| 1 |
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\section{Systematics Uncertainties in the Background Prediction} |
| 2 |
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\label{sec:systematics} |
| 3 |
< |
|
| 4 |
< |
The methodology for determining the systematics on the background |
| 5 |
< |
predictions has not changed with respect to the nominal analysis. |
| 6 |
< |
Because the template method has not changed, the same |
| 7 |
< |
systematic uncertainty is assessed on this prediction (32\%). |
| 8 |
< |
The 50\% uncertainty on the WZ and ZZ background is also unchanged. |
| 9 |
< |
The systematic uncertainty in the OF background prediction based on |
| 10 |
< |
e$\mu$ events has changed, due to the different composition of this |
| 11 |
< |
sample after vetoing events containing b-tagged jets. |
| 12 |
< |
|
| 13 |
< |
As in the nominal analysis, we do not require the e$\mu$ events |
| 14 |
< |
to satisfy the dilepton mass requirement and apply a scaling factor K, |
| 15 |
< |
extracted from MC, to account for the fraction of e$\mu$ events |
| 16 |
< |
which satisfy the dilepton mass requirement. This procedure is used |
| 17 |
< |
in order to improve the statistical precision of the OF background estimate. |
| 18 |
< |
|
| 19 |
< |
For the selection used in the nominal analysis, |
| 20 |
< |
the e$\mu$ sample is completely dominated by $t\bar{t}$ |
| 21 |
< |
events, and we observe that K is statistically consistent with constant with |
| 22 |
< |
respect to the \MET\ requirement. However, in this analysis, the $t\bar{t}$ |
| 23 |
< |
background is strongly suppressed by the b-veto, and hence the non-$t\bar{t}$ |
| 24 |
< |
backgrounds (specifically, $Z\to\tau\tau$ and VV) become more relevant. |
| 25 |
< |
At low \MET, the $Z\to\tau\tau$ background is pronounced, while $t\bar{t}$ |
| 26 |
< |
and VV dominate at high \MET\ (see App.~\ref{app:kinemu}). |
| 27 |
< |
Therefore, the sample composition changes |
| 28 |
< |
as the \MET\ requirement is varied, and as a result K depends |
| 29 |
< |
on the \MET\ requirement. |
| 30 |
< |
|
| 31 |
< |
We thus measure K in MC separately for each |
| 32 |
< |
\MET\ requirement, as displayed in Fig.~\ref{fig:kvmet} (left). |
| 33 |
< |
%The systematic uncertainty on K is determined separately for each \MET\ |
| 34 |
< |
%requirement by comparing the relative difference in K in data vs. MC. |
| 35 |
< |
The values of K used are the MC predictions |
| 36 |
< |
%and the total systematic uncertainty on the OF prediction |
| 37 |
< |
%as shown in |
| 38 |
< |
(Table \ref{fig:kvmettable}). |
| 39 |
< |
The contribution to the total OF prediction systematic uncertainty |
| 40 |
< |
from K is assessed from the ratio of K in data and MC, |
| 41 |
< |
shown in Fig.~\ref{fig:kvmet} (right). |
| 42 |
< |
The ratio is consistent with unity to roughly 17\%, |
| 43 |
< |
so we take this value as the systematic from K. |
| 44 |
< |
17\% added in quadrature with 7\% from |
| 45 |
< |
the electron to muon efficieny ratio |
| 46 |
< |
(as assessed in the inclusive analysis) |
| 47 |
< |
yields a total systematic of $\sim$18\% |
| 48 |
< |
which we round up to 20\%. |
| 49 |
< |
For \MET\ $>$ 150, there are no OF events in data inside the Z mass window |
| 50 |
< |
so we take a systematic based on the statistical uncertainty |
| 51 |
< |
of the MC prediction for K. |
| 52 |
< |
This value is 25\% for \MET\ $>$ 150 GeV and 60\% for \MET\ $>$ 200 GeV. |
| 53 |
< |
%Although we cannot check the value of K in data for \MET\ $>$ 150 |
| 54 |
< |
%because we find no OF events inside the Z mass window for this \MET\ |
| 55 |
< |
%cut, the overall OF yields with no dilepton mass requirement |
| 56 |
< |
%agree to roughly 20\% (9 data vs 7.0 $\pm$ 1.1 MC). |
| 57 |
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|
| 58 |
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|
| 59 |
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%Below Old |
| 60 |
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|
| 61 |
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%In reevaluating the systematics on the OF prediction, however, |
| 62 |
< |
%we observed a different behavior of K as a function of \MET\ |
| 63 |
< |
%as was seen in the inclusive analysis. |
| 64 |
< |
|
| 65 |
< |
%Recall that K is the ratio of the number of \emu\ events |
| 66 |
< |
%inside the Z window to the total number of \emu\ events. |
| 67 |
< |
%In the inclusive analysis, it is taken from \ttbar\ MC |
| 68 |
< |
%and used to scale the inclusive \emu\ yield in data. |
| 69 |
< |
%The yield scaled by K is then corrected for |
| 70 |
< |
%the $e$ vs $\mu$ efficiency difference to obtain the |
| 71 |
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%final OF prediction. |
| 72 |
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|
| 73 |
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%Based on the plot in figure \ref{fig:kvmet}, |
| 74 |
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%we choose to use a different |
| 75 |
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%K for each \MET\ cut and assess a systematic uncertainty |
| 76 |
< |
%on the OF prediction based on the difference between |
| 77 |
< |
%K in data and MC. |
| 78 |
< |
%The variation of K as a function of \MET\ is caused |
| 79 |
< |
%by a change in sample composition with increasing \MET. |
| 80 |
< |
%At \MET\ $<$ 60 GeV, the contribution of Z plus jets is |
| 81 |
< |
%not negligible (as it was in the inclusive analysis) |
| 82 |
< |
%because of the b veto. (See appendix \ref{app:kinemu}.) |
| 83 |
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%At higher \MET, \ttbar\ and diboson backgrounds dominate. |
| 1 |
> |
%\section{Systematics Uncertainties on the Background Prediction} |
| 2 |
> |
%\label{sec:systematics} |
| 3 |
|
|
| 4 |
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\subsection{Uncertainty on the \ttll\ Acceptance} |
| 5 |
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|
| 6 |
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The \ttbar\ background prediction is obtained from MC, with corrections |
| 7 |
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derived from control samples in data. The uncertainty associated with |
| 8 |
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the theoretical modeling of the \ttbar\ production and decay is |
| 9 |
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estimated by comparing the background predictions obtained using |
| 10 |
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alternative MC samples. It should be noted that the full analysis is |
| 11 |
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performed with the alternative samples under consideration, |
| 12 |
+ |
including the derivation of the various data-to-MC scale factors. |
| 13 |
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The variations considered are |
| 14 |
+ |
|
| 15 |
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\begin{itemize} |
| 16 |
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\item Top mass: The alternative values for the top mass differ |
| 17 |
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from the central value by $5~\GeV$: $m_{\mathrm{top}} = 178.5~\GeV$ and $m_{\mathrm{top}} |
| 18 |
+ |
= 166.5~\GeV$. |
| 19 |
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\item Jet-parton matching scale: This corresponds to variations in the |
| 20 |
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scale at which the Matrix Element partons from Madgraph are matched |
| 21 |
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to Parton Shower partons from Pythia. The nominal value is |
| 22 |
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$x_q>20~\GeV$. The alternative values used are $x_q>10~\GeV$ and |
| 23 |
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$x_q>40~\GeV$. |
| 24 |
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\item Renormalization and factorization scale: The alternative samples |
| 25 |
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correspond to variations in the scale $\times 2$ and $\times 0.5$. The nominal |
| 26 |
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value for the scale used is $Q^2 = m_{\mathrm{top}}^2 + |
| 27 |
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\sum_{\mathrm{jets}} \pt^2$. |
| 28 |
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\item Alternative generators: Samples produced with different |
| 29 |
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generators include MC@NLO and Powheg (NLO generators) and |
| 30 |
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Pythia (LO). It may also be noted that MC@NLO uses Herwig6 for the |
| 31 |
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hadronisation, while POWHEG uses Pythia6. |
| 32 |
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\item Modeling of taus: The alternative sample does not include |
| 33 |
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Tauola and is otherwise identical to the Powheg sample. |
| 34 |
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\item The PDF uncertainty is estimated following the PDF4LHC |
| 35 |
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recommendations[CITE]. The events are reweighted using alternative |
| 36 |
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PDF sets for CT10 and MSTW2008 and the uncertainties for each are derived using the |
| 37 |
+ |
alternative eigenvector variations and the ``master equation''. In |
| 38 |
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addition, the NNPDF2.1 set with 100 replicas. The central value is |
| 39 |
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determined from the mean and the uncertainty is derived from the |
| 40 |
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$1\sigma$ range. The overall uncertainty is derived from the envelope of the |
| 41 |
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alternative predictions and their uncertainties. |
| 42 |
+ |
\end{itemize} |
| 43 |
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|
| 44 |
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|
| 45 |
|
\begin{figure}[hbt] |
| 46 |
|
\begin{center} |
| 47 |
< |
\includegraphics[width=0.48\linewidth]{plots/kvmet_data_ttbm.pdf} |
| 91 |
< |
\includegraphics[width=0.48\linewidth]{plots/kvmet_ratio.pdf} |
| 47 |
> |
\includegraphics[width=0.8\linewidth]{plots/n_dl_syst_comp.png} |
| 48 |
|
\caption{ |
| 49 |
< |
\label{fig:kvmet}\protect |
| 50 |
< |
The left plot shows |
| 51 |
< |
K as a function of \MET\ in MC (red) and data (black). |
| 52 |
< |
The bin low edge corresponds to the \MET\ cut, and the |
| 53 |
< |
bins are inclusive. |
| 54 |
< |
The MC used is a sum of all SM MC used in the yield table of |
| 55 |
< |
section \ref{sec:yields}. |
| 56 |
< |
The right plot is the ratio of K in data to MC. |
| 57 |
< |
The ratio is fit to a line whose slope is consistent with zero |
| 58 |
< |
(the fit parameters are |
| 59 |
< |
0.9 $\pm$ 0.4 for the intercept and |
| 60 |
< |
0.001 $\pm$ 0.005 for the slope). |
| 61 |
< |
} |
| 62 |
< |
\end{center} |
| 63 |
< |
\end{figure} |
| 64 |
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|
| 65 |
< |
|
| 66 |
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|
| 67 |
< |
\begin{table}[htb] |
| 68 |
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\begin{center} |
| 69 |
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\caption{\label{fig:kvmettable} The values of K used in the OF background prediction. |
| 70 |
< |
The uncertainties shown are the total relative systematic used for the OF prediction, |
| 71 |
< |
which is the systematic uncertainty from K added in quadrature with |
| 72 |
< |
a 7\% uncertainty from the electron to muon efficieny ratio as assessed in the |
| 73 |
< |
inclusive analysis. |
| 74 |
< |
} |
| 75 |
< |
\begin{tabular}{lcc} |
| 76 |
< |
\hline |
| 77 |
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\MET\ Cut & K & Relative Systematic \\ |
| 78 |
< |
\hline |
| 79 |
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%the met zero row is used only for normalization of the money plot. |
| 80 |
< |
%0 & 0.1 & \\ |
| 81 |
< |
30 & 0.12 & 20\% \\ |
| 82 |
< |
60 & 0.13 & 20\% \\ |
| 83 |
< |
80 & 0.12 & 20\% \\ |
| 84 |
< |
100 & 0.12 & 20\% \\ |
| 85 |
< |
150 & 0.09 & 25\% \\ |
| 86 |
< |
200 & 0.06 & 60\% \\ |
| 87 |
< |
\hline |
| 88 |
< |
\end{tabular} |
| 89 |
< |
\end{center} |
| 90 |
< |
\end{table} |
| 49 |
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\label{fig:ttllsyst}%\protect |
| 50 |
> |
Central Prediction |
| 51 |
> |
Band: |
| 52 |
> |
- total stat. error for all Data and MC samples |
| 53 |
> |
- N jets scaling uncertainty (ISR/FSR) |
| 54 |
> |
Alternative Sample Predictions |
| 55 |
> |
Error bars: uncorrelated stat. error from alternative ttbar sample only} |
| 56 |
> |
\end{center} |
| 57 |
> |
\end{figure} |
| 58 |
> |
|
| 59 |
> |
|
| 60 |
> |
|
| 61 |
> |
% |
| 62 |
> |
% |
| 63 |
> |
%The methodology for determining the systematics on the background |
| 64 |
> |
%predictions has not changed with respect to the nominal analysis. |
| 65 |
> |
%Because the template method has not changed, the same |
| 66 |
> |
%systematic uncertainty is assessed on this prediction (32\%). |
| 67 |
> |
%The 50\% uncertainty on the WZ and ZZ background is also unchanged. |
| 68 |
> |
%The systematic uncertainty in the OF background prediction based on |
| 69 |
> |
%e$\mu$ events has changed, due to the different composition of this |
| 70 |
> |
%sample after vetoing events containing b-tagged jets. |
| 71 |
> |
% |
| 72 |
> |
%As in the nominal analysis, we do not require the e$\mu$ events |
| 73 |
> |
%to satisfy the dilepton mass requirement and apply a scaling factor K, |
| 74 |
> |
%extracted from MC, to account for the fraction of e$\mu$ events |
| 75 |
> |
%which satisfy the dilepton mass requirement. This procedure is used |
| 76 |
> |
%in order to improve the statistical precision of the OF background estimate. |
| 77 |
> |
% |
| 78 |
> |
%For the selection used in the nominal analysis, |
| 79 |
> |
%the e$\mu$ sample is completely dominated by $t\bar{t}$ |
| 80 |
> |
%events, and we observe that K is statistically consistent with constant with |
| 81 |
> |
%respect to the \MET\ requirement. However, in this analysis, the $t\bar{t}$ |
| 82 |
> |
%background is strongly suppressed by the b-veto, and hence the non-$t\bar{t}$ |
| 83 |
> |
%backgrounds (specifically, $Z\to\tau\tau$ and VV) become more relevant. |
| 84 |
> |
%At low \MET, the $Z\to\tau\tau$ background is pronounced, while $t\bar{t}$ |
| 85 |
> |
%and VV dominate at high \MET\ (see App.~\ref{app:kinemu}). |
| 86 |
> |
%Therefore, the sample composition changes |
| 87 |
> |
%as the \MET\ requirement is varied, and as a result K depends |
| 88 |
> |
%on the \MET\ requirement. |
| 89 |
> |
% |
| 90 |
> |
%We thus measure K in MC separately for each |
| 91 |
> |
%\MET\ requirement, as displayed in Fig.~\ref{fig:kvmet} (left). |
| 92 |
> |
%%The systematic uncertainty on K is determined separately for each \MET\ |
| 93 |
> |
%%requirement by comparing the relative difference in K in data vs. MC. |
| 94 |
> |
%The values of K used are the MC predictions |
| 95 |
> |
%%and the total systematic uncertainty on the OF prediction |
| 96 |
> |
%%as shown in |
| 97 |
> |
%(Table \ref{fig:kvmettable}). |
| 98 |
> |
%The contribution to the total OF prediction systematic uncertainty |
| 99 |
> |
%from K is assessed from the ratio of K in data and MC, |
| 100 |
> |
%shown in Fig.~\ref{fig:kvmet} (right). |
| 101 |
> |
%The ratio is consistent with unity to roughly 17\%, |
| 102 |
> |
%so we take this value as the systematic from K. |
| 103 |
> |
%17\% added in quadrature with 7\% from |
| 104 |
> |
%the electron to muon efficieny ratio |
| 105 |
> |
%(as assessed in the inclusive analysis) |
| 106 |
> |
%yields a total systematic of $\sim$18\% |
| 107 |
> |
%which we round up to 20\%. |
| 108 |
> |
%For \MET\ $>$ 150, there are no OF events in data inside the Z mass window |
| 109 |
> |
%so we take a systematic based on the statistical uncertainty |
| 110 |
> |
%of the MC prediction for K. |
| 111 |
> |
%This value is 25\% for \MET\ $>$ 150 GeV and 60\% for \MET\ $>$ 200 GeV. |
| 112 |
> |
%%Although we cannot check the value of K in data for \MET\ $>$ 150 |
| 113 |
> |
%%because we find no OF events inside the Z mass window for this \MET\ |
| 114 |
> |
%%cut, the overall OF yields with no dilepton mass requirement |
| 115 |
> |
%%agree to roughly 20\% (9 data vs 7.0 $\pm$ 1.1 MC). |
| 116 |
> |
% |
| 117 |
> |
% |
| 118 |
> |
%%Below Old |
| 119 |
> |
% |
| 120 |
> |
%%In reevaluating the systematics on the OF prediction, however, |
| 121 |
> |
%%we observed a different behavior of K as a function of \MET\ |
| 122 |
> |
%%as was seen in the inclusive analysis. |
| 123 |
> |
% |
| 124 |
> |
%%Recall that K is the ratio of the number of \emu\ events |
| 125 |
> |
%%inside the Z window to the total number of \emu\ events. |
| 126 |
> |
%%In the inclusive analysis, it is taken from \ttbar\ MC |
| 127 |
> |
%%and used to scale the inclusive \emu\ yield in data. |
| 128 |
> |
%%The yield scaled by K is then corrected for |
| 129 |
> |
%%the $e$ vs $\mu$ efficiency difference to obtain the |
| 130 |
> |
%%final OF prediction. |
| 131 |
> |
% |
| 132 |
> |
%%Based on the plot in figure \ref{fig:kvmet}, |
| 133 |
> |
%%we choose to use a different |
| 134 |
> |
%%K for each \MET\ cut and assess a systematic uncertainty |
| 135 |
> |
%%on the OF prediction based on the difference between |
| 136 |
> |
%%K in data and MC. |
| 137 |
> |
%%The variation of K as a function of \MET\ is caused |
| 138 |
> |
%%by a change in sample composition with increasing \MET. |
| 139 |
> |
%%At \MET\ $<$ 60 GeV, the contribution of Z plus jets is |
| 140 |
> |
%%not negligible (as it was in the inclusive analysis) |
| 141 |
> |
%%because of the b veto. (See appendix \ref{app:kinemu}.) |
| 142 |
> |
%%At higher \MET, \ttbar\ and diboson backgrounds dominate. |
| 143 |
> |
% |
| 144 |
> |
% |
| 145 |
> |
% |
| 146 |
> |
% |
| 147 |
> |
%\begin{figure}[hbt] |
| 148 |
> |
% \begin{center} |
| 149 |
> |
% \includegraphics[width=0.48\linewidth]{plots/kvmet_data_ttbm.pdf} |
| 150 |
> |
% \includegraphics[width=0.48\linewidth]{plots/kvmet_ratio.pdf} |
| 151 |
> |
% \caption{ |
| 152 |
> |
% \label{fig:kvmet}\protect |
| 153 |
> |
% The left plot shows |
| 154 |
> |
% K as a function of \MET\ in MC (red) and data (black). |
| 155 |
> |
% The bin low edge corresponds to the \MET\ cut, and the |
| 156 |
> |
% bins are inclusive. |
| 157 |
> |
% The MC used is a sum of all SM MC used in the yield table of |
| 158 |
> |
% section \ref{sec:yields}. |
| 159 |
> |
% The right plot is the ratio of K in data to MC. |
| 160 |
> |
% The ratio is fit to a line whose slope is consistent with zero |
| 161 |
> |
% (the fit parameters are |
| 162 |
> |
% 0.9 $\pm$ 0.4 for the intercept and |
| 163 |
> |
% 0.001 $\pm$ 0.005 for the slope). |
| 164 |
> |
% } |
| 165 |
> |
% \end{center} |
| 166 |
> |
%\end{figure} |
| 167 |
> |
% |
| 168 |
> |
% |
| 169 |
> |
% |
| 170 |
> |
%\begin{table}[htb] |
| 171 |
> |
%\begin{center} |
| 172 |
> |
%\caption{\label{fig:kvmettable} The values of K used in the OF background prediction. |
| 173 |
> |
%The uncertainties shown are the total relative systematic used for the OF prediction, |
| 174 |
> |
%which is the systematic uncertainty from K added in quadrature with |
| 175 |
> |
%a 7\% uncertainty from the electron to muon efficieny ratio as assessed in the |
| 176 |
> |
%inclusive analysis. |
| 177 |
> |
%} |
| 178 |
> |
%\begin{tabular}{lcc} |
| 179 |
> |
%\hline |
| 180 |
> |
%\MET\ Cut & K & Relative Systematic \\ |
| 181 |
> |
%\hline |
| 182 |
> |
%%the met zero row is used only for normalization of the money plot. |
| 183 |
> |
%%0 & 0.1 & \\ |
| 184 |
> |
%30 & 0.12 & 20\% \\ |
| 185 |
> |
%60 & 0.13 & 20\% \\ |
| 186 |
> |
%80 & 0.12 & 20\% \\ |
| 187 |
> |
%100 & 0.12 & 20\% \\ |
| 188 |
> |
%150 & 0.09 & 25\% \\ |
| 189 |
> |
%200 & 0.06 & 60\% \\ |
| 190 |
> |
%\hline |
| 191 |
> |
%\end{tabular} |
| 192 |
> |
%\end{center} |
| 193 |
> |
%\end{table} |
