| 4 |
|
An important component |
| 5 |
|
of the background calculation is the ratio of the number of events with $M_T$ in the signal region |
| 6 |
|
to the number of events with $50 < M_T < 80$~GeV. |
| 7 |
< |
As discussed in Section~\ref{sec:ljbg-general}, these ratios are different for $W +$ jets and |
| 7 |
> |
As discussed in Section~\ref{sec:ljbg-general}, these ratios are different for \wjets\ and |
| 8 |
|
top events. |
| 9 |
|
|
| 10 |
|
|
| 17 |
|
Sample & SRA & SRB & SRC & SRD & SRE & SRF & SRG\\ |
| 18 |
|
\hline |
| 19 |
|
\hline |
| 20 |
< |
$R^{\mu}_{top}$ & $0.015 \pm 0.001$ & $0.035 \pm 0.002$ & $0.021 \pm 0.002$ & $0.021 \pm 0.004$ & $0.025 \pm 0.007$ & $0.015 \pm 0.009$ & $0.021 \pm 0.015$ \\ |
| 21 |
< |
$R^{\mu}_{wjet}$ & $0.040 \pm 0.001$ & $0.071 \pm 0.003$ & $0.062 \pm 0.004$ & $0.064 \pm 0.006$ & $0.065 \pm 0.009$ & $0.067 \pm 0.012$ & $0.065 \pm 0.016$ \\ |
| 20 |
> |
\multicolumn{8}{c}{Muons} \\ |
| 21 |
|
\hline |
| 22 |
+ |
$R^{MC}_{top}$ & $0.015 \pm 0.001$ & $0.035 \pm 0.002$ & $0.021 \pm 0.002$ & $0.021 \pm 0.004$ & $0.025 \pm 0.007$ & $0.015 \pm 0.009$ & $0.021 \pm 0.015$ \\ |
| 23 |
+ |
$R^{MC}_{wjet}$ & $0.040 \pm 0.001$ & $0.071 \pm 0.003$ & $0.062 \pm 0.004$ & $0.064 \pm 0.006$ & $0.065 \pm 0.009$ & $0.067 \pm 0.012$ & $0.065 \pm 0.016$ \\ |
| 24 |
|
\hline |
| 25 |
< |
$R^e_{top}$ & $0.015 \pm 0.001$ & $0.031 \pm 0.002$ & $0.026 \pm 0.003$ & $0.025 \pm 0.005$ & $0.009 \pm 0.005$ & $0.021 \pm 0.012$ & $0.034 \pm 0.024$ \\ |
| 26 |
< |
$R^e_{wjet}$ & $0.040 \pm 0.002$ & $0.075 \pm 0.004$ & $0.067 \pm 0.005$ & $0.063 \pm 0.007$ & $0.061 \pm 0.010$ & $0.067 \pm 0.015$ & $0.070 \pm 0.021$ \\ |
| 25 |
> |
\hline |
| 26 |
> |
\hline |
| 27 |
> |
\multicolumn{8}{c}{Electrons} \\ |
| 28 |
> |
\hline |
| 29 |
> |
$R^{MC}_{top}$ & $0.015 \pm 0.001$ & $0.031 \pm 0.002$ & $0.026 \pm 0.003$ & $0.025 \pm 0.005$ & $0.009 \pm 0.005$ & $0.021 \pm 0.012$ & $0.034 \pm 0.024$ \\ |
| 30 |
> |
$R^{MC}_{wjet}$ & $0.040 \pm 0.002$ & $0.075 \pm 0.004$ & $0.067 \pm 0.005$ & $0.063 \pm 0.007$ & $0.061 \pm 0.010$ & $0.067 \pm 0.015$ & $0.070 \pm 0.021$ \\ |
| 31 |
|
\hline |
| 32 |
|
\end{tabular}} |
| 33 |
|
\caption{ Ratio of MC events in the \mt-tail over events in the \mt-peak for |
| 37 |
|
\end{center} |
| 38 |
|
\end{table} |
| 39 |
|
|
| 40 |
< |
The MC value of these ratios are shown in Table~\ref{tab:ttp}. |
| 41 |
< |
In addition the studies of CR1 and CR2 (Sections~\ref{sec:cr1} and~\ref{sec:cr2}) |
| 42 |
< |
lead to data/MC scale factors |
| 43 |
< |
$SFR_{wjets}$ (Table~\ref{tab:cr1yields}) and |
| 44 |
< |
$SFR_{top}$ (Table~\ref{tab:cr2yields}) |
| 40 |
> |
The MC values of these ratios are shown in Table~\ref{tab:ttp}. The e and $\mu$ channel results are averaged before corrections are made. |
| 41 |
> |
|
| 42 |
> |
The MC value of $R^{MC}_{wjet}$ is corrected based on the studies of CR1 (Section~\ref{sec:cr1}), which |
| 43 |
> |
lead to the data/MC scale factor $SFR_{wjet}$ (Table~\ref{tab:cr1yields}). The corrected $R_{wjet}$ is thus given by $R^{MC}_{wjet} \times SFR_{wjet}$. |
| 44 |
> |
|
| 45 |
> |
%$SFR_{top}$ (Table~\ref{tab:cr2yields}) |
| 46 |
> |
|
| 47 |
> |
There is no similar scale factor to correct the MC value of $R^{MC}_{top}$ due to the lack of events in CR2 (Section~\ref{sec:cr2}). |
| 48 |
> |
We must therefore use a different procedure to derive a corrected value of $R_{top}$. |
| 49 |
> |
|
| 50 |
> |
We start by defining optimistic (too small) and pessimistic (too large) predictions for $R_{top}$. |
| 51 |
> |
|
| 52 |
> |
For the pessimistic prediction, we use the \wjets\ MC tail-to-peak ratio and data/MC scale factor, $R^{MC}_{wjet}$ and $SFR_{wjet}$ (i.e. the pessimistic prediction is the same as $R_{wjet}$). |
| 53 |
> |
This prediction is too large because in \wjets\ events the $M_T$ tail comes from |
| 54 |
> |
off-shell Ws and resolution effects, while in top events to first order |
| 55 |
> |
only resolution effects matter. |
| 56 |
> |
|
| 57 |
> |
For the optimistic prediction, we use the \ttsl\ MC tail-to-peak ratio $R^{MC}_{top}$, but take the \wjets\ data/MC scale factor $SFR_{wjet}$. |
| 58 |
> |
This prediction is too small because |
| 59 |
> |
the true top scale factor is to first order the same as for on-shell Ws, |
| 60 |
> |
while $SFR_{wjet}$ is a weighted average of the |
| 61 |
> |
scale factor for on-shell Ws (which is $>1$) and the |
| 62 |
> |
scale factor for off-shell Ws (which is close to 1 as it is well modeled by MC). |
| 63 |
> |
|
| 64 |
> |
The final prediction for $R_{top}$ is given by the average of the optimistic and pessimistic predictions, and |
| 65 |
> |
the systematic uncertainty is given by half the difference between the two. |
| 66 |
> |
|
| 67 |
> |
The corrected values of $R_{wjet}$ and $R_{top}$ and their uncertainties are given in Table~\ref{tab:ttpcorr}. |
| 68 |
> |
|
| 69 |
> |
\begin{table}[!h] |
| 70 |
> |
\begin{center} |
| 71 |
> |
{\footnotesize |
| 72 |
> |
\begin{tabular}{l||c|c|c|c|c|c|c} |
| 73 |
> |
\hline |
| 74 |
> |
Sample & SRA & SRB & SRC & SRD & SRE & SRF & SRG\\ |
| 75 |
> |
\hline |
| 76 |
> |
\hline |
| 77 |
> |
$R_{top}$ & $0.045 \pm 0.023$ & $0.074 \pm 0.031$ & $0.055 \pm 0.031$ & $0.042 \pm 0.028$ & $0.041 \pm 0.036$ & $0.052 \pm 0.049$ & $0.053 \pm 0.066$ \\ |
| 78 |
> |
$R_{wjet}$ & $0.066 \pm 0.015$ & $0.101 \pm 0.022$ & $0.081 \pm 0.025$ & $0.061 \pm 0.029$ & $0.064 \pm 0.042$ & $0.082 \pm 0.062$ & $0.075 \pm 0.088$ \\ |
| 79 |
> |
\hline |
| 80 |
> |
\end{tabular}} |
| 81 |
> |
\caption{ Corrected values of $R_{wjet}$ and $R_{top}$. Both statistical and systematic uncertainties are included. |
| 82 |
> |
\label{tab:ttpcorr}} |
| 83 |
> |
\end{center} |
| 84 |
> |
\end{table} |
| 85 |
|
|
| 86 |
|
\clearpage |
