(\epsilon[\epsilon(N_{l}+N_{t})-N_{t}]}{(\epsilon -p)^2})^2 \times \Delta p^2 |
| 89 |
< |
+ (\frac{(p\epsilon)}{(\epsilon -p)})^2 \times \Delta N_{l}^2 + (\frac{[p(\epsilon -1 )]}{(\epsilon -p)})^2 \times \Delta N_{t}^2} |
| 89 |
< |
%\Delta N_j ^{tight} = \frac{\sqrt{(p_{fake}[N_{tight} - p_{fake}(N_{loose}+N_{tight})])^2 \dot \Delta \epsilon^2 |
| 90 |
< |
%+(\epsilon[\epsilon(N_{loose}+N_{tight})-N_{tight}]^2 \dot \Delta p_{fake}^2 |
| 91 |
< |
%+ (p_{fake}\epsilon)^2 \dot N_{loose} + [p_{fake}(\epsilon -1 )]^2 \dot N_{tight}}}{\epsilon_{tight} - p_{fake}} |
| 87 |
> |
\Delta N_j ^{t} = \sqrt{\left(\frac{p\left(N_t - pN_l\right)}{\left(\epsilon -p\right)^2}\right)^2 \times \Delta \epsilon^2 |
| 88 |
> |
+\left(\frac{\epsilon\left(\epsilon N_{l}-N_{t}\right)}{\left(\epsilon -p\right)^2}\right)^2 \times \Delta p^2 |
| 89 |
> |
+ \frac{p^2\left(\epsilon^2\Delta N_{l}^2 - \Delta N_{t}^2\left(2\epsilon -1\right)\right)}{\left(\epsilon -p\right)^2}} |
| 90 |
|
\end{equation} |
| 91 |
|
where $N_{t}$,$\Delta N_{t}$ and $N_{l}$,$\Delta N_{l}$ represents |
| 92 |
|
respectivement the number of events in the tight sample and in the |
| 95 |
|
on this value.$p$ gives the probability for a fake loose electron to |
| 96 |
|
pass also the tight criteria and $\Delta p$ its error. |
| 97 |
|
|
| 98 |
< |
The overall error from the background substraction is 18\%. |
| 98 |
> |
The overall error from the background substraction is XXX %18\%. |
| 99 |
|
|
| 100 |
|
\subsection{Summary of Systematics} |
| 101 |
|
|
| 117 |
|
\label{tab:FullSys} |
| 118 |
|
\end{table} |
| 119 |
|
|
| 122 |
– |
\subsection{Background Substraction} |
