| 86 |
|
\begin{center} |
| 87 |
|
\includegraphics[width=0.45\linewidth]{figs/bdt-medium-frpt.png} |
| 88 |
|
\includegraphics[width=0.45\linewidth]{figs/frMu.png} |
| 89 |
– |
\includegraphics[width=0.45\linewidth]{figs/frMu.png} |
| 89 |
|
\caption{ Muon and Electron Fake Rates.} |
| 90 |
|
\label{fig:FR} |
| 91 |
|
\end{center} |
| 104 |
|
\multicolumn{2}{c}{Z1-Inclusive $\ell\ell jj$ Yields} \\ |
| 105 |
|
\hline |
| 106 |
|
$Z1 + \mu\mu$ & $0.057 \pm X$ \\ |
| 107 |
< |
$Z1 + ee$ & $X \pm Y$ \\ |
| 107 |
> |
$Z1 + ee$ & $1.8 \pm 1$ \\ |
| 108 |
|
\hline |
| 109 |
|
\multicolumn{2}{c}{Per-Channel $\ell\ell jj$ Yields} \\ |
| 110 |
|
\hline |
| 111 |
|
$4\mu$ & $0.044 \pm X$ \\ |
| 112 |
< |
$4e$ & $X \pm Y$ \\ |
| 113 |
< |
$2e2\mu$ & $(0.013 + Z) \pm Y$ \\ |
| 112 |
> |
$4e$ & $0.4 \pm 0.3$ \\ |
| 113 |
> |
$2e2\mu$ & $(0.013 + 1.4) \pm 0.9$ \\ |
| 114 |
|
\hline |
| 115 |
|
\end{tabular} |
| 116 |
|
\caption{Expected $\ell\ell jj$ Events.} |
| 152 |
|
|
| 153 |
|
%This difference can be understood as a result of differences in the composition of the prediction sample (mainly light flavor) and that used to measure the fakerate (a mix of light and heavy flavor). |
| 154 |
|
|
| 155 |
< |
{\bf For electrons ...} |
| 155 |
> |
For electrons, in order to isolate a pure sample of W+jets where the jet fakes an electron, a cross-flavor same-sign sample was chosen with a well-identified muon satisfying $iso_{PF}/P_{T} < 0.025$ and $p_{T}>25$. This region also contains Z+jets and dijet backgrounds. The W+jets and Z+jets components are represented by templates from Monte Carlo while the dijet is modelled by a Rayleigh distribution. The three are fitted to the observed same-sign events on the left of Figure~\ref{fig:ssEle}. The region with $MET>30~GeV$ is enriched in W+jets, so is chosen to test closure in the mass spectrum. The center of the same figure shows this observation compared to the fake prediction computed in the same way as in the muon case, and shows an overall under-prediction of $4\%$. The right of this figure shows that the observed shape discrepancy comes from an under-prediction of $33\%$ for $p_{T}<20$ and an over-prediction of $20\%$ for $p_{T}>20$. We thus take an overall systematic of $33\%$ on the fake prediction. |
| 156 |
> |
|
| 157 |
> |
An additional cross-check of the electron fake rates was performed on a sample of single-Z plus one fakeable object in both data and $Z+jets$ monte carlo. The largest observed discrepancy between observation and fake rate prediction of these four estimates was $20\%$, well within the systematic used above. |
| 158 |
|
%For electrons, charge misidentification is significant enough to result in a noticible Z-peak. The jet background is however easily estimated from a fit with a same-sign MC Z template and an exponential background PDF. Events selected in data are shown in Figures~\ref{fig:ssMuon} and (\ref{fig:ssEle}) as points. Table~\ref{tab:ssfakes} lists the total number of observed events in the muon-channel and the electron-channel background determined from the fit. |
| 159 |
|
|
| 160 |
|
%------------------------------------------------- |
| 162 |
|
\begin{center} |
| 163 |
|
\includegraphics[width=0.45\linewidth]{figs/ssEleMET.png} |
| 164 |
|
\includegraphics[width=0.45\linewidth]{figs/ssEleMZ1.png} |
| 165 |
< |
\caption{ Fakerate Predictions for Same-sign Electron Events. {\bf Plots are currently for muons ... }} |
| 166 |
< |
\label{fig:ssEle} |
| 165 |
> |
\includegraphics[width=0.45\linewidth]{figs/ssElePtLoose.png} |
| 166 |
> |
\caption{ Fakerate Predictions for Same-sign Electron Events.} |
| 167 |
> |
\label{fig:ssEle} |
| 168 |
|
\end{center} |
| 169 |
|
\end{figure} |
| 170 |
|
%------------------------------------------------- |
| 171 |
|
|
| 172 |
< |
Table summarizes the results of this section. We take $47.2\%$ ($X\%$) as the systematic uncertainty on the muon (electron) fakerate to account for potential biases in our prediction due to differences in light flavor composition. |
| 172 |
> |
Table summarizes the results of this section. We take $47.2\%$ ($15\%$) as the systematic uncertainty on the muon (electron) fakerate to account for potential biases in our prediction due to differences in light flavor composition. |
| 173 |
|
|
| 174 |
|
%------------------------------------------------- |
| 175 |
|
\begin{table}[tbh] |
| 176 |
|
\begin{center} |
| 177 |
|
\begin{tabular}{c|c|c|c} |
| 178 |
|
\hline |
| 179 |
< |
channel & observed & predicted & systematic \\ |
| 179 |
> |
channel & observed & predicted & systematic \\ |
| 180 |
|
\hline |
| 181 |
< |
${\rm same~sign} \mu\mu$ & $159$ & $108.04$ & $47.2\%$\\ |
| 182 |
< |
${\rm same~sign} ee$ & $X$ & $Y$ & $Z\%$ \\ |
| 181 |
> |
${\rm same~sign} \mu\mu$ & $159$ & $108.04$ & $47.2\%$\\ |
| 182 |
> |
${\rm same~sign} ee (total) $ & $5333$ & $5132$ & $33\%$ \\ |
| 183 |
> |
${\rm same~sign} ee (p_{T}<20)$ & $2783$ & $1993$ & $33\%$ \\ |
| 184 |
> |
${\rm same~sign} ee (p_{T}>20)$ & $1550$ & $3138$ & $20\%$ \\ |
| 185 |
|
\hline |
| 186 |
|
\end{tabular} |
| 187 |
|
\caption{Same-sign Control Yields and Systematic} |
| 226 |
|
%_________________________________________________________________ |
| 227 |
|
The estimate of $WZ$ background in Table~\ref{tab:MCBG} is entirely MC-based. In addition to the leptons from $W$ and $Z$ decay, an additional ``fake'' lepton is needed for this process to contribute in the $4\ell$ signal region. We cross-check MC predictions with an estimate obtained from the fakeable object method. |
| 228 |
|
|
| 229 |
< |
We begin by requiring three fully selected leptons (two from the Z1 plus one additional) and $1+$ denominator objects. We then perform a single loop to associate the denominator objects with the third lepton. As before, we weight the denominators with $\epsilon_{FR}(p_{T},\eta)/(1-\epsilon_{FR}(p_{T},\eta))$, apply opposite-sign, same-flavor and kinematic selections and sum. The additional, identified lepton with which the denominators are paired is either a fake (from $Z+jets$) or a real lepton (from $WZ$ or $ZZ$ where one of the leptons is not reconstructed). In order to extract the $WZ$ component of the measurement, we need to subtract off the $3\ell$ contribution predicted by MC for $ZZ$ as well as the double-fake estimate described in Section~\ref{sec:fakes}. The latter is double-counted when performing a single denominator loop. |
| 229 |
> |
We begin by requiring three fully selected leptons (two from the Z1 plus one additional) and $1+$ denominator objects. We then perform a single loop to associate the denominator objects with the third lepton. As before, we weight the denominators with $\epsilon_{FR}(p_{T},\eta)/(1-\epsilon_{FR}(p_{T},\eta))$, apply opposite-sign, same-flavor and kinematic selections and sum. The additional, identified lepton with which the denominators are paired is either a fake (from $Z+jets$) or a real lepton (from $WZ$, $Z\gamma$, or $ZZ$ where one of the leptons is not reconstructed). In order to extract the $WZ$ component of the measurement, we need to subtract off the $3\ell$ contribution predicted by MC for $ZZ$ and $Z\gamma$, as well as the double-fake estimate described in Section~\ref{sec:fakes}. The latter is double-counted when performing a single denominator loop. |
| 230 |
|
|
| 231 |
|
\begin{eqnarray} |
| 232 |
|
N(WZ) &=& \ell\ell\ell~\Sigma_{i=0}^{Nd}~\frac{\epsilon(\eta^{i},p_{T}^{i})}{1-\epsilon(\eta^{i},p_{T}^{i})} \\ |
| 233 |
|
~ &-& 2\times \ell\ell~\Sigma_{i=0}^{Nd}\Sigma_{j=i+1}^{Nd}~\frac{\epsilon(\eta^{i},p_{T}^{i})}{1-\epsilon(\eta^{i},p_{T}^{i})}~\frac{\epsilon(\eta^{j},p_{T}^{j})}{1-\epsilon(\eta^{j},p_{T}^{j})} \\ |
| 234 |
< |
~ &-& N(WZ) |
| 234 |
> |
~ &-& N(ZZ) |
| 235 |
|
\end{eqnarray} |
| 236 |
|
|
| 237 |
|
Table~\ref{tab:WZfake} lists values for the terms in the equation above. The result ... {\bf fill in the table and quote a systematic for WZ}. |
| 239 |
|
%------------------------------------------------- |
| 240 |
|
\begin{table}[tbh] |
| 241 |
|
\begin{center} |
| 242 |
< |
\begin{tabular}{|c|c|c|} |
| 242 |
> |
\begin{tabular}{|c|c|c|c|} |
| 243 |
> |
\hline |
| 244 |
> |
& $4e$ & $4\mu$ & $2e2\mu$ \\ |
| 245 |
> |
\hline |
| 246 |
> |
single loop & $9.1\pm 2$ & $Z\pm Y$ & $6.6 + Z\pm 1.7 + Y$ \\ |
| 247 |
> |
\hline |
| 248 |
> |
double loop & $2.6\pm 0.5$ & $Z\pm Y$ & $2.2 + \pm 0.4 + Y$ \\ |
| 249 |
> |
\hline |
| 250 |
> |
$ZZ$ & $0.49\pm 0.005$ & $Z\pm Y$ & $0.67 + Z\pm 0.01 + Y$ \\ |
| 251 |
|
\hline |
| 252 |
< |
$4e$ & $4\mu$ & $2e2\mu$ \\ |
| 252 |
> |
$Z\gamma$ & $0.9\pm 0.4$ & $Z\pm Y$ & $0.8 + Z\pm 0.5 + Y$ \\ |
| 253 |
|
\hline |
| 254 |
< |
$X\pm Y$ & $Z\pm Y$ & $Z\pm Y$ \\ |
| 254 |
> |
WZ estimate & $2.5\pm 2.1$ & $Z\pm Y$ & $0.7 + Z\pm 1.8 + Y$ \\ |
| 255 |
|
\hline |
| 256 |
|
\end{tabular} |
| 257 |
|
\caption{Data-driven Expected $WZ$ Yields} |
