| 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} |
| 154 |
|
15\% in SRG. |
| 155 |
|
|
| 156 |
|
|
| 157 |
< |
\subsection{Uncertainty on the \ttll\ Acceptance} |
| 158 |
< |
|
| 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 |
> |
|
| 182 |
> |
\subsubsection{Check of the uncertainty on the \ttll\ Background} |
| 183 |
> |
|
| 184 |
> |
We check that the systematic uncertainty assigned to the \ttll\ background prediction |
| 185 |
> |
covers the uncertainty associated with |
| 186 |
> |
the theoretical modeling of the \ttbar\ production and decay |
| 187 |
> |
by comparing the background predictions obtained using |
| 188 |
|
alternative MC samples. It should be noted that the full analysis is |
| 189 |
|
performed with the alternative samples under consideration, |
| 190 |
|
including the derivation of the various data-to-MC scale factors. |
| 192 |
|
|
| 193 |
|
\begin{itemize} |
| 194 |
|
\item Top mass: The alternative values for the top mass differ |
| 195 |
< |
from the central value by $5~\GeV$: $m_{\mathrm{top}} = 178.5~\GeV$ and $m_{\mathrm{top}} |
| 195 |
> |
from the central value by $6~\GeV$: $m_{\mathrm{top}} = 178.5~\GeV$ and $m_{\mathrm{top}} |
| 196 |
|
= 166.5~\GeV$. |
| 197 |
|
\item Jet-parton matching scale: This corresponds to variations in the |
| 198 |
|
scale at which the Matrix Element partons from Madgraph are matched |
| 209 |
|
Tauola and is otherwise identical to the Powheg sample. |
| 210 |
|
This effect was studied earlier using 7~TeV samples and found to be negligible. |
| 211 |
|
\item The PDF uncertainty is estimated following the PDF4LHC |
| 212 |
< |
recommendations[CITE]. The events are reweighted using alternative |
| 212 |
> |
recommendations. The events are reweighted using alternative |
| 213 |
|
PDF sets for CT10 and MSTW2008 and the uncertainties for each are derived using the |
| 214 |
< |
alternative eigenvector variations and the ``master equation''. In |
| 215 |
< |
addition, the NNPDF2.1 set with 100 replicas. The central value is |
| 214 |
> |
alternative eigenvector variations and the ``master equation''. |
| 215 |
> |
The NNPDF2.1 set with 100 replicas is also used. The central value is |
| 216 |
|
determined from the mean and the uncertainty is derived from the |
| 217 |
|
$1\sigma$ range. The overall uncertainty is derived from the envelope of the |
| 218 |
|
alternative predictions and their uncertainties. |
| 280 |
|
statistics. |
| 281 |
|
\item Within the limited statistics, there is no evidence that the |
| 282 |
|
situation changes as we go from signal region A to signal region E. |
| 283 |
< |
Therefore, we assess a systematic based on the relatively high |
| 284 |
< |
statistics |
| 285 |
< |
test in signal region A, and apply the same systematic uncertainty |
| 286 |
< |
to all other regions. |
| 283 |
> |
%Therefore, we assess a systematic based on the relatively high |
| 284 |
> |
%statistics |
| 285 |
> |
%test in signal region A, and apply the same systematic uncertainty |
| 286 |
> |
%to all other regions. |
| 287 |
> |
\item In signal regions B and above, the uncertainties assigned in Section~\ref{sec:ttdilbkgunc} |
| 288 |
> |
fully cover the alternative MC variations. |
| 289 |
|
\item In order to fully (as opposed as 1$\sigma$) cover the |
| 290 |
|
alternative MC variations in region A we would have to take a |
| 291 |
|
systematic |
| 292 |
< |
uncertainty of $\approx 10\%$. This would be driven by the |
| 292 |
> |
uncertainty of $\approx 10\%$ instead of $5\%$. This would be driven by the |
| 293 |
|
scale up/scale down variations, see Table~\ref{tab:fracdiff}. |
| 294 |
|
\end{itemize} |
| 295 |
|
|
| 323 |
|
These are described below. |
| 324 |
|
|
| 325 |
|
The first piece of information is that the jet multiplicity in the scale |
| 326 |
< |
up/scale down sample is the most inconsistent with the data. This can be shown |
| 326 |
> |
up/scale down sample is the most inconsistent with the data. This is shown |
| 327 |
|
in Table~\ref{tab:njetskfactors_met100}, where we tabulate the |
| 328 |
< |
$K_3$ and $K_4$ factors of Section~\ref{tab:njetskfactors_met100} for |
| 328 |
> |
$K_3$ and $K_4$ factors of Section~\ref{sec:jetmultiplicity} for |
| 329 |
|
different \ttbar\ MC samples. The data/MC disagreement in the $N_{jets}$ |
| 330 |
|
distribution |
| 331 |
|
for the scale up/scale down samples is also shown in Fig.~\ref{fig:dileptonnjets_scaleup} |
| 386 |
|
up/scale |
| 387 |
|
down variations by a factor 2, we can see that a systematic |
| 388 |
|
uncertainty |
| 389 |
< |
of 6\% would fully cover all of the variations from different MC |
| 390 |
< |
samples in SRA and SRB. |
| 391 |
< |
{\bf Thus, we take a 6\% systematic uncertainty, constant as a |
| 392 |
< |
function of signal region, as the systematic due to alternative MC |
| 393 |
< |
models.}. |
| 394 |
< |
Note that this 6\% is also consistent with the level at which we are |
| 395 |
< |
able |
| 396 |
< |
to test the closure of the method in CR5 for the high statistics |
| 397 |
< |
regions |
| 398 |
< |
(Table~\ref{tab:hugecr5yields}). |
| 399 |
< |
|
| 389 |
> |
of 5\% covers the range of reasonable variations from different MC |
| 390 |
> |
models in SRA and SRB. |
| 391 |
> |
%The alternative MC models indicate that a 6\% systematic uncertainty |
| 392 |
> |
%covers the range of reasonable variations. |
| 393 |
> |
Note that this 5\% is also consistent with the level at which we are |
| 394 |
> |
able to test the closure of the method with alternative samples in CR5 for the high statistics |
| 395 |
> |
regions (Table~\ref{tab:hugecr5yields}). |
| 396 |
> |
The range of reasonable variations obtained with the alternative |
| 397 |
> |
samples are consistent with the uncertainties assigned for |
| 398 |
> |
the \ttll\ background based on the closure of the background |
| 399 |
> |
predictions and data in CR4 and CR5. |
| 400 |
|
|
| 401 |
|
|
| 402 |
|
|
| 627 |
|
$P_T > 10$ GeV in $|\eta| < 2.4$. This fraction is about 1/3, see |
| 628 |
|
Table~\ref{tab:trueisotrk}. |
| 629 |
|
The uncertainty for these events |
| 630 |
< |
is 6\% and is obtained from Tag and Probe studies of Section~\ref{sec:trkveto} |
| 630 |
> |
is 6\% and is obtained from tag-and-probe studies, see Section~\ref{sec:trkveto}. |
| 631 |
|
|
| 632 |
|
\begin{table}[!h] |
| 633 |
|
\begin{center} |
| 676 |
|
Second, hadronic tracks may undergo nuclear interactions and hence their tracks may not be reconstructed. |
| 677 |
|
As discussed above, independent studies show that the MC reproduces the hadronic tracking efficiency within 4\%, |
| 678 |
|
leading to a total background uncertainty of less than 0.5\% (after taking into account the fraction of the total background |
| 679 |
< |
due to hadronic $\tau$ decays with \pt\ $>$ 10 GeV tracks), and we hence regard this effect as neglgigible. |
| 679 |
> |
due to hadronic $\tau$ decays with \pt\ $>$ 10 GeV tracks), and we hence regard this effect as negligible. |
| 680 |
|
|
| 681 |
|
The tag-and-probe studies are performed in the full data sample, and compared with the DYJets madgraph sample. |
| 682 |
|
All events must contain a tag-probe pair (details below) with opposite-sign and satisfying the Z mass requirement 76--106 GeV. |
| 733 |
|
The absolute track isolation distributions for passing probes are displayed in Fig.~\ref{fig:tnp}. In general we observe |
| 734 |
|
good agreement between data and MC. To be more quantitative, we compare the data vs. MC efficiencies to satisfy |
| 735 |
|
absolute track isolation requirements varying from $>$ 1 GeV to $>$ 5 GeV, as summarized in Table~\ref{tab:isotrk}. |
| 736 |
< |
In the $\geq$0 and $\geq$1 jet bins where the efficiencies can be tested with statistical precision, the data and MC |
| 736 |
> |
In the $\geq 0$ and $\geq 1$ jet bins where the efficiencies can be tested with statistical precision, the data and MC |
| 737 |
|
efficiencies agree within 6\%, and we apply this as a systematic uncertainty on the isolated track veto efficiency. |
| 738 |
|
For the higher jet multiplicity bins the statistical precision decreases, but we do not observe any evidence for |
| 739 |
|
a data vs. MC discrepancy in the isolated track veto efficiency. |
| 766 |
|
|
| 767 |
|
\begin{table}[!ht] |
| 768 |
|
\begin{center} |
| 741 |
– |
\caption{\label{tab:isotrk} Comparison of the data vs. MC efficiencies to satisfy the indicated requirements |
| 742 |
– |
on the absolute track isolation, and the ratio of these two efficiencies. Results are indicated separately for electrons and muons and for various |
| 743 |
– |
jet multiplicity requirements.} |
| 769 |
|
\begin{tabular}{l|c|c|c|c|c} |
| 770 |
|
|
| 771 |
|
%Electrons: |
| 863 |
|
\hline |
| 864 |
|
|
| 865 |
|
\end{tabular} |
| 866 |
+ |
\caption{\label{tab:isotrk} Comparison of the data vs. MC efficiencies to satisfy the indicated requirements |
| 867 |
+ |
on the absolute track isolation, and the ratio of these two efficiencies. Results are indicated separately for electrons and muons and for various |
| 868 |
+ |
jet multiplicity requirements.} |
| 869 |
|
\end{center} |
| 870 |
|
\end{table} |
| 871 |
|
|
| 872 |
+ |
\clearpage |
| 873 |
+ |
\subsection{Summary of uncertainties} |
| 874 |
+ |
\label{sec:bgunc-bottomline} |
| 875 |
+ |
|
| 876 |
+ |
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}). |
| 877 |
+ |
|
| 878 |
+ |
\input{uncertainties_table.tex} |
| 879 |
+ |
|
| 880 |
+ |
|
| 881 |
+ |
|
| 882 |
+ |
|
| 883 |
|
|
| 884 |
|
%Figure.~\ref{fig:reliso} compares the relative track isolation |
| 885 |
|
%for events with a track with $\pt > 10~\GeV$ in addition to a selected |
| 961 |
|
% \end{center} |
| 962 |
|
%\end{figure} |
| 963 |
|
|
| 964 |
< |
% \subsection{Summary of uncertainties} |
| 926 |
< |
% \label{sec:bgunc-bottomline}. |
| 964 |
> |
|
| 965 |
|
|
| 966 |
|
% THIS NEEDS TO BE WRITTEN |
