| 78 |
|
|
| 79 |
|
\begin{equation} |
| 80 |
|
R_{\mu e} = \sqrt{\frac{N_{\mu\mu}^{\rm{offline}}}{N_{ee}^{\rm{offline}}}} = \sqrt{\frac{N_{\mu\mu}^{\rm{trig}}/\epsilon_{\mu\mu}^{\rm{trig}}}{N_{ee}^{\rm{trig}}/\epsilon_{ee}^{\rm{trig}}}} |
| 81 |
< |
= \sqrt{\frac{304953/0.88}{239661/0.95}} = 1.17\pm0.07. |
| 81 |
> |
= \sqrt{\frac{234132/0.86}{185555/0.95}} = 1.18\pm0.07. |
| 82 |
|
\end{equation} |
| 83 |
|
|
| 84 |
|
Here we have used the Z$\to\mu\mu$ and Z$\to$ee yields from Table~\ref{table:zyields_2j} and the trigger efficiencies quoted in Sec.~\ref{sec:datasets}. |
| 87 |
|
|
| 88 |
|
\begin{itemize} |
| 89 |
|
\item $N_{ee}^{\rm{predicted}} = \frac {N_{e\mu}^{\rm{trig}}} {\epsilon_{e\mu}^{\rm{trig}}} \frac {\epsilon_{ee}^{\rm{trig}}} {2 R_{\mu e}} |
| 90 |
< |
= \frac{N_{e\mu}^{\rm{trig}}}{0.92}\frac{0.95}{2\times1.17} = (0.44\pm0.05) \times N_{e\mu}^{\rm{trig}}$ , |
| 90 |
> |
= \frac{N_{e\mu}^{\rm{trig}}}{0.93}\frac{0.95}{2\times1.18} = (0.43\pm0.05) \times N_{e\mu}^{\rm{trig}}$ , |
| 91 |
|
\item $N_{\mu\mu}^{\rm{predicted}} = \frac {N_{e\mu}^{\rm{trig}}} {\epsilon_{e\mu}^{\rm{trig}}} \frac {\epsilon_{\mu\mu}^{\rm{trig}} R_{\mu e}} {2} |
| 92 |
< |
= \frac {N_{e\mu}^{\rm{trig}}} {0.95} \frac {0.88 \times 1.17}{2} = (0.54\pm0.07) \times N_{e\mu}^{\rm{trig}}$, |
| 92 |
> |
= \frac {N_{e\mu}^{\rm{trig}}} {0.95} \frac {0.86 \times 1.18}{2} = (0.53\pm0.07) \times N_{e\mu}^{\rm{trig}}$, |
| 93 |
|
\end{itemize} |
| 94 |
|
|
| 95 |
|
and the predicted yield in the combined ee and $\mu\mu$ channel is simply the sum of these two predictions: |
| 96 |
|
|
| 97 |
|
\begin{itemize} |
| 98 |
< |
\item $N_{ee+\mu\mu}^{\rm{predicted}} = (0.98\pm0.06)\times N_{e\mu}^{\rm{trig}}$. |
| 98 |
> |
\item $N_{ee+\mu\mu}^{\rm{predicted}} = (0.97\pm0.06)\times N_{e\mu}^{\rm{trig}}$. |
| 99 |
|
\end{itemize} |
| 100 |
|
|
| 101 |
|
Note that the relative uncertainty in the combined ee and $\mu\mu$ prediction is smaller than those for the individual ee and $\mu\mu$ predictions |
| 104 |
|
To improve the statistical precision of the FS background estimate, we remove the requirement that the e$\mu$ lepton pair falls in the Z mass window. |
| 105 |
|
Instead we scale the e$\mu$ yield by $K$, the efficiency for e$\mu$ events to satisfy the Z mass requirement, extracted from simulation. In Fig.~\ref{fig:K_incl} |
| 106 |
|
we display the value of $K$ in data and simulation, for a variety of \MET\ requirements, for the inclusive analysis. |
| 107 |
< |
Based on this we chose $K=0.14\pm0.02$ for the lower \MET\ regions, $K=0.14\pm0.04$ for the \MET\ $>$ 200 GeV region,and $K=0.14\pm0.09$ for \MET\ $>$ 300 GeV, |
| 107 |
> |
Based on this we chose $K=0.14\pm0.02$ for the lower \MET\ regions, $K=0.14\pm0.04$ for the \MET\ $>$ 200 GeV region, and $K=0.14\pm0.08$ for \MET\ $>$ 300 GeV, |
| 108 |
|
where the larger uncertainties reflect the reduced statistical precision at large \MET. |
| 109 |
|
The corresponding plot for the targeted analysis, including the b-veto, is displayed in Fig.~\ref{fig:K_targeted}. |
| 110 |
< |
Based on this we chose $K=0.13\pm0.02$ |
| 111 |
< |
for all \MET\ regions up to \MET\ $>$ 150 GeV. For the \MET\ $>$ 200 GeV region we choose $K=0.13\pm0.05$, due to the reduced statistical precision. |
| 110 |
> |
Based on this we chose $K=0.13\pm0.02$ for all \MET\ regions up to \MET\ $>$ 100 GeV. |
| 111 |
> |
For the \MET\ $>$ 150 GeV region we choose $K=0.13\pm0.03$ |
| 112 |
> |
and for the \MET\ $>$ 200 GeV region we choose $K=0.13\pm0.05$, |
| 113 |
> |
due to the reduced statistical precision. |
| 114 |
|
|
| 115 |
|
\begin{figure}[!ht] |
| 116 |
|
\begin{center} |
| 121 |
|
\caption{\label{fig:K_incl} |
| 122 |
|
The efficiency for e$\mu$ events to satisfy the dilepton mass requirement, $K$, in data and simulation for inclusive \MET\ intervals (left) and |
| 123 |
|
exclusive \MET\ intervals (right) for the inclusive analysis. |
| 124 |
+ |
Based on this we chose $K=0.14\pm0.02$ for the lower \MET\ regions, $K=0.14\pm0.04$ for the \MET\ $>$ 200 GeV region, and $K=0.14\pm0.08$ for \MET\ $>$ 300 GeV. |
| 125 |
|
} |
| 126 |
|
|
| 127 |
|
\begin{comment} |
| 335 |
|
The efficiency for e$\mu$ events to satisfy the dilepton mass requirement, $K$, in data and simulation for inclusive \MET\ intervals (left) and |
| 336 |
|
exclusive \MET\ intervals (right) for the targeted analysis, including the b-veto. |
| 337 |
|
Based on this we chose $K=0.13\pm0.02$ for the \MET\ regions up to \MET\ $>$ 100 GeV. |
| 338 |
< |
For higher \MET\ regions we chose $K=0.13\pm0.07$. |
| 338 |
> |
For \MET\ $>$ 150 we choose $K=0.13\pm0.03$, for \MET\ $>$ 200 GeV we choose $K=0.13\pm0.05$. |
| 339 |
|
%{\bf FIXME plots made with 10\% of \zjets\ MC statistics, to be remade with full statistics} |
| 340 |
|
\label{fig:K_targeted} |
| 341 |
|
} |
