| 1 |
< |
\clearpage |
| 1 |
> |
%\clearpage |
| 2 |
|
\section{Background Estimation Techniques} |
| 3 |
|
\label{sec:bkg} |
| 4 |
|
|
| 5 |
|
In this section we describe the techniques used to estimate the SM backgrounds in our signal regions defined by requirements of large \MET. |
| 6 |
< |
The SM backgrounds fall into four categories: |
| 6 |
> |
The SM backgrounds fall into three categories: |
| 7 |
|
|
| 8 |
|
\begin{itemize} |
| 9 |
|
\item \zjets: this is the dominant background after the preselection. The \MET\ in \zjets\ events is estimated with the |
| 13 |
|
is estimated using a data control sample of e$\mu$ events as described in Sec.~\ref{sec:bkg_fs}; |
| 14 |
|
\item WZ and ZZ backgrounds: this background is estimated from MC, after validating the MC modeling of these processes using data control |
| 15 |
|
samples with jets and exactly 3 leptons (WZ control sample) and exactly 4 leptons (ZZ control sample) as described in Sec.~\ref{sec:bkg_vz}; |
| 16 |
< |
\item Rare SM backgrounds: this background contains rare processes such as $t\bar{t}$V and triple vector boson processes VVV (V=W,Z). |
| 17 |
< |
This background is estimated from MC as described in Sec.~\ref{sec:bkg_raresm}. {\bf TODO: add rare MC} |
| 16 |
> |
%\item Rare SM backgrounds: this background contains rare processes such as $t\bar{t}$V and triple vector boson processes VVV (V=W,Z). |
| 17 |
> |
%This background is estimated from MC as described in Sec.~\ref{sec:bkg_raresm}. {\bf FIXME: add rare MC} |
| 18 |
|
\end{itemize} |
| 19 |
|
|
| 20 |
|
\subsection{Estimating the \zjets\ Background with \MET\ Templates} |
| 21 |
|
\label{sec:bkg_zjets} |
| 22 |
|
|
| 23 |
< |
The premise of this data driven technique is that \MET in \zjets\ events |
| 23 |
> |
The premise of this data driven technique is that \MET\ in \zjets\ events |
| 24 |
|
is produced by the hadronic recoil system and {\it not} by the leptons making up the Z. |
| 25 |
|
Therefore, the basic idea of the \MET\ template method is to measure the \MET\ distribution in |
| 26 |
|
a control sample which has no true MET and the same general attributes regarding |
| 39 |
|
|
| 40 |
|
To account for kinematic differences between the hadronic systems in the control vs. signal |
| 41 |
|
samples, we measure the \MET\ distributions in the \gjets\ sample in bins of the number of jets |
| 42 |
< |
and the scalar sum of jet transverse energies (\Ht). These \MET distributions are normalized to unit area to form ``MET templates''. |
| 43 |
< |
The prediction of the MET in each \Z event is the template which corresponds to the \njets\ and |
| 44 |
< |
\Ht in the \zjets\ event. The prediction for the \Z sample is simply the sum of all such templates. |
| 45 |
< |
These templates are displayed in App.~\ref{app:templates}. |
| 42 |
> |
and the scalar sum of jet transverse energies (\Ht). These \MET\ templates are extracted separately from the 5 single photon |
| 43 |
> |
triggers with thresholds 22, 36, 50, 75, and 90 GeV, so that the templates are effectively binned in photon \pt. |
| 44 |
> |
All \MET distributions are normalized to unit area to form ``MET templates''. |
| 45 |
> |
The prediction of the MET in each \Z event is the template which corresponds to the \njets, |
| 46 |
> |
\Ht, and Z \pt in the \zjets\ event. The prediction for the \Z sample is simply the sum of all such templates. |
| 47 |
> |
All templates are displayed in App.~\ref{app:templates}. |
| 48 |
|
|
| 49 |
|
While there is in principle a small contribution from backgrounds other than \zjets\ in the preselection regions, |
| 50 |
|
this contribution is only $\approx$3\% ($\approx$2\%) of the total sample in the inclusive search (targeted search), |
| 51 |
< |
as shown in Table~\ref{table:zyields_2j} (Table~\ref{table:zyields_2j_targeted}, and is therefore negligible compared to the total |
| 51 |
> |
as shown in Table~\ref{table:zyields_2j} (Table~\ref{table:zyields_2j_targeted}), and is therefore negligible compared to the total |
| 52 |
|
background uncertainty. |
| 53 |
|
|
| 54 |
|
\subsection{Estimating the Flavor-Symmetric Background with e$\mu$ Events} |
| 71 |
|
\item $N_{e\mu}^{\rm{trig}} = \epsilon_{e\mu}^{\rm{trig}}N_{e\mu}^{\rm{offline}}$. |
| 72 |
|
\end{itemize} |
| 73 |
|
|
| 74 |
< |
Here $N_{\ell\ell}^{\rm{trig}}$ denotes the number of selected events in the $\ell\ell$ channel passing the offline and trigger selection |
| 75 |
< |
(in other words, the number of recorded events), $\epsilon_{\ell\ell}^{\rm{trig}}$ is the trigger efficiency, and |
| 76 |
< |
$N_{e\mu}^{\rm{offline}}$ is the number of events that would have passed the offline selection if the trigger had an efficiency of 100\%. |
| 74 |
> |
Here $N_{\ell\ell}^{\rm{trig}}$ denotes the number of selected Z events in the $\ell\ell$ channel passing the offline and trigger selection |
| 75 |
> |
(in other words, the number of recorded and selected events), $\epsilon_{\ell\ell}^{\rm{trig}}$ is the trigger efficiency, and |
| 76 |
> |
$N_{\ell\ell}^{\rm{offline}}$ is the number of events that would have passed the offline selection if the trigger had an efficiency of 100\%. |
| 77 |
|
Thus we calculate the quantity: |
| 78 |
|
|
| 79 |
|
\begin{equation} |
| 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}. |
| 85 |
< |
The indicated uncertainty is due to the 3\% uncertainties in the trigger efficiencies. {\bf TODO: check for variation w.r.t. lepton \pt}. |
| 85 |
> |
The indicated uncertainty is due to the 3\% uncertainties in the trigger efficiencies. %{\bf FIXME: check for variation w.r.t. lepton \pt}. |
| 86 |
|
The predicted yields in the ee and $\mu\mu$ final states are calculated from the observed e$\mu$ yield as |
| 87 |
|
|
| 88 |
|
\begin{itemize} |
| 89 |
|
\item $N_{ee}^{\rm{predicted}} = \frac {N_{e\mu}^{\rm{trig}}} {\epsilon_{e\mu}^{\rm{trig}}} \frac {\epsilon_{ee}^{\rm{trig}}} {2 R_{\mu e}} |
| 90 |
< |
= \frac{N_{e\mu}^{\rm{trig}}}{0.92}\frac{0.95}{2\times1.26} = (0.41\pm0.04) \times N_{e\mu}^{\rm{trig}}$ , |
| 90 |
> |
= \frac{N_{e\mu}^{\rm{trig}}}{0.92}\frac{0.95}{2\times1.26} = (0.41\pm0.05) \times N_{e\mu}^{\rm{trig}}$ , |
| 91 |
|
\item $N_{\mu\mu}^{\rm{predicted}} = \frac {N_{e\mu}^{\rm{trig}}} {\epsilon_{e\mu}^{\rm{trig}}} \frac {\epsilon_{\mu\mu}^{\rm{trig}} R_{\mu e}} {2} |
| 92 |
< |
= \frac {N_{e\mu}^{\rm{trig}}} {0.95} \frac {0.88 \times 1.26}{2} = (0.58\pm0.06) \times N_{e\mu}^{\rm{trig}}$, |
| 92 |
> |
= \frac {N_{e\mu}^{\rm{trig}}} {0.95} \frac {0.88 \times 1.26}{2} = (0.58\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: |
| 98 |
|
\item $N_{ee+\mu\mu}^{\rm{predicted}} = (0.99\pm0.06)\times N_{e\mu}^{\rm{trig}}$. |
| 99 |
|
\end{itemize} |
| 100 |
|
|
| 101 |
< |
Note that the relative uncertainty in the combined ee and $\mu\mu$ prediction is smaller than the those for the individual ee and $\mu\mu$ predictions |
| 102 |
< |
because the uncertainty in $R_{\mu e}$ cancels when summing the ee and $\mu\mu$ predictions. {\bf N.B. these uncertainties are preliminary}. |
| 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 |
| 102 |
> |
because the uncertainty in $R_{\mu e}$ cancels when summing the ee and $\mu\mu$ predictions. %{\bf N.B. these uncertainties are preliminary}. |
| 103 |
|
|
| 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} |
| 120 |
|
The efficiency for e$\mu$ events to satisfy the dilepton mass requirement, $K$, in data and simulation for inclusive \MET\ intervals (left) and |
| 121 |
|
exclusive \MET\ intervals (right) for the inclusive analysis. Based on this we chose $K=0.14\pm0.02$ for all \MET\ regions except \MET\ $>$ 300 GeV, |
| 122 |
|
where we chose $K=0.14\pm0.08$. |
| 123 |
< |
{\bf plots made with 10\% of \zjets\ MC statistics, to be remade with full statistics} |
| 123 |
> |
%{\bf FIXME plots made with 10\% of \zjets\ MC statistics, to be remade with full statistics} |
| 124 |
|
\label{fig:K_incl} |
| 125 |
|
} |
| 126 |
|
\end{center} |
| 137 |
|
exclusive \MET\ intervals (right) for the targeted analysis, including the b-veto. |
| 138 |
|
Based on this we chose $K=0.13\pm0.02$ for the \MET\ regions up to \MET\ $>$ 100 GeV. |
| 139 |
|
For higher \MET\ regions we chose $K=0.13\pm0.07$. |
| 140 |
< |
{\bf plots made with 10\% of \zjets\ MC statistics, to be remade with full statistics} |
| 140 |
> |
%{\bf FIXME plots made with 10\% of \zjets\ MC statistics, to be remade with full statistics} |
| 141 |
|
\label{fig:K_targeted} |
| 142 |
|
} |
| 143 |
|
\end{center} |
| 181 |
|
and we therefore check that the MC does a reasonable job of reproducing the \pt distributions of the |
| 182 |
|
leptonically decaying \Z. While the inclusive WZ yields are in reasonable agreement, we observe |
| 183 |
|
an excess in data in events with at least 2 jets, corresponding to the jet multiplicity requirement |
| 184 |
< |
in our preselection. We observe 60 events in data while the MC predicts $34\pm5.2$~(stat)), representing an excess of 78\%, |
| 185 |
< |
as indicated in Table~\ref{tab:wz2j}. |
| 184 |
< |
We note some possible causes for this discrepancy: |
| 184 |
> |
in our preselection. We observe 60 events in data while the MC predicts $34\pm5.2$~(stat), representing an excess of 78\%, |
| 185 |
> |
as indicated in Table~\ref{tab:wz2j}. We note some possible contributions to this discrepancy: |
| 186 |
|
|
| 187 |
|
\begin{itemize} |
| 188 |
|
|
| 190 |
|
yield passing a \MET $>$ 50 GeV requirement is under-estimated in MC and second, because the fake |
| 191 |
|
rate is typically under-estimated in the MC. To get a rough idea for how much the excess depends |
| 192 |
|
on the \zjets\ yield, if the \zjets\ yield is doubled then the excess is reduced from 78\% to 55\%. |
| 193 |
< |
{\bf currently using 10\% of \zjets\ MC, and there is 1 event with a weight of about 5, plots and tables to be remade with full \zjets\ stats}. |
| 193 |
> |
Also note that we are currently using 10\% of the \zjets\ MC sample and there is 1 event with a weight |
| 194 |
> |
of about 5, so the plots and tables will be remade with full \zjets\ sample. |
| 195 |
|
|
| 196 |
|
\item The \ttbar\ contribution is under-estimated here because the fake |
| 197 |
|
rate is typically under-estimated in the MC. To get a rough idea for how much the excess depends |
| 198 |
|
on the \ttbar\ yield, if the \ttbar\ yield is doubled then the excess is reduced from 78\% to 57\%. |
| 199 |
|
|
| 200 |
|
\item Currently no attempt is made to reject jets from pile-up interactions, which may be responsible |
| 201 |
< |
for some of this excess. To check this, we increase the jet \pt requirement to 40 GeV which |
| 202 |
< |
helps to suppress PU jets and observe 39 events in data vs. an MC prediction of $25\pm5.2$~(stat), |
| 201 |
> |
for some of the excess at large \njets. To check this, we increase the jet \pt threhsold to 40 GeV, which |
| 202 |
> |
helps to suppress PU jets, and observe 39 events in data vs. an MC prediction of $25\pm5.2$~(stat), |
| 203 |
|
decreasing the excess from 78\% to 58\%. In the future this may be improved by explicitly |
| 204 |
|
requiring the jets to be consistent with originating from the signal primary vertex. |
| 205 |
|
|
| 212 |
|
\caption{\label{tab:wz} Data and Monte Carlo yields passing the WZ preselection. } |
| 213 |
|
\begin{tabular}{lccccc} |
| 214 |
|
\hline |
| 215 |
+ |
\hline |
| 216 |
|
Sample & ee & $\mu\mu$ & e$\mu$ & total \\ |
| 217 |
|
\hline |
| 218 |
|
WZ & 58.9 $\pm$ 0.7 & 82.2 $\pm$ 0.8 & 4.0 $\pm$ 0.2 &145.1 $\pm$ 1.0 \\ |
| 236 |
|
\caption{\label{tab:wz2j} Data and Monte Carlo yields passing the WZ preselection and \njets\ $>$ 2. } |
| 237 |
|
\begin{tabular}{lccccc} |
| 238 |
|
\hline |
| 236 |
– |
Sample & ee & $\mu\mu$ & e$\mu$ & total \\ |
| 239 |
|
\hline |
| 240 |
+ |
Sample & ee & $\mu\mu$ & e$\mu$ & total \\ |
| 241 |
|
\hline |
| 242 |
|
WZ & 9.8 $\pm$ 0.3 & 13.3 $\pm$ 0.3 & 0.6 $\pm$ 0.1 & 23.6 $\pm$ 0.4 \\ |
| 243 |
|
\ttbar & 0.2 $\pm$ 0.2 & 2.0 $\pm$ 0.9 & 2.2 $\pm$ 1.2 & 4.4 $\pm$ 1.5 \\ |
| 246 |
|
WW & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.1 $\pm$ 0.0 \\ |
| 247 |
|
single top & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 \\ |
| 248 |
|
\hline |
| 249 |
< |
tot SM MC & 10.3 $\pm$ 0.3 & 20.8 $\pm$ 5.0 & 2.8 $\pm$ 1.2 & 33.8 $\pm$ 5.2 \\ |
| 247 |
< |
\hline |
| 249 |
> |
total SM MC & 10.3 $\pm$ 0.3 & 20.8 $\pm$ 5.0 & 2.8 $\pm$ 1.2 & 33.8 $\pm$ 5.2 \\ |
| 250 |
|
data & 23 & 32 & 5 & 60 \\ |
| 251 |
|
\hline |
| 252 |
|
\hline |
| 280 |
|
The data and MC yields passing the above selection are in Table~\ref{tab:zz}. Again we observe an |
| 281 |
|
excess in data with respect to the MC prediction (29 observed vs. $17.3\pm0.1$~(stat) MC predicted). |
| 282 |
|
After requiring at least 2 jets, we observe 2 events and the MC predicts $1.5\pm0.1$~(stat). |
| 283 |
< |
Based on this we apply an uncertainty of 80\% to the ZZ background. |
| 283 |
> |
However, we have recently discovered that we may be using the wrong (too small) cross section for the ZZ sample, |
| 284 |
> |
and we are in contact with the MC generator group to determine the correct cross section. |
| 285 |
> |
Based on this we currently apply an uncertainty of 80\% to the ZZ background. |
| 286 |
|
|
| 287 |
|
\begin{table}[htb] |
| 288 |
|
\begin{center} |
| 289 |
|
\caption{\label{tab:zz} Data and Monte Carlo yields for the ZZ preselection. } |
| 290 |
|
\begin{tabular}{lccccc} |
| 291 |
|
\hline |
| 288 |
– |
Sample & ee & $\mu\mu$ & e$\mu$ & total \\ |
| 292 |
|
\hline |
| 293 |
< |
|
| 293 |
> |
Sample & ee & $\mu\mu$ & e$\mu$ & total \\ |
| 294 |
|
\hline |
| 295 |
|
ZZ & 6.6 $\pm$ 0.0 & 9.9 $\pm$ 0.0 & 0.4 $\pm$ 0.0 & 17.0 $\pm$ 0.1 \\ |
| 296 |
|
WZ & 0.1 $\pm$ 0.0 & 0.2 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.3 $\pm$ 0.0 \\ |
| 300 |
|
single top & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 & 0.0 $\pm$ 0.0 \\ |
| 301 |
|
\hline |
| 302 |
|
total SM MC & 6.7 $\pm$ 0.0 & 10.1 $\pm$ 0.1 & 0.5 $\pm$ 0.0 & 17.3 $\pm$ 0.1 \\ |
| 300 |
– |
\hline |
| 303 |
|
data & 13 & 16 & 0 & 29 \\ |
| 304 |
|
\hline |
| 303 |
– |
|
| 305 |
|
\hline |
| 306 |
|
\end{tabular} |
| 307 |
|
\end{center} |
| 311 |
|
\begin{center} |
| 312 |
|
\includegraphics[width=1\linewidth]{plots/ZZ.pdf} |
| 313 |
|
\caption{\label{fig:zz}\protect |
| 314 |
< |
Data vs. MC comparisons for the $ZZ$ selection discussed in the text for \lumi. |
| 315 |
< |
The number of jets, missing transverse energy, and $Z$ boson transverse momentum are displayed. |
| 314 |
> |
Data vs. MC comparisons for the ZZ selection discussed in the text for \lumi. |
| 315 |
> |
The number of jets, missing transverse energy, and Z boson transverse momentum are displayed. |
| 316 |
|
} |
| 317 |
|
\end{center} |
| 318 |
|
\end{figure} |
| 320 |
|
|
| 321 |
|
|
| 322 |
|
|
| 323 |
< |
\subsection{Estimating the Rare SM Backgrounds with MC} |
| 324 |
< |
\label{sec:bkg_raresm} |
| 323 |
> |
%\subsection{Estimating the Rare SM Backgrounds with MC} |
| 324 |
> |
%\label{sec:bkg_raresm} |
| 325 |
|
|
| 326 |
< |
{\bf TODO: list samples, yields in preselection region, and \MET distribution} |
| 326 |
> |
%{\bf TODO: list samples, yields in preselection region, and show \MET\ distribution} |
