| 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 |
| 30 |
< |
Section~\ref{sec:bgunc-bottomline}. |
| 31 |
< |
First, however, we discuss the uncertainties one-by-one and we comment |
| 28 |
> |
are carefully accounted for. |
| 29 |
> |
%%%TO ADD BACK IN IF WE HAVE SYSTEMATICS TABLE. |
| 30 |
> |
%The contribution to the overall |
| 31 |
> |
%uncertainty from each BG source is tabulated in |
| 32 |
> |
%Section~\ref{sec:bgunc-bottomline}. |
| 33 |
> |
Here we discuss the uncertainties one-by-one and comment |
| 34 |
|
on their impact on the overall result, at least to first order. |
| 35 |
|
Second order effects, such as the one described, are also included. |
| 36 |
|
|
| 39 |
|
These vary between 2\% and 20\%, depending on the signal region |
| 40 |
|
(different |
| 41 |
|
signal regions have different \met\ requirements, thus they also have |
| 42 |
< |
different $M_T$ regions used as control. |
| 42 |
> |
different $M_T$ regions used as control). |
| 43 |
|
Since |
| 44 |
< |
the major BG, eg, $t\bar{t}$ are normalized to the peak regions, this |
| 44 |
> |
the major backgrounds, eg, $t\bar{t}$ are normalized to the peak regions, this |
| 45 |
|
fractional uncertainty is pretty much carried through all the way to |
| 46 |
|
the end. There is also an uncertainty from the finite MC event counts |
| 47 |
|
in the $M_T$ peak regions. This is also included, but it is smaller. |
| 49 |
|
Normalizing to the $M_T$ peak has the distinct advantages that |
| 50 |
|
uncertainties on luminosity, cross-sections, trigger efficiency, |
| 51 |
|
lepton ID, cancel out. |
| 52 |
< |
For the low statistics regions with high \met requirements, the |
| 53 |
< |
price to pay in terms of event count statistical uncertainties starts |
| 52 |
> |
For the low statistics regions with high \met\ requirements, the |
| 53 |
> |
price to pay in terms of event count is that statistical uncertainties start |
| 54 |
|
to become significant. In the future we may consider a different |
| 55 |
|
normalization startegy in the low statistics regions. |
| 56 |
|
|
| 60 |
|
If the $M_T$ peak region is not well modelled, this would introduce an |
| 61 |
|
uncertainty. |
| 62 |
|
|
| 63 |
< |
We have tested this possibility by recalculating the post veto scale factors for a different |
| 63 |
> |
We have tested this possibility by recalculating the post-veto scale factors for a different |
| 64 |
|
choice |
| 65 |
|
of $M_T$ peak region ($40 < M_T < 100$ GeV instead of the default |
| 66 |
< |
$50 < M_T < 80$ GeV. This is shown in Table~\ref{tab:mtpeaksf2}. |
| 66 |
> |
$50 < M_T < 80$ GeV). This is shown in Table~\ref{tab:mtpeaksf2}. |
| 67 |
|
The two results for the scale factors are very compatible. |
| 68 |
|
We do not take any systematic uncertainty for this possible effect. |
| 69 |
|
|
| 113 |
|
\end{table} |
| 114 |
|
|
| 115 |
|
|
| 116 |
< |
\subsection{Uncertainty on the Wjets cross-section and the rare MC cross-sections} |
| 116 |
> |
\subsection{Uncertainty on the \wjets\ cross-section and the rare MC cross-sections} |
| 117 |
|
These are taken as 50\%, uncorrelated. |
| 118 |
|
The primary effect is to introduce a 50\% |
| 119 |
|
uncertainty |
| 127 |
|
scaled to the number of $t\bar{t}$ events in the peak, the $t\bar{t}$ |
| 128 |
|
BG goes down. |
| 129 |
|
|
| 130 |
< |
\subsection{Scale factors for the tail-to-peak ratios for lepton + |
| 130 |
> |
\subsection{Tail-to-peak ratios for lepton + |
| 131 |
|
jets top and W events} |
| 132 |
< |
These tail-to-peak ratios are described in Section~\ref{sec:ttp}. |
| 133 |
< |
They are studied in CR1 and CR2. The studies are described |
| 134 |
< |
in Sections~\ref{sec:cr1} and~\ref{sec:cr2}), respectively, where |
| 135 |
< |
we also give the uncertainty on the scale factors. See |
| 136 |
< |
Tables~\ref{tab:cr1yields} |
| 135 |
< |
and~\ref{tab:cr2yields}, scale factors $SFR_{wjet}$ and $SFR_{top})$. |
| 132 |
> |
The tail-to-peak ratios $R_{top}$ and $R_{wjet}$ are described in Section~\ref{sec:ttp}. |
| 133 |
> |
The data/MC scale factors are studied in CR1 and CR2 (Sections~\ref{sec:cr1} and~\ref{sec:cr2}). |
| 134 |
> |
Only the scale factor for \wjets, $SFR_{wjet}$, is used, and its uncertainty is given in Table~\ref{tab:cr1yields}). 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} |
| 167 |
|
|
| 168 |
|
\begin{itemize} |
| 169 |
|
\item Top mass: The alternative values for the top mass differ |
| 170 |
< |
from the central value by $5~\GeV$: $m_{\mathrm{top}} = 178.5~\GeV$ and $m_{\mathrm{top}} |
| 170 |
> |
from the central value by $6~\GeV$: $m_{\mathrm{top}} = 178.5~\GeV$ and $m_{\mathrm{top}} |
| 171 |
|
= 166.5~\GeV$. |
| 172 |
|
\item Jet-parton matching scale: This corresponds to variations in the |
| 173 |
|
scale at which the Matrix Element partons from Madgraph are matched |
| 184 |
|
Tauola and is otherwise identical to the Powheg sample. |
| 185 |
|
This effect was studied earlier using 7~TeV samples and found to be negligible. |
| 186 |
|
\item The PDF uncertainty is estimated following the PDF4LHC |
| 187 |
< |
recommendations[CITE]. The events are reweighted using alternative |
| 187 |
> |
recommendations. The events are reweighted using alternative |
| 188 |
|
PDF sets for CT10 and MSTW2008 and the uncertainties for each are derived using the |
| 189 |
< |
alternative eigenvector variations and the ``master equation''. In |
| 190 |
< |
addition, the NNPDF2.1 set with 100 replicas. The central value is |
| 189 |
> |
alternative eigenvector variations and the ``master equation''. |
| 190 |
> |
The NNPDF2.1 set with 100 replicas is also used. The central value is |
| 191 |
|
determined from the mean and the uncertainty is derived from the |
| 192 |
|
$1\sigma$ range. The overall uncertainty is derived from the envelope of the |
| 193 |
|
alternative predictions and their uncertainties. |
| 296 |
|
These are described below. |
| 297 |
|
|
| 298 |
|
The first piece of information is that the jet multiplicity in the scale |
| 299 |
< |
up/scale down sample is the most inconsistent with the data. This can be shown |
| 299 |
> |
up/scale down sample is the most inconsistent with the data. This is shown |
| 300 |
|
in Table~\ref{tab:njetskfactors_met100}, where we tabulate the |
| 301 |
< |
$K_3$ and $K_4$ factors of Section~\ref{tab:njetskfactors_met100} for |
| 301 |
> |
$K_3$ and $K_4$ factors of Section~\ref{sec:jetmultiplicity} for |
| 302 |
|
different \ttbar\ MC samples. The data/MC disagreement in the $N_{jets}$ |
| 303 |
|
distribution |
| 304 |
|
for the scale up/scale down samples is also shown in Fig.~\ref{fig:dileptonnjets_scaleup} |
| 363 |
|
samples in SRA and SRB. |
| 364 |
|
{\bf Thus, we take a 6\% systematic uncertainty, constant as a |
| 365 |
|
function of signal region, as the systematic due to alternative MC |
| 366 |
< |
models.}. |
| 366 |
> |
models.} |
| 367 |
|
Note that this 6\% is also consistent with the level at which we are |
| 368 |
|
able |
| 369 |
|
to test the closure of the method in CR5 for the high statistics |
| 600 |
|
$P_T > 10$ GeV in $|\eta| < 2.4$. This fraction is about 1/3, see |
| 601 |
|
Table~\ref{tab:trueisotrk}. |
| 602 |
|
The uncertainty for these events |
| 603 |
< |
is 6\% and is obtained from Tag and Probe studies of Section~\ref{sec:trkveto} |
| 603 |
> |
is 6\% and is obtained from tag-and-probe studies, see Section~\ref{sec:trkveto}. |
| 604 |
|
|
| 605 |
|
\begin{table}[!h] |
| 606 |
|
\begin{center} |
| 649 |
|
Second, hadronic tracks may undergo nuclear interactions and hence their tracks may not be reconstructed. |
| 650 |
|
As discussed above, independent studies show that the MC reproduces the hadronic tracking efficiency within 4\%, |
| 651 |
|
leading to a total background uncertainty of less than 0.5\% (after taking into account the fraction of the total background |
| 652 |
< |
due to hadronic $\tau$ decays with \pt\ $>$ 10 GeV tracks), and we hence regard this effect as neglgigible. |
| 652 |
> |
due to hadronic $\tau$ decays with \pt\ $>$ 10 GeV tracks), and we hence regard this effect as negligible. |
| 653 |
|
|
| 654 |
|
The tag-and-probe studies are performed in the full data sample, and compared with the DYJets madgraph sample. |
| 655 |
|
All events must contain a tag-probe pair (details below) with opposite-sign and satisfying the Z mass requirement 76--106 GeV. |
| 706 |
|
The absolute track isolation distributions for passing probes are displayed in Fig.~\ref{fig:tnp}. In general we observe |
| 707 |
|
good agreement between data and MC. To be more quantitative, we compare the data vs. MC efficiencies to satisfy |
| 708 |
|
absolute track isolation requirements varying from $>$ 1 GeV to $>$ 5 GeV, as summarized in Table~\ref{tab:isotrk}. |
| 709 |
< |
In the $\geq$0 and $\geq$1 jet bins where the efficiencies can be tested with statistical precision, the data and MC |
| 709 |
> |
In the $\geq 0$ and $\geq 1$ jet bins where the efficiencies can be tested with statistical precision, the data and MC |
| 710 |
|
efficiencies agree within 6\%, and we apply this as a systematic uncertainty on the isolated track veto efficiency. |
| 711 |
|
For the higher jet multiplicity bins the statistical precision decreases, but we do not observe any evidence for |
| 712 |
|
a data vs. MC discrepancy in the isolated track veto efficiency. |
| 739 |
|
|
| 740 |
|
\begin{table}[!ht] |
| 741 |
|
\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.} |
| 742 |
|
\begin{tabular}{l|c|c|c|c|c} |
| 743 |
|
|
| 744 |
|
%Electrons: |
| 836 |
|
\hline |
| 837 |
|
|
| 838 |
|
\end{tabular} |
| 839 |
+ |
\caption{\label{tab:isotrk} Comparison of the data vs. MC efficiencies to satisfy the indicated requirements |
| 840 |
+ |
on the absolute track isolation, and the ratio of these two efficiencies. Results are indicated separately for electrons and muons and for various |
| 841 |
+ |
jet multiplicity requirements.} |
| 842 |
|
\end{center} |
| 843 |
|
\end{table} |
| 844 |
|
|
