| 14 |
|
region, |
| 15 |
|
for electrons and muons separately. |
| 16 |
|
|
| 17 |
< |
The choice to normalizing to the peak region of $M_T$ has the |
| 17 |
> |
The choice to normalize to the peak region of $M_T$ has the |
| 18 |
|
advantage that some uncertainties, e.g., luminosity, cancel. |
| 19 |
|
It does however introduce complications because it couples |
| 20 |
|
some of the uncertainties in non-trivial ways. For example, |
| 25 |
|
the $t\bar{t} \to$ dilepton BG estimate because it changes the |
| 26 |
|
$t\bar{t}$ normalization to the peak region (because some of the |
| 27 |
|
events in the peak region are from rare processes). These effects |
| 28 |
< |
are carefully accounted for. The contribution to the overall |
| 29 |
< |
uncertainty from each BG source is tabulated in |
| 28 |
> |
are carefully accounted for. The contribution to the overall |
| 29 |
> |
uncertainty from each background source is tabulated in |
| 30 |
|
Section~\ref{sec:bgunc-bottomline}. |
| 31 |
< |
First, however, we discuss the uncertainties one-by-one and we comment |
| 31 |
> |
Here we discuss the uncertainties one-by-one and comment |
| 32 |
|
on their impact on the overall result, at least to first order. |
| 33 |
|
Second order effects, such as the one described, are also included. |
| 34 |
|
|
| 37 |
|
These vary between 2\% and 20\%, depending on the signal region |
| 38 |
|
(different |
| 39 |
|
signal regions have different \met\ requirements, thus they also have |
| 40 |
< |
different $M_T$ regions used as control. |
| 40 |
> |
different $M_T$ regions used as control). |
| 41 |
|
Since |
| 42 |
< |
the major BG, eg, $t\bar{t}$ are normalized to the peak regions, this |
| 42 |
> |
the major backgrounds, eg, $t\bar{t}$ are normalized to the peak regions, this |
| 43 |
|
fractional uncertainty is pretty much carried through all the way to |
| 44 |
|
the end. There is also an uncertainty from the finite MC event counts |
| 45 |
|
in the $M_T$ peak regions. This is also included, but it is smaller. |
| 47 |
|
Normalizing to the $M_T$ peak has the distinct advantages that |
| 48 |
|
uncertainties on luminosity, cross-sections, trigger efficiency, |
| 49 |
|
lepton ID, cancel out. |
| 50 |
< |
For the low statistics regions with high \met requirements, the |
| 51 |
< |
price to pay in terms of event count statistical uncertainties starts |
| 50 |
> |
For the low statistics regions with high \met\ requirements, the |
| 51 |
> |
price to pay in terms of event count is that statistical uncertainties start |
| 52 |
|
to become significant. In the future we may consider a different |
| 53 |
|
normalization startegy in the low statistics regions. |
| 54 |
|
|
| 58 |
|
If the $M_T$ peak region is not well modelled, this would introduce an |
| 59 |
|
uncertainty. |
| 60 |
|
|
| 61 |
< |
We have tested this possibility by recalculating the post veto scale factors for a different |
| 61 |
> |
We have tested this possibility by recalculating the post-veto scale factors for a different |
| 62 |
|
choice |
| 63 |
|
of $M_T$ peak region ($40 < M_T < 100$ GeV instead of the default |
| 64 |
< |
$50 < M_T < 80$ GeV. This is shown in Table~\ref{tab:mtpeaksf2}. |
| 64 |
> |
$50 < M_T < 80$ GeV). This is shown in Table~\ref{tab:mtpeaksf2}. |
| 65 |
|
The two results for the scale factors are very compatible. |
| 66 |
|
We do not take any systematic uncertainty for this possible effect. |
| 67 |
|
|
| 111 |
|
\end{table} |
| 112 |
|
|
| 113 |
|
|
| 114 |
< |
\subsection{Uncertainty on the Wjets cross-section and the rare MC cross-sections} |
| 114 |
> |
\subsection{Uncertainty on the \wjets\ cross-section and the rare MC cross-sections} |
| 115 |
|
These are taken as 50\%, uncorrelated. |
| 116 |
|
The primary effect is to introduce a 50\% |
| 117 |
|
uncertainty |
| 125 |
|
scaled to the number of $t\bar{t}$ events in the peak, the $t\bar{t}$ |
| 126 |
|
BG goes down. |
| 127 |
|
|
| 128 |
< |
\subsection{Scale factors for the tail-to-peak ratios for lepton + |
| 128 |
> |
\subsection{Tail-to-peak ratios for lepton + |
| 129 |
|
jets top and W events} |
| 130 |
< |
These tail-to-peak ratios are described in Section~\ref{sec:ttp}. |
| 131 |
< |
They are studied in CR1 and CR2. The studies are described |
| 132 |
< |
in Sections~\ref{sec:cr1} and~\ref{sec:cr2}), respectively, where |
| 133 |
< |
we also give the uncertainty on the scale factors. See |
| 134 |
< |
Tables~\ref{tab:cr1yields} |
| 135 |
< |
and~\ref{tab:cr2yields}, scale factors $SFR_{wjet}$ and $SFR_{top})$. |
| 130 |
> |
The tail-to-peak ratios $R_{top}$ and $R_{wjet}$ are described in Section~\ref{sec:ttp}. |
| 131 |
> |
The data/MC scale factors are studied in CR1 and CR2 (Sections~\ref{sec:cr1} and~\ref{sec:cr2}). |
| 132 |
> |
Only the scale factor for \wjets, $SFR_{wjet}$, is used, and its |
| 133 |
> |
uncertainty is given in Table~\ref{tab:cr1yields}. |
| 134 |
> |
This uncertainty affects both $R_{wjet}$ and $R_{top}$. |
| 135 |
> |
The additional systematic uncertainty on $R_{top}$ from the variation between optimistic and pessimistic scenarios is given in Section~\ref{sec:ttp}. |
| 136 |
> |
|
| 137 |
|
|
| 138 |
|
\subsection{Uncertainty on extra jet radiation for dilepton |
| 139 |
|
background} |
| 143 |
|
dilepton MC is rescaled by the factors $K_3$ and $K_4$ to make |
| 144 |
|
it agree with the data. The 3\% uncertainties on $K_3$ and $K_4$ |
| 145 |
|
comes from data/MC statistics. This |
| 146 |
< |
result directly in a 3\% uncertainty on the dilepton BG, which is by far |
| 146 |
> |
results directly in a 3\% uncertainty on the dilepton background, which is by far |
| 147 |
|
the most important one. |
| 148 |
|
|
| 149 |
+ |
\subsection{Uncertainty from MC statistics} |
| 150 |
+ |
This affects mostly the \ttll\ background estimate, which is taken |
| 151 |
+ |
from |
| 152 |
+ |
Monte Carlo with appropriate correction factors. This uncertainty |
| 153 |
+ |
is negligible in the low \met\ signal regions, and grows to about |
| 154 |
+ |
15\% in SRG. |
| 155 |
|
|
| 149 |
– |
\subsection{Uncertainty on the \ttll\ Acceptance} |
| 156 |
|
|
| 157 |
+ |
\subsection{Uncertainty on the \ttll\ Background} |
| 158 |
+ |
\label{sec:ttdilbkgunc} |
| 159 |
|
The \ttbar\ background prediction is obtained from MC, with corrections |
| 160 |
|
derived from control samples in data. The uncertainty associated with |
| 161 |
< |
the theoretical modeling of the \ttbar\ production and decay is |
| 162 |
< |
estimated by comparing the background predictions obtained using |
| 161 |
> |
the \ttbar\ background is derived from the level of closure of the |
| 162 |
> |
background prediction in CR4 (Table~\ref{tab:cr4yields}) and |
| 163 |
> |
CR5 (Table~\ref{tab:cr5yields}). The results from these control region |
| 164 |
> |
checks are shown in Figure~\ref{fig:ttdlunc}. The uncertainties assigned |
| 165 |
> |
to the \ttdl\ background prediction based on these tests are |
| 166 |
> |
5\% (SRA), 10\% (SRB), 15\% (SRC), 25\% (SRD), 40\% (SRE-G). |
| 167 |
> |
|
| 168 |
> |
\begin{figure}[hbt] |
| 169 |
> |
\begin{center} |
| 170 |
> |
\includegraphics[width=0.6\linewidth]{plots/ttdilepton_uncertainty.pdf} |
| 171 |
> |
\caption{ |
| 172 |
> |
\label{fig:ttdlunc}%\protect |
| 173 |
> |
Results of the comparison of yields in the \mt\ tail comparing the MC prediction (after |
| 174 |
> |
applying SFs) to data for CR4 and CR5 for all the signal |
| 175 |
> |
region requirements considered (A-G). The bands indicate the |
| 176 |
> |
systematic uncertainties assigned based on these tests, |
| 177 |
> |
ranging from $5\%$ for SRA to $40\%$ for SRE-G.} |
| 178 |
> |
\end{center} |
| 179 |
> |
\end{figure} |
| 180 |
> |
|
| 181 |
> |
\clearpage |
| 182 |
> |
\subsubsection{Check of the impact of Signal Contamination} |
| 183 |
> |
|
| 184 |
> |
We examine the contribution of possible signal events in the \ttll\ |
| 185 |
> |
control regions (CR4 and CR5). It should be emphasized that these |
| 186 |
> |
regions are not used to apply data/MC SFs. They are used to quantify |
| 187 |
> |
the level of data/MC agreement and assign a corresponding uncertainty. |
| 188 |
> |
|
| 189 |
> |
To illustrate how much signal is expected to populate these control |
| 190 |
> |
regions, we examine signal points near the edge of the analysis' |
| 191 |
> |
sensitivity (m(stop) = 450 m($\chi^0$) = 0 for T2tt, m(stop) = 450 |
| 192 |
> |
m($\chi^0$) = 0 for T2bw with x=0.75 and m(stop) = 350 |
| 193 |
> |
m($\chi^0$) = 0 for T2bw with x=0.5). |
| 194 |
> |
Table~\ref{tab:signalcontamination} compares the expected signal |
| 195 |
> |
yields and the raw total MC background prediction in the control |
| 196 |
> |
regions with the \met\ and \mt\ requirements corresponding to SRB, SRC |
| 197 |
> |
and SRD (these are the signal regions that dominate the |
| 198 |
> |
sensitivity). The signal contamination is smaller than the uncertainty |
| 199 |
> |
on the dilepton background and smaller than the signal/background in |
| 200 |
> |
the signal regions, with the exception of the T2bw scenario with x=0.5. |
| 201 |
> |
However, based on the fact that the CR4 and CR5 are not used to extract |
| 202 |
> |
data/MC SFs and that CR4 shows a slight deficit of data compared to |
| 203 |
> |
the MC prediction, indicating that we do not observe evidence of |
| 204 |
> |
signal contamination, we do not assign an additional uncertainty. |
| 205 |
> |
|
| 206 |
> |
\begin{table}[!h] |
| 207 |
> |
\begin{center} |
| 208 |
> |
{\small |
| 209 |
> |
\begin{tabular}{l l||c|c|c} |
| 210 |
> |
\hline |
| 211 |
> |
\multicolumn{2}{c||}{Sample} & CR B & CR C & CR D \\ |
| 212 |
> |
\hline |
| 213 |
> |
\hline |
| 214 |
> |
\multirow{4}{*}{CR4} & Raw MC & $168.2 \pm 4.5$& $51.5 \pm 2.5$& $19.6 \pm 1.5$ \\ |
| 215 |
> |
%\hline |
| 216 |
> |
& T2tt m(stop) = 450 m($\chi^0$) = 0 & $2.6 \pm 0.3$ $(2\%)$ & $2.0 \pm 0.2$ $(4\%)$ & $1.4 \pm 0.2$ $(7\%)$ \\ |
| 217 |
> |
& T2bw x=0.75 m(stop) = 450 m($\chi^0$) = 0 & $10.5 \pm 0.4$ $(6\%)$ &$6.1 \pm 0.3$ $(12\%)$ & $3.1 \pm 0.2$ $(16\%)$ \\ |
| 218 |
> |
& T2bw x=0.5 m(stop) = 350 m($\chi^0$) = 0 & $32.1 \pm 1.5$ $(19\%)$ & $14.7 \pm 1.0$ $(29\%)$ & $5.5 \pm 0.6$ $(28\%)$ \\ |
| 219 |
> |
\hline |
| 220 |
> |
\hline |
| 221 |
> |
\multirow{4}{*}{CR5} & Raw MC & $306.5 \pm 6.2$& $101.8 \pm 3.6$& $38.0 \pm 2.2$ \\ |
| 222 |
> |
%\hline |
| 223 |
> |
& T2tt m(stop) = 450 m($\chi^0$) = 0 & $10.6 \pm 0.6$ $(3\%)$ & $7.8 \pm 0.5$ $(8\%)$ & $5.4 \pm 0.4$ $(14\%)$ \\ |
| 224 |
> |
& T2bw x=0.75 m(stop) = 450 m($\chi^0$) = 0 & $17.3 \pm 0.5$ $(6\%)$ &$11.3 \pm 0.4$ $(11\%)$ & $6.2 \pm 0.3$ $(16\%)$\\ |
| 225 |
> |
& T2bw x=0.5 m(stop) = 350 m($\chi^0$) = 0 & $33.0 \pm 1.5$ $(11\%)$& $14.4 \pm 1.0$ $(14\%)$& $5.7 \pm 0.6$ $(15\%)$ \\ |
| 226 |
> |
\hline |
| 227 |
> |
\hline |
| 228 |
> |
\hline |
| 229 |
> |
\multirow{4}{*}{SIGNAL} & Raw MC & $486.3 \pm 7.8$& $164.3 \pm 4.5$& $61.5 \pm 2.8$ \\ |
| 230 |
> |
& T2tt m(stop) = 450 m($\chi^0$) = 0 & $65.3 \pm 1.4$ $(13\%)$& $48.8 \pm 1.2$ $(30\%)$& $32.9 \pm 1.0$ $(53\%)$ \\ |
| 231 |
> |
& T2bw x=0.75 m(stop) = 450 m($\chi^0$) = 0 & $69.3 \pm 1.0$ $(14\%)$& $47.3 \pm 0.8$ $(29\%)$& $27.3 \pm 0.6$ $(44\%)$ \\ |
| 232 |
> |
& T2bw x=0.5 m(stop) = 350 m($\chi^0$) = 0 & $105.5 \pm 2.8$ $(22\%)$& $44.6 \pm 1.8$ $(27\%)$& $15.9 \pm 1.1$ $(26\%)$ \\ |
| 233 |
> |
\hline |
| 234 |
> |
\end{tabular}} |
| 235 |
> |
\caption{ Yields in \mt\ tail comparing the raw SM MC prediction to the |
| 236 |
> |
yields for a few signal points on the edge of our sensitivity in the \ttll\ |
| 237 |
> |
control regions CR4, CR5 and in the corresponding signal region. |
| 238 |
> |
The numbers in parenthesis are the expected signal yield divided by |
| 239 |
> |
the total background. The uncertainties are statistical only. |
| 240 |
> |
\label{tab:signalcontamination}} |
| 241 |
> |
\end{center} |
| 242 |
> |
\end{table} |
| 243 |
> |
|
| 244 |
> |
%CR5 DUMP |
| 245 |
> |
%Total & $880.3 \pm 10.4$& $560.0 \pm 8.3$& $306.5 \pm 6.2$& $101.8 \pm 3.6$& $38.0 \pm 2.2$& $16.4 \pm 1.4$& $8.2 \pm 1.0$& $4.6 \pm 0.8$ \\ |
| 246 |
> |
%\hline |
| 247 |
> |
%\hline |
| 248 |
> |
%Data & $941$& $559$& $287$& $95$& $26$& $8$& $5$& $3$ \\ |
| 249 |
> |
%\hline |
| 250 |
> |
%T2tt m(stop) = 250 m($\chi^0$) = 0 & $84.3 \pm 9.2$& $61.9 \pm 7.9$& $35.7 \pm 6.0$& $5.9 \pm 2.4$& $1.0 \pm 1.0$& $1.0 \pm 1.0$& $0.0 \pm 0.0$& $0.0 \pm 0.0$ \\ |
| 251 |
> |
%\hline |
| 252 |
> |
%T2tt m(stop) = 300 m($\chi^0$) = 50 & $61.4 \pm 4.7$& $53.6 \pm 4.4$& $42.0 \pm 3.9$& $14.3 \pm 2.3$& $7.2 \pm 1.6$& $1.8 \pm 0.8$& $0.7 \pm 0.5$& $0.0 \pm 0.0$ \\ |
| 253 |
> |
%\hline |
| 254 |
> |
%T2tt m(stop) = 300 m($\chi^0$) = 100 & $33.3 \pm 3.5$& $28.6 \pm 3.2$& $19.2 \pm 2.6$& $6.1 \pm 1.5$& $1.8 \pm 0.8$& $0.4 \pm 0.4$& $0.4 \pm 0.4$& $0.4 \pm 0.4$ \\ |
| 255 |
> |
%\hline |
| 256 |
> |
%T2tt m(stop) = 350 m($\chi^0$) = 0 & $33.4 \pm 2.2$& $29.8 \pm 2.1$& $27.3 \pm 2.0$& $15.3 \pm 1.5$& $5.6 \pm 0.9$& $1.9 \pm 0.5$& $0.3 \pm 0.2$& $0.0 \pm 0.0$ \\ |
| 257 |
> |
%\hline |
| 258 |
> |
%T2tt m(stop) = 450 m($\chi^0$) = 0 & $12.0 \pm 0.6$& $11.3 \pm 0.6$& $10.6 \pm 0.6$& $7.8 \pm 0.5$& $5.4 \pm 0.4$& $3.1 \pm 0.3$& $1.8 \pm 0.2$& $0.6 \pm 0.1$ \\ |
| 259 |
> |
%\hline |
| 260 |
> |
%T2bw m(stop) = 350 x=0.5 m($\chi^0$) = 0 & $48.5 \pm 1.9$& $40.2 \pm 1.7$& $33.0 \pm 1.5$& $14.4 \pm 1.0$& $5.7 \pm 0.6$& $2.7 \pm 0.4$& $1.3 \pm 0.3$& $0.5 \pm 0.2$ \\ |
| 261 |
> |
%\hline |
| 262 |
> |
%T2bw m(stop) = 450 x=0.75 m($\chi^0$) = 0 & $22.3 \pm 0.6$& $20.2 \pm 0.6$& $17.3 \pm 0.5$& $11.3 \pm 0.4$& $6.2 \pm 0.3$& $3.1 \pm 0.2$& $1.3 \pm 0.1$& $0.7 \pm 0.1$ \\ |
| 263 |
> |
%\hline |
| 264 |
> |
|
| 265 |
> |
%CR4 DUMP |
| 266 |
> |
%\hline |
| 267 |
> |
%Total & $510.1 \pm 8.0$& $324.2 \pm 6.3$& $168.2 \pm 4.5$& $51.5 \pm 2.5$& $19.6 \pm 1.5$& $7.8 \pm 1.0$& $2.6 \pm 0.6$& $1.1 \pm 0.3$ \\ |
| 268 |
> |
%\hline |
| 269 |
> |
%\hline |
| 270 |
> |
%Data & $462$& $289$& $169$& $45$& $10$& $7$& $5$& $3$ \\ |
| 271 |
> |
%\hline |
| 272 |
> |
%T2tt m(stop) = 250 m($\chi^0$) = 0 & $37.7 \pm 6.1$& $30.9 \pm 5.5$& $18.0 \pm 4.2$& $6.0 \pm 2.5$& $2.0 \pm 1.4$& $0.0 \pm 0.0$& $0.0 \pm 0.0$& $0.0 \pm 0.0$ \\ |
| 273 |
> |
%\hline |
| 274 |
> |
%T2tt m(stop) = 300 m($\chi^0$) = 50 & $16.6 \pm 2.4$& $14.4 \pm 2.3$& $11.3 \pm 2.0$& $5.6 \pm 1.4$& $3.2 \pm 1.1$& $1.8 \pm 0.8$& $0.0 \pm 0.0$& $0.0 \pm 0.0$ \\ |
| 275 |
> |
%\hline |
| 276 |
> |
%T2tt m(stop) = 300 m($\chi^0$) = 100 & $9.6 \pm 1.8$& $6.4 \pm 1.5$& $4.6 \pm 1.3$& $0.7 \pm 0.5$& $0.4 \pm 0.4$& $0.0 \pm 0.0$& $0.0 \pm 0.0$& $0.0 \pm 0.0$ \\ |
| 277 |
> |
%\hline |
| 278 |
> |
%T2tt m(stop) = 350 m($\chi^0$) = 0 & $8.2 \pm 1.1$& $7.6 \pm 1.0$& $5.7 \pm 0.9$& $3.4 \pm 0.7$& $1.9 \pm 0.5$& $0.6 \pm 0.3$& $0.3 \pm 0.2$& $0.1 \pm 0.1$ \\ |
| 279 |
> |
%\hline |
| 280 |
> |
%T2tt m(stop) = 450 m($\chi^0$) = 0 & $3.1 \pm 0.3$& $2.9 \pm 0.3$& $2.6 \pm 0.3$& $2.0 \pm 0.2$& $1.4 \pm 0.2$& $1.0 \pm 0.2$& $0.4 \pm 0.1$& $0.2 \pm 0.1$ \\ |
| 281 |
> |
%\hline |
| 282 |
> |
%T2bw m(stop) = 350 x=0.5 m($\chi^0$) = 0 & $52.6 \pm 1.9$& $42.6 \pm 1.7$& $32.1 \pm 1.5$& $14.7 \pm 1.0$& $5.5 \pm 0.6$& $1.9 \pm 0.4$& $0.6 \pm 0.2$& $0.3 \pm 0.1$ \\ |
| 283 |
> |
%\hline |
| 284 |
> |
%T2bw m(stop) = 450 x=0.75 m($\chi^0$) = 0 & $16.9 \pm 0.5$& $14.9 \pm 0.5$& $10.5 \pm 0.4$& $6.1 \pm 0.3$& $3.1 \pm 0.2$& $1.5 \pm 0.1$& $0.6 \pm 0.1$& $0.3 \pm 0.1$ \\ |
| 285 |
> |
%\hline |
| 286 |
> |
|
| 287 |
> |
|
| 288 |
> |
\subsubsection{Check of the uncertainty on the \ttll\ Background} |
| 289 |
> |
|
| 290 |
> |
We check that the systematic uncertainty assigned to the \ttll\ background prediction |
| 291 |
> |
covers the uncertainty associated with |
| 292 |
> |
the theoretical modeling of the \ttbar\ production and decay |
| 293 |
> |
by comparing the background predictions obtained using |
| 294 |
|
alternative MC samples. It should be noted that the full analysis is |
| 295 |
|
performed with the alternative samples under consideration, |
| 296 |
|
including the derivation of the various data-to-MC scale factors. |
| 298 |
|
|
| 299 |
|
\begin{itemize} |
| 300 |
|
\item Top mass: The alternative values for the top mass differ |
| 301 |
< |
from the central value by $5~\GeV$: $m_{\mathrm{top}} = 178.5~\GeV$ and $m_{\mathrm{top}} |
| 301 |
> |
from the central value by $6~\GeV$: $m_{\mathrm{top}} = 178.5~\GeV$ and $m_{\mathrm{top}} |
| 302 |
|
= 166.5~\GeV$. |
| 303 |
|
\item Jet-parton matching scale: This corresponds to variations in the |
| 304 |
|
scale at which the Matrix Element partons from Madgraph are matched |
| 315 |
|
Tauola and is otherwise identical to the Powheg sample. |
| 316 |
|
This effect was studied earlier using 7~TeV samples and found to be negligible. |
| 317 |
|
\item The PDF uncertainty is estimated following the PDF4LHC |
| 318 |
< |
recommendations[CITE]. The events are reweighted using alternative |
| 318 |
> |
recommendations. The events are reweighted using alternative |
| 319 |
|
PDF sets for CT10 and MSTW2008 and the uncertainties for each are derived using the |
| 320 |
< |
alternative eigenvector variations and the ``master equation''. In |
| 321 |
< |
addition, the NNPDF2.1 set with 100 replicas. The central value is |
| 320 |
> |
alternative eigenvector variations and the ``master equation''. |
| 321 |
> |
The NNPDF2.1 set with 100 replicas is also used. The central value is |
| 322 |
|
determined from the mean and the uncertainty is derived from the |
| 323 |
|
$1\sigma$ range. The overall uncertainty is derived from the envelope of the |
| 324 |
|
alternative predictions and their uncertainties. |
| 386 |
|
statistics. |
| 387 |
|
\item Within the limited statistics, there is no evidence that the |
| 388 |
|
situation changes as we go from signal region A to signal region E. |
| 389 |
< |
Therefore, we assess a systematic based on the relatively high |
| 390 |
< |
statistics |
| 391 |
< |
test in signal region A, and apply the same systematic uncertainty |
| 392 |
< |
to all other regions. |
| 389 |
> |
%Therefore, we assess a systematic based on the relatively high |
| 390 |
> |
%statistics |
| 391 |
> |
%test in signal region A, and apply the same systematic uncertainty |
| 392 |
> |
%to all other regions. |
| 393 |
> |
\item In signal regions B and above, the uncertainties assigned in Section~\ref{sec:ttdilbkgunc} |
| 394 |
> |
fully cover the alternative MC variations. |
| 395 |
|
\item In order to fully (as opposed as 1$\sigma$) cover the |
| 396 |
|
alternative MC variations in region A we would have to take a |
| 397 |
|
systematic |
| 398 |
< |
uncertainty of $\approx 10\%$. This would be driven by the |
| 398 |
> |
uncertainty of $\approx 10\%$ instead of $5\%$. This would be driven by the |
| 399 |
|
scale up/scale down variations, see Table~\ref{tab:fracdiff}. |
| 400 |
|
\end{itemize} |
| 401 |
|
|
| 429 |
|
These are described below. |
| 430 |
|
|
| 431 |
|
The first piece of information is that the jet multiplicity in the scale |
| 432 |
< |
up/scale down sample is the most inconsistent with the data. This can be shown |
| 432 |
> |
up/scale down sample is the most inconsistent with the data. This is shown |
| 433 |
|
in Table~\ref{tab:njetskfactors_met100}, where we tabulate the |
| 434 |
< |
$K_3$ and $K_4$ factors of Section~\ref{tab:njetskfactors_met100} for |
| 434 |
> |
$K_3$ and $K_4$ factors of Section~\ref{sec:jetmultiplicity} for |
| 435 |
|
different \ttbar\ MC samples. The data/MC disagreement in the $N_{jets}$ |
| 436 |
|
distribution |
| 437 |
|
for the scale up/scale down samples is also shown in Fig.~\ref{fig:dileptonnjets_scaleup} |
| 492 |
|
up/scale |
| 493 |
|
down variations by a factor 2, we can see that a systematic |
| 494 |
|
uncertainty |
| 495 |
< |
of 6\% would fully cover all of the variations from different MC |
| 496 |
< |
samples in SRA and SRB. |
| 497 |
< |
{\bf Thus, we take a 6\% systematic uncertainty, constant as a |
| 498 |
< |
function of signal region, as the systematic due to alternative MC |
| 499 |
< |
models.}. |
| 500 |
< |
Note that this 6\% is also consistent with the level at which we are |
| 501 |
< |
able |
| 502 |
< |
to test the closure of the method in CR5 for the high statistics |
| 503 |
< |
regions |
| 504 |
< |
(Table~\ref{tab:hugecr5yields}). |
| 505 |
< |
|
| 495 |
> |
of 5\% covers the range of reasonable variations from different MC |
| 496 |
> |
models in SRA and SRB. |
| 497 |
> |
%The alternative MC models indicate that a 6\% systematic uncertainty |
| 498 |
> |
%covers the range of reasonable variations. |
| 499 |
> |
Note that this 5\% is also consistent with the level at which we are |
| 500 |
> |
able to test the closure of the method with alternative samples in CR5 for the high statistics |
| 501 |
> |
regions (Table~\ref{tab:hugecr5yields}). |
| 502 |
> |
The range of reasonable variations obtained with the alternative |
| 503 |
> |
samples are consistent with the uncertainties assigned for |
| 504 |
> |
the \ttll\ background based on the closure of the background |
| 505 |
> |
predictions and data in CR4 and CR5. |
| 506 |
|
|
| 507 |
|
|
| 508 |
|
|
| 733 |
|
$P_T > 10$ GeV in $|\eta| < 2.4$. This fraction is about 1/3, see |
| 734 |
|
Table~\ref{tab:trueisotrk}. |
| 735 |
|
The uncertainty for these events |
| 736 |
< |
is 6\% and is obtained from Tag and Probe studies of Section~\ref{sec:trkveto} |
| 736 |
> |
is 6\% and is obtained from tag-and-probe studies, see Section~\ref{sec:trkveto}. |
| 737 |
|
|
| 738 |
|
\begin{table}[!h] |
| 739 |
|
\begin{center} |
| 782 |
|
Second, hadronic tracks may undergo nuclear interactions and hence their tracks may not be reconstructed. |
| 783 |
|
As discussed above, independent studies show that the MC reproduces the hadronic tracking efficiency within 4\%, |
| 784 |
|
leading to a total background uncertainty of less than 0.5\% (after taking into account the fraction of the total background |
| 785 |
< |
due to hadronic $\tau$ decays with \pt\ $>$ 10 GeV tracks), and we hence regard this effect as neglgigible. |
| 785 |
> |
due to hadronic $\tau$ decays with \pt\ $>$ 10 GeV tracks), and we hence regard this effect as negligible. |
| 786 |
|
|
| 787 |
|
The tag-and-probe studies are performed in the full data sample, and compared with the DYJets madgraph sample. |
| 788 |
|
All events must contain a tag-probe pair (details below) with opposite-sign and satisfying the Z mass requirement 76--106 GeV. |
| 839 |
|
The absolute track isolation distributions for passing probes are displayed in Fig.~\ref{fig:tnp}. In general we observe |
| 840 |
|
good agreement between data and MC. To be more quantitative, we compare the data vs. MC efficiencies to satisfy |
| 841 |
|
absolute track isolation requirements varying from $>$ 1 GeV to $>$ 5 GeV, as summarized in Table~\ref{tab:isotrk}. |
| 842 |
< |
In the $\geq$0 and $\geq$1 jet bins where the efficiencies can be tested with statistical precision, the data and MC |
| 842 |
> |
In the $\geq 0$ and $\geq 1$ jet bins where the efficiencies can be tested with statistical precision, the data and MC |
| 843 |
|
efficiencies agree within 6\%, and we apply this as a systematic uncertainty on the isolated track veto efficiency. |
| 844 |
|
For the higher jet multiplicity bins the statistical precision decreases, but we do not observe any evidence for |
| 845 |
|
a data vs. MC discrepancy in the isolated track veto efficiency. |
| 872 |
|
|
| 873 |
|
\begin{table}[!ht] |
| 874 |
|
\begin{center} |
| 734 |
– |
\caption{\label{tab:isotrk} Comparison of the data vs. MC efficiencies to satisfy the indicated requirements |
| 735 |
– |
on the absolute track isolation, and the ratio of these two efficiencies. Results are indicated separately for electrons and muons and for various |
| 736 |
– |
jet multiplicity requirements.} |
| 875 |
|
\begin{tabular}{l|c|c|c|c|c} |
| 876 |
|
|
| 877 |
|
%Electrons: |
| 969 |
|
\hline |
| 970 |
|
|
| 971 |
|
\end{tabular} |
| 972 |
+ |
\caption{\label{tab:isotrk} Comparison of the data vs. MC efficiencies to satisfy the indicated requirements |
| 973 |
+ |
on the absolute track isolation, and the ratio of these two efficiencies. Results are indicated separately for electrons and muons and for various |
| 974 |
+ |
jet multiplicity requirements.} |
| 975 |
|
\end{center} |
| 976 |
|
\end{table} |
| 977 |
|
|
| 978 |
+ |
\clearpage |
| 979 |
+ |
\subsection{Summary of uncertainties} |
| 980 |
+ |
\label{sec:bgunc-bottomline} |
| 981 |
+ |
|
| 982 |
+ |
The contribution from each source to the total uncertainty on the background yield is given in Tables~\ref{tab:relativeuncertaintycomponents} and~\ref{tab:uncertaintycomponents} for the relative and absolute uncertainties, respectively. In the low-\met\ regions the dominant uncertainty comes from the top tail-to-peak ratio, $R_{top}$ (Section~\ref{sec:ttp}), while in the high-\met\ regions the \ttll\ systematic uncertainty dominates (Section~\ref{sec:ttdilbkgunc}). |
| 983 |
+ |
|
| 984 |
+ |
\input{uncertainties_table.tex} |
| 985 |
+ |
|
| 986 |
+ |
|
| 987 |
+ |
|
| 988 |
+ |
|
| 989 |
|
|
| 990 |
|
%Figure.~\ref{fig:reliso} compares the relative track isolation |
| 991 |
|
%for events with a track with $\pt > 10~\GeV$ in addition to a selected |
| 1067 |
|
% \end{center} |
| 1068 |
|
%\end{figure} |
| 1069 |
|
|
| 1070 |
< |
% \subsection{Summary of uncertainties} |
| 919 |
< |
% \label{sec:bgunc-bottomline}. |
| 1070 |
> |
|
| 1071 |
|
|
| 1072 |
|
% THIS NEEDS TO BE WRITTEN |
