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%\section{Systematics Uncertainties on the Background Prediction} |
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%\label{sec:systematics} |
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\subsection{Uncertainty on the \ttll\ Acceptance} |
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In this Section we discuss the systematic uncertainty on the BG |
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prediction. This prediction is assembled from the event |
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counts in the peak region of the transverse mass distribution as |
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well as Monte Carlo |
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with a number of correction factors, as described previously. |
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The |
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final uncertainty on the prediction is built up from the uncertainties in these |
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individual |
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components. |
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The calculation is done for each signal |
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region, |
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for electrons and muons separately. |
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|
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The choice to normalize to the peak region of $M_T$ has the |
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advantage that some uncertainties, e.g., luminosity, cancel. |
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It does however introduce complications because it couples |
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some of the uncertainties in non-trivial ways. For example, |
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the primary effect of an uncertainty on the rare MC cross-section |
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is to introduce an uncertainty in the rare MC background estimate |
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which comes entirely from MC. But this uncertainty also affects, |
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for example, |
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the $t\bar{t} \to$ dilepton BG estimate because it changes the |
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$t\bar{t}$ normalization to the peak region (because some of the |
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events in the peak region are from rare processes). These effects |
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are carefully accounted for. The contribution to the overall |
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uncertainty from each background source is tabulated in |
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Section~\ref{sec:bgunc-bottomline}. |
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Here we discuss the uncertainties one-by-one and comment |
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on their impact on the overall result, at least to first order. |
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Second order effects, such as the one described, are also included. |
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|
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\subsection{Statistical uncertainties on the event counts in the $M_T$ |
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peak regions} |
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These vary between 2\% and 20\%, depending on the signal region |
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(different |
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signal regions have different \met\ requirements, thus they also have |
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different $M_T$ regions used as control). |
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Since |
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the major backgrounds, eg, $t\bar{t}$ are normalized to the peak regions, this |
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fractional uncertainty is pretty much carried through all the way to |
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the end. There is also an uncertainty from the finite MC event counts |
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in the $M_T$ peak regions. This is also included, but it is smaller. |
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|
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Normalizing to the $M_T$ peak has the distinct advantages that |
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uncertainties on luminosity, cross-sections, trigger efficiency, |
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lepton ID, cancel out. |
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For the low statistics regions with high \met\ requirements, the |
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price to pay in terms of event count is that statistical uncertainties start |
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to become significant. In the future we may consider a different |
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normalization startegy in the low statistics regions. |
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|
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\subsection{Uncertainty from the choice of $M_T$ peak region} |
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|
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This choice affects the scale factors of Table~\ref{tab:mtpeaksf}. |
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If the $M_T$ peak region is not well modelled, this would introduce an |
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uncertainty. |
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|
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We have tested this possibility by recalculating the post-veto scale factors for a different |
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choice |
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of $M_T$ peak region ($40 < M_T < 100$ GeV instead of the default |
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$50 < M_T < 80$ GeV). This is shown in Table~\ref{tab:mtpeaksf2}. |
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The two results for the scale factors are very compatible. |
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We do not take any systematic uncertainty for this possible effect. |
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|
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\begin{table}[!h] |
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\begin{center} |
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{\footnotesize |
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\begin{tabular}{l||c|c|c|c|c|c|c} |
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\hline |
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Sample & SRA & SRB & SRC & SRD & SRE & SRF & SRG\\ |
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\hline |
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\hline |
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\multicolumn{8}{c}{$50 \leq \mt \leq 80$} \\ |
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\hline |
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$\mu$ pre-veto \mt-SF & $1.02 \pm 0.02$ & $0.95 \pm 0.03$ & $0.90 \pm 0.05$ & $0.98 \pm 0.08$ & $0.97 \pm 0.13$ & $0.85 \pm 0.18$ & $0.92 \pm 0.31$ \\ |
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$\mu$ post-veto \mt-SF & $1.00 \pm 0.02$ & $0.95 \pm 0.03$ & $0.91 \pm 0.05$ & $1.00 \pm 0.09$ & $0.99 \pm 0.13$ & $0.85 \pm 0.18$ & $0.96 \pm 0.31$ \\ |
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\hline |
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$\mu$ veto \mt-SF & $0.98 \pm 0.01$ & $0.99 \pm 0.01$ & $1.01 \pm 0.02$ & $1.02 \pm 0.04$ & $1.02 \pm 0.06$ & $1.00 \pm 0.09$ & $1.04 \pm 0.11$ \\ |
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\hline |
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\hline |
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e pre-veto \mt-SF & $0.95 \pm 0.02$ & $0.95 \pm 0.03$ & $0.94 \pm 0.06$ & $0.85 \pm 0.09$ & $0.84 \pm 0.13$ & $1.05 \pm 0.23$ & $1.04 \pm 0.33$ \\ |
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e post-veto \mt-SF & $0.92 \pm 0.02$ & $0.91 \pm 0.03$ & $0.91 \pm 0.06$ & $0.74 \pm 0.08$ & $0.75 \pm 0.13$ & $0.91 \pm 0.22$ & $1.01 \pm 0.33$ \\ |
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\hline |
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e veto \mt-SF & $0.97 \pm 0.01$ & $0.96 \pm 0.02$ & $0.97 \pm 0.03$ & $0.87 \pm 0.05$ & $0.89 \pm 0.08$ & $0.86 \pm 0.11$ & $0.97 \pm 0.14$ \\ |
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\hline |
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\hline |
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\multicolumn{8}{c}{$40 \leq \mt \leq 100$} \\ |
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\hline |
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$\mu$ pre-veto \mt-SF & $1.02 \pm 0.01$ & $0.97 \pm 0.02$ & $0.91 \pm 0.05$ & $0.95 \pm 0.06$ & $0.97 \pm 0.10$ & $0.80 \pm 0.14$ & $0.74 \pm 0.22$ \\ |
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$\mu$ post-veto \mt-SF & $1.00 \pm 0.01$ & $0.96 \pm 0.02$ & $0.90 \pm 0.04$ & $0.98 \pm 0.07$ & $1.00 \pm 0.11$ & $0.80 \pm 0.15$ & $0.81 \pm 0.24$ \\ |
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\hline |
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$\mu$ veto \mt-SF & $0.98 \pm 0.01$ & $0.99 \pm 0.01$ & $0.99 \pm 0.02$ & $1.03 \pm 0.03$ & $1.03 \pm 0.05$ & $1.01 \pm 0.08$ & $1.09 \pm 0.09$ \\ |
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\hline |
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\hline |
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e pre-veto \mt-SF & $0.97 \pm 0.01$ & $0.93 \pm 0.02$ & $0.94 \pm 0.04$ & $0.81 \pm 0.06$ & $0.86 \pm 0.10$ & $0.95 \pm 0.17$ & $1.06 \pm 0.26$ \\ |
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e post-veto \mt-SF & $0.94 \pm 0.01$ & $0.91 \pm 0.02$ & $0.91 \pm 0.04$ & $0.71 \pm 0.06$ & $0.82 \pm 0.10$ & $0.93 \pm 0.17$ & $1.09 \pm 0.27$ \\ |
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\hline |
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e veto \mt-SF & $0.97 \pm 0.01$ & $0.98 \pm 0.01$ & $0.97 \pm 0.02$ & $0.88 \pm 0.04$ & $0.95 \pm 0.06$ & $0.98 \pm 0.08$ & $1.03 \pm 0.09$ \\ |
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\hline |
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\end{tabular}} |
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\caption{ \mt\ peak Data/MC scale factors. The pre-veto SFs are applied to the |
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\ttdl\ sample, while the post-veto SFs are applied to the single |
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lepton samples. The veto SF is shown for comparison across channels. |
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The raw MC is used for backgrounds from rare processes. |
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The uncertainties are statistical only. |
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\label{tab:mtpeaksf2}} |
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\end{center} |
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\end{table} |
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|
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|
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\subsection{Uncertainty on the \wjets\ cross-section and the rare MC cross-sections} |
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These are taken as 50\%, uncorrelated. |
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The primary effect is to introduce a 50\% |
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uncertainty |
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on the $W +$ jets and rare BG |
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background predictions, respectively. However they also |
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have an effect on the other BGs via the $M_T$ peak normalization |
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in a way that tends to reduce the uncertainty. This is easy |
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to understand: if the $W$ cross-section is increased by 50\%, then |
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the $W$ background goes up. But the number of $M_T$ peak events |
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attributed to $t\bar{t}$ goes down, and since the $t\bar{t}$ BG is |
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scaled to the number of $t\bar{t}$ events in the peak, the $t\bar{t}$ |
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BG goes down. |
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|
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\subsection{Tail-to-peak ratios for lepton + |
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jets top and W events} |
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The tail-to-peak ratios $R_{top}$ and $R_{wjet}$ are described in Section~\ref{sec:ttp}. |
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The data/MC scale factors are studied in CR1 and CR2 (Sections~\ref{sec:cr1} and~\ref{sec:cr2}). |
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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 $R_{top}$. |
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The additional systematic uncertainty on $R_{top}$ from the variation between optimistic and pessimistic scenarios is given in Section~\ref{sec:ttp}. |
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|
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|
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\subsection{Uncertainty on extra jet radiation for dilepton |
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background} |
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As discussed in Section~\ref{sec:jetmultiplicity}, the |
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jet distribution in |
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$t\bar{t} \to$ |
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dilepton MC is rescaled by the factors $K_3$ and $K_4$ to make |
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it agree with the data. The 3\% uncertainties on $K_3$ and $K_4$ |
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comes from data/MC statistics. This |
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results directly in a 3\% uncertainty on the dilepton background, which is by far |
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the most important one. |
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|
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\subsection{Uncertainty from MC statistics} |
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This affects mostly the \ttll\ background estimate, which is taken |
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from |
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Monte Carlo with appropriate correction factors. This uncertainty |
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is negligible in the low \met\ signal regions, and grows to about |
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15\% in SRG. |
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|
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|
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\subsection{Uncertainty on the \ttll\ Background} |
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|
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The \ttbar\ background prediction is obtained from MC, with corrections |
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derived from control samples in data. The uncertainty associated with |
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the \ttbar\ background is derived from the level of closure of the |
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background prediction in CR4 (Table~\ref{tab:cr4yields}) and |
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CR5 (Table~\ref{tab:cr5yields}). The results from these control region |
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checks are shown in Figure~\ref{fig:ttdlunc}. The uncertainties assigned |
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to the \ttdl\ background prediction based on these tests are |
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5\% (SRA), 10\% (SRB), 15\% (SRC), 25\% (SRD), 40\% (SRE-G). |
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|
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\begin{figure}[hbt] |
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\begin{center} |
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\includegraphics[width=0.6\linewidth]{plots/ttdilepton_uncertainty.pdf} |
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\caption{ |
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\label{fig:ttdlunc}%\protect |
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Results of the comparison of yields in the \mt\ tail comparing the MC prediction (after |
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applying SFs) to data for CR4 and CR5 for all the signal |
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region requirements considered (A-G). The bands indicate the |
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systematic uncertainties assigned based on these tests, |
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ranging from $5\%$ for SRA to $40\%$ for SRE-G.} |
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\end{center} |
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\end{figure} |
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|
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|
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\subsubsection{Check of the uncertainty on the \ttll\ Acceptance} |
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|
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The uncertainty associated with |
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the theoretical modeling of the \ttbar\ production and decay is |
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estimated by comparing the background predictions obtained using |
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checked by comparing the background predictions obtained using |
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alternative MC samples. It should be noted that the full analysis is |
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performed with the alternative samples under consideration, |
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including the derivation of the various data-to-MC scale factors. |
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|
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\begin{itemize} |
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\item Top mass: The alternative values for the top mass differ |
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from the central value by $5~\GeV$: $m_{\mathrm{top}} = 178.5~\GeV$ and $m_{\mathrm{top}} |
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from the central value by $6~\GeV$: $m_{\mathrm{top}} = 178.5~\GeV$ and $m_{\mathrm{top}} |
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= 166.5~\GeV$. |
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\item Jet-parton matching scale: This corresponds to variations in the |
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scale at which the Matrix Element partons from Madgraph are matched |
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value for the scale used is $Q^2 = m_{\mathrm{top}}^2 + |
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\sum_{\mathrm{jets}} \pt^2$. |
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\item Alternative generators: Samples produced with different |
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generators include MC@NLO and Powheg (NLO generators) and |
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Pythia (LO). It may also be noted that MC@NLO uses Herwig6 for the |
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hadronisation, while POWHEG uses Pythia6. |
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generators, Powheg (our default) and Madgraph. |
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\item Modeling of taus: The alternative sample does not include |
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Tauola and is otherwise identical to the Powheg sample. |
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Tauola and is otherwise identical to the Powheg sample. |
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This effect was studied earlier using 7~TeV samples and found to be negligible. |
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\item The PDF uncertainty is estimated following the PDF4LHC |
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recommendations[CITE]. The events are reweighted using alternative |
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recommendations. The events are reweighted using alternative |
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PDF sets for CT10 and MSTW2008 and the uncertainties for each are derived using the |
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alternative eigenvector variations and the ``master equation''. In |
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addition, the NNPDF2.1 set with 100 replicas. The central value is |
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alternative eigenvector variations and the ``master equation''. |
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The NNPDF2.1 set with 100 replicas is also used. The central value is |
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determined from the mean and the uncertainty is derived from the |
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$1\sigma$ range. The overall uncertainty is derived from the envelope of the |
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alternative predictions and their uncertainties. |
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\end{itemize} |
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|
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alternative predictions and their uncertainties. |
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This effect was studied earlier using 7~TeV samples and found to be negligible. |
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\end{itemize} |
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|
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\begin{figure}[hbt] |
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\begin{center} |
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\includegraphics[width=0.8\linewidth]{plots/n_dl_syst_comp.png} |
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\includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRA.pdf}% |
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\includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRB.pdf} |
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\includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRC.pdf}% |
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\includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRD.pdf} |
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\includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRE.pdf} |
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\caption{ |
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\label{fig:ttllsyst}%\protect |
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\label{fig:ttllsyst}\protect |
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Comparison of the \ttll\ central prediction with those using |
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alternative MC samples. The blue band corresponds to the |
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total statistical error for all data and MC samples. The |
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alternative sample predictions are indicated by the |
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datapoints. The uncertainties on the alternative predictions |
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correspond to the uncorrelated statistical uncertainty from |
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the size of the alternative sample only.} |
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the size of the alternative sample only. Note the |
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suppressed vertical scales.} |
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\end{center} |
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\end{figure} |
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|
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|
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\begin{table}[!h] |
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\begin{center} |
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{\footnotesize |
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\begin{tabular}{l||c|c|c|c|c|c|c} |
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\hline |
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$\Delta/N$ [\%] & Madgraph & Mass Up & Mass Down & Scale Up & Scale Down & |
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Match Up & Match Down \\ |
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\hline |
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+ |
\hline |
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SRA & $2$ & $2$ & $5$ & $12$ & $7$ & $0$ & $2$ \\ |
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+ |
\hline |
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SRB & $6$ & $0$ & $6$ & $5$ & $12$ & $5$ & $6$ \\ |
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+ |
\hline |
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% SRC & $10$ & $3$ & $2$ & $12$ & $14$ & $16$ & $4$ \\ |
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% \hline |
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% SRD & $10$ & $6$ & $6$ & $21$ & $15$ & $19$ & $0$ \\ |
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% \hline |
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% SRE & $6$ & $17$ & $15$ & $2$ & $12$ & $17$ & $8$ \\ |
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\hline |
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\end{tabular}} |
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\caption{ Relative difference in \ttdl\ predictions for alternative MC |
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samples in |
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the higher statistics regions SRA and SRB. These differences |
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are based on the central values of the predictions. For a fuller |
| 264 |
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picture |
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of the situation, including statistical uncertainites, see Fig.~\ref{fig:ttllsyst}. |
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\label{tab:fracdiff}} |
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\end{center} |
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\end{table} |
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|
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|
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In Fig.~\ref{fig:ttllsyst} we compare the alternate MC \ttll\ background predictions |
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for regions A through E. We can make the following observations based |
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on this Figure. |
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|
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\begin{itemize} |
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\item In the tighter signal regions we are running out of |
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statistics. |
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\item Within the limited statistics, there is no evidence that the |
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situation changes as we go from signal region A to signal region E. |
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Therefore, we assess a systematic based on the relatively high |
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statistics |
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test in signal region A, and apply the same systematic uncertainty |
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to all other regions. |
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\item In order to fully (as opposed as 1$\sigma$) cover the |
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alternative MC variations in region A we would have to take a |
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systematic |
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uncertainty of $\approx 10\%$. This would be driven by the |
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scale up/scale down variations, see Table~\ref{tab:fracdiff}. |
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\end{itemize} |
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|
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\begin{table}[!ht] |
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\begin{center} |
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\begin{tabular}{l|c|c} |
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\hline |
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Sample |
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& K3 & K4\\ |
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\hline |
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\hline |
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Powheg & $1.01 \pm 0.03$ & $0.93 \pm 0.04$ \\ |
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Madgraph & $1.01 \pm 0.04$ & $0.92 \pm 0.04$ \\ |
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Mass Up & $1.00 \pm 0.04$ & $0.92 \pm 0.04$ \\ |
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Mass Down & $1.06 \pm 0.04$ & $0.99 \pm 0.05$ \\ |
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Scale Up & $1.14 \pm 0.04$ & $1.23 \pm 0.06$ \\ |
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Scale Down & $0.89 \pm 0.03$ & $0.74 \pm 0.03$ \\ |
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Match Up & $1.02 \pm 0.04$ & $0.97 \pm 0.04$ \\ |
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Match Down & $1.02 \pm 0.04$ & $0.91 \pm 0.04$ \\ |
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\hline |
| 308 |
+ |
\end{tabular} |
| 309 |
+ |
\caption{$\met>100$ GeV: Data/MC scale factors used to account for differences in the |
| 310 |
+ |
fraction of events with additional hard jets from radiation in |
| 311 |
+ |
\ttll\ events. \label{tab:njetskfactors_met100}} |
| 312 |
+ |
\end{center} |
| 313 |
+ |
\end{table} |
| 314 |
+ |
|
| 315 |
+ |
|
| 316 |
+ |
However, we have two pieces of information indicating that the |
| 317 |
+ |
scale up/scale down variations are inconsistent with the data. |
| 318 |
+ |
These are described below. |
| 319 |
+ |
|
| 320 |
+ |
The first piece of information is that the jet multiplicity in the scale |
| 321 |
+ |
up/scale down sample is the most inconsistent with the data. This is shown |
| 322 |
+ |
in Table~\ref{tab:njetskfactors_met100}, where we tabulate the |
| 323 |
+ |
$K_3$ and $K_4$ factors of Section~\ref{sec:jetmultiplicity} for |
| 324 |
+ |
different \ttbar\ MC samples. The data/MC disagreement in the $N_{jets}$ |
| 325 |
+ |
distribution |
| 326 |
+ |
for the scale up/scale down samples is also shown in Fig.~\ref{fig:dileptonnjets_scaleup} |
| 327 |
+ |
and~\ref{fig:dileptonnjets_scaledw}. This should be compared with the |
| 328 |
+ |
equivalent $N_{jets}$ plots for the default Powheg MC, see |
| 329 |
+ |
Fig.~\ref{fig:dileptonnjets}, which agrees much better with data. |
| 330 |
+ |
|
| 331 |
+ |
\begin{figure}[hbt] |
| 332 |
+ |
\begin{center} |
| 333 |
+ |
\includegraphics[width=0.5\linewidth]{plots/njets_all_met50_mueg_scaleup.pdf} |
| 334 |
+ |
\includegraphics[width=0.5\linewidth]{plots/njets_all_met50_diel_scaleup.pdf}% |
| 335 |
+ |
\includegraphics[width=0.5\linewidth]{plots/njets_all_met50_dimu_scaleup.pdf} |
| 336 |
+ |
\caption{ |
| 337 |
+ |
\label{fig:dileptonnjets_scaleup}%\protect |
| 338 |
+ |
SCALE UP: Comparison of the jet multiplicity distribution in data and MC for dilepton events in the \E-\M\ |
| 339 |
+ |
(top), \E-\E\ (bottom left) and \M-\M\ (bottom right) channels.} |
| 340 |
+ |
\end{center} |
| 341 |
+ |
\end{figure} |
| 342 |
+ |
|
| 343 |
+ |
\begin{figure}[hbt] |
| 344 |
+ |
\begin{center} |
| 345 |
+ |
\includegraphics[width=0.5\linewidth]{plots/njets_all_met50_mueg_scaledw.pdf} |
| 346 |
+ |
\includegraphics[width=0.5\linewidth]{plots/njets_all_met50_diel_scaledw.pdf}% |
| 347 |
+ |
\includegraphics[width=0.5\linewidth]{plots/njets_all_met50_dimu_scaledw.pdf} |
| 348 |
+ |
\caption{ |
| 349 |
+ |
\label{fig:dileptonnjets_scaledw}%\protect |
| 350 |
+ |
SCALE DOWN: Comparison of the jet multiplicity distribution in data and MC for dilepton events in the \E-\M\ |
| 351 |
+ |
(top), \E-\E\ (bottom left) and \M-\M\ (bottom right) channels.} |
| 352 |
+ |
\end{center} |
| 353 |
+ |
\end{figure} |
| 354 |
+ |
|
| 355 |
+ |
|
| 356 |
+ |
\clearpage |
| 357 |
+ |
|
| 358 |
+ |
The second piece of information is that we have performed closure |
| 359 |
+ |
tests in CR5 using the alternative MC samples. These are exactly |
| 360 |
+ |
the same tests as the one performed in Section~\ref{sec:CR5} on the |
| 361 |
+ |
Powheg sample. As we argued previously, this is a very powerful |
| 362 |
+ |
test of the background calculation. |
| 363 |
+ |
The results of this test are summarized in Table~\ref{tab:hugecr5yields}. |
| 364 |
+ |
Concentrating on the relatively high statistics CR5A region, we see |
| 365 |
+ |
for all \ttbar\ MC samples except scale up/scale down we obtain |
| 366 |
+ |
closure within 1$\sigma$. The scale up/scale down tests closes |
| 367 |
+ |
worse, only within 2$\sigma$. This again is evidence that the |
| 368 |
+ |
scale up/scale down variations are in disagreement with the data. |
| 369 |
+ |
|
| 370 |
+ |
\input{hugeCR5Table.tex} |
| 371 |
+ |
|
| 372 |
+ |
Based on the two observations above, we argue that the MC |
| 373 |
+ |
scale up/scale down variations are too extreme. We feel that |
| 374 |
+ |
a reasonable choice would be to take one-half of the scale up/scale |
| 375 |
+ |
down variations in our MC. This factor of 1/2 would then bring |
| 376 |
+ |
the discrepancy in the closure test of |
| 377 |
+ |
Table~\ref{tab:hugecr5yields} for the scale up/scale down variations |
| 378 |
+ |
from about 2$\sigma$ to about 1$\sigma$. |
| 379 |
+ |
|
| 380 |
+ |
Then, going back to Table~\ref{tab:fracdiff}, and reducing the scale |
| 381 |
+ |
up/scale |
| 382 |
+ |
down variations by a factor 2, we can see that a systematic |
| 383 |
+ |
uncertainty |
| 384 |
+ |
of 6\% would fully cover all of the variations from different MC |
| 385 |
+ |
samples in SRA and SRB. |
| 386 |
+ |
The alternative MC models indicate that a 6\% systematic uncertainty to |
| 387 |
+ |
cover the range of reasonable variations. |
| 388 |
+ |
Note that this 6\% is also consistent with the level at which we are |
| 389 |
+ |
able to test the closure of the method with alternative samples in CR5 for the high statistics |
| 390 |
+ |
regions (Table~\ref{tab:hugecr5yields}). |
| 391 |
+ |
The range of reasonable variations obtained with the alternative |
| 392 |
+ |
samples are consistent with the uncertainties assigned for |
| 393 |
+ |
the \ttll\ background based on the closure of the background |
| 394 |
+ |
predictions and data in CR4 and CR5. |
| 395 |
+ |
|
| 396 |
+ |
|
| 397 |
+ |
|
| 398 |
+ |
|
| 399 |
+ |
|
| 400 |
+ |
%\begin{table}[!h] |
| 401 |
+ |
%\begin{center} |
| 402 |
+ |
%{\footnotesize |
| 403 |
+ |
%\begin{tabular}{l||c||c|c|c|c|c|c|c} |
| 404 |
+ |
%\hline |
| 405 |
+ |
%Sample & Powheg & Madgraph & Mass Up & Mass Down & Scale |
| 406 |
+ |
%Up & Scale Down & |
| 407 |
+ |
%Match Up & Match Down \\ |
| 408 |
+ |
%\hline |
| 409 |
+ |
%\hline |
| 410 |
+ |
%SRA & $579 \pm 10$ & $569 \pm 16$ & $591 \pm 18$ & $610 \pm 22$ & $651 \pm 22$ & $537 \pm 16$ & $578 \pm 18$ & $570 \pm 17$ \\ |
| 411 |
+ |
%\hline |
| 412 |
+ |
%SRB & $328 \pm 7$ & $307 \pm 11$ & $329 \pm 13$ & $348 \pm 15$ & $344 \pm 15$ & $287 \pm 10$ & $313 \pm 13$ & $307 \pm 12$ \\ |
| 413 |
+ |
%\hline |
| 414 |
+ |
%SRC & $111 \pm 4$ & $99 \pm 5$ & $107 \pm 7$ & $113 \pm 8$ & $124 \pm 8$ & $95 \pm 6$ & $93 \pm 6$ & $106 \pm 6$ \\ |
| 415 |
+ |
%\hline |
| 416 |
+ |
%SRD & $39 \pm 2$ & $35 \pm 3$ & $41 \pm 4$ & $41 \pm 5$ & $47 \pm 5$ & $33 \pm 3$ & $31 \pm 3$ & $39 \pm 4$ \\ |
| 417 |
+ |
%\hline |
| 418 |
+ |
%SRE & $14 \pm 1$ & $15 \pm 2$ & $17 \pm 3$ & $12 \pm 3$ & $15 \pm 3$ & $13 \pm 2$ & $12 \pm 2$ & $16 \pm 2$ \\ |
| 419 |
+ |
%\hline |
| 420 |
+ |
%\end{tabular}} |
| 421 |
+ |
%\caption{ \ttdl\ predictions for alternative MC samples. The uncertainties are statistical only. |
| 422 |
+ |
%\label{tab:ttdlalt}} |
| 423 |
+ |
%\end{center} |
| 424 |
+ |
%\end{table} |
| 425 |
+ |
|
| 426 |
+ |
|
| 427 |
+ |
|
| 428 |
+ |
|
| 429 |
+ |
%\begin{table}[!h] |
| 430 |
+ |
%\begin{center} |
| 431 |
+ |
%{\footnotesize |
| 432 |
+ |
%\begin{tabular}{l||c|c|c|c|c|c|c} |
| 433 |
+ |
%\hline |
| 434 |
+ |
%$N \sigma$ & Madgraph & Mass Up & Mass Down & Scale Up & Scale Down & |
| 435 |
+ |
%Match Up & Match Down \\ |
| 436 |
+ |
%\hline |
| 437 |
+ |
%\hline |
| 438 |
+ |
%SRA & $0.38$ & $0.42$ & $1.02$ & $2.34$ & $1.58$ & $0.01$ & $0.33$ \\ |
| 439 |
+ |
%\hline |
| 440 |
+ |
%SRB & $1.17$ & $0.07$ & $0.98$ & $0.76$ & $2.29$ & $0.78$ & $1.11$ \\ |
| 441 |
+ |
%\hline |
| 442 |
+ |
%SRC & $1.33$ & $0.37$ & $0.26$ & $1.24$ & $1.82$ & $1.97$ & $0.54$ \\ |
| 443 |
+ |
%\hline |
| 444 |
+ |
%SRD & $0.82$ & $0.46$ & $0.38$ & $1.32$ & $1.27$ & $1.47$ & $0.00$ \\ |
| 445 |
+ |
%\hline |
| 446 |
+ |
%SRE & $0.32$ & $0.75$ & $0.66$ & $0.07$ & $0.66$ & $0.83$ & $0.38$ \\ |
| 447 |
+ |
%\hline |
| 448 |
+ |
%\end{tabular}} |
| 449 |
+ |
%\caption{ N $\sigma$ difference in \ttdl\ predictions for alternative MC samples. |
| 450 |
+ |
%\label{tab:nsig}} |
| 451 |
+ |
%\end{center} |
| 452 |
+ |
%\end{table} |
| 453 |
+ |
|
| 454 |
+ |
|
| 455 |
+ |
%\begin{table}[!h] |
| 456 |
+ |
%\begin{center} |
| 457 |
+ |
%\begin{tabular}{l||c|c|c|c} |
| 458 |
+ |
%\hline |
| 459 |
+ |
%Av. $\Delta$ Evt. & Alt. Gen. & $\Delta$ Mass & $\Delta$ Scale |
| 460 |
+ |
%& $\Delta$ Match \\ |
| 461 |
+ |
%\hline |
| 462 |
+ |
%\hline |
| 463 |
+ |
%SRA & $5.0$ ($1\%$) & $9.6$ ($2\%$) & $56.8$ ($10\%$) & $4.4$ ($1\%$) \\ |
| 464 |
+ |
%\hline |
| 465 |
+ |
%SRB & $10.4$ ($3\%$) & $9.6$ ($3\%$) & $28.2$ ($9\%$) & $2.8$ ($1\%$) \\ |
| 466 |
+ |
%\hline |
| 467 |
+ |
%SRC & $5.7$ ($5\%$) & $3.1$ ($3\%$) & $14.5$ ($13\%$) & $6.4$ ($6\%$) \\ |
| 468 |
+ |
%\hline |
| 469 |
+ |
%SRD & $1.9$ ($5\%$) & $0.1$ ($0\%$) & $6.9$ ($18\%$) & $3.6$ ($9\%$) \\ |
| 470 |
+ |
%\hline |
| 471 |
+ |
%SRE & $0.5$ ($3\%$) & $2.3$ ($16\%$) & $1.0$ ($7\%$) & $1.8$ ($12\%$) \\ |
| 472 |
+ |
%\hline |
| 473 |
+ |
%\end{tabular} |
| 474 |
+ |
%\caption{ Av. difference in \ttdl\ events for alternative sample pairs. |
| 475 |
+ |
%\label{tab:devt}} |
| 476 |
+ |
%\end{center} |
| 477 |
+ |
%\end{table} |
| 478 |
+ |
|
| 479 |
+ |
|
| 480 |
+ |
|
| 481 |
+ |
\clearpage |
| 482 |
|
|
| 483 |
|
% |
| 484 |
|
% |
| 613 |
|
%\end{tabular} |
| 614 |
|
%\end{center} |
| 615 |
|
%\end{table} |
| 616 |
+ |
|
| 617 |
+ |
\subsection{Uncertainty from the isolated track veto} |
| 618 |
+ |
This is the uncertainty associated with how well the isolated track |
| 619 |
+ |
veto performance is modeled by the Monte Carlo. This uncertainty |
| 620 |
+ |
only applies to the fraction of dilepton BG events that have |
| 621 |
+ |
a second e/$\mu$ or a one prong $\tau \to h$, with |
| 622 |
+ |
$P_T > 10$ GeV in $|\eta| < 2.4$. This fraction is about 1/3, see |
| 623 |
+ |
Table~\ref{tab:trueisotrk}. |
| 624 |
+ |
The uncertainty for these events |
| 625 |
+ |
is 6\% and is obtained from tag-and-probe studies, see Section~\ref{sec:trkveto}. |
| 626 |
+ |
|
| 627 |
+ |
\begin{table}[!h] |
| 628 |
+ |
\begin{center} |
| 629 |
+ |
{\footnotesize |
| 630 |
+ |
\begin{tabular}{l||c|c|c|c|c|c|c} |
| 631 |
+ |
\hline |
| 632 |
+ |
Sample & SRA & SRB & SRC & SRD & SRE & SRF & SRG \\ |
| 633 |
+ |
\hline |
| 634 |
+ |
\hline |
| 635 |
+ |
$\mu$ Frac. \ttdl\ with true iso. trk. & $0.32 \pm 0.03$ & $0.30 \pm 0.03$ & $0.32 \pm 0.06$ & $0.34 \pm 0.10$ & $0.35 \pm 0.16$ & $0.40 \pm 0.24$ & $0.50 \pm 0.32$ \\ |
| 636 |
+ |
\hline |
| 637 |
+ |
\hline |
| 638 |
+ |
e Frac. \ttdl\ with true iso. trk. & $0.32 \pm 0.03$ & $0.31 \pm 0.04$ & $0.33 \pm 0.06$ & $0.38 \pm 0.11$ & $0.38 \pm 0.19$ & $0.60 \pm 0.31$ & $0.61 \pm 0.45$ \\ |
| 639 |
+ |
\hline |
| 640 |
+ |
\end{tabular}} |
| 641 |
+ |
\caption{ Fraction of \ttdl\ events with a true isolated track. |
| 642 |
+ |
\label{tab:trueisotrk}} |
| 643 |
+ |
\end{center} |
| 644 |
+ |
\end{table} |
| 645 |
+ |
|
| 646 |
+ |
\subsubsection{Isolated Track Veto: Tag and Probe Studies} |
| 647 |
+ |
\label{sec:trkveto} |
| 648 |
+ |
|
| 649 |
+ |
|
| 650 |
+ |
In this section we compare the performance of the isolated track veto in data and MC using tag-and-probe studies |
| 651 |
+ |
with samples of Z$\to$ee and Z$\to\mu\mu$. The purpose of these studies is to demonstrate that the efficiency |
| 652 |
+ |
to satisfy the isolated track veto requirements is well-reproduced in the MC, since if this were not the case |
| 653 |
+ |
we would need to apply a data-to-MC scale factor in order to correctly |
| 654 |
+ |
predict the \ttll\ background. |
| 655 |
+ |
|
| 656 |
+ |
This study |
| 657 |
+ |
addresses possible data vs. MC discrepancies for the {\bf efficiency} to identify (and reject) events with a |
| 658 |
+ |
second {\bf genuine} lepton (e, $\mu$, or $\tau\to$1-prong). It does not address possible data vs. MC discrepancies |
| 659 |
+ |
in the fake rate for rejecting events without a second genuine lepton; this is handled separately in the top normalization |
| 660 |
+ |
procedure by scaling the \ttlj\ contribution to match the data in the \mt\ peak after applying the isolated track veto. |
| 661 |
+ |
|
| 662 |
+ |
Furthermore, we test the data and MC |
| 663 |
+ |
isolated track veto efficiencies for electrons and muons since we are using a Z tag-and-probe technique, but we do not |
| 664 |
+ |
directly test the performance for hadronic tracks from $\tau$ decays. The performance for hadronic $\tau$ decay products |
| 665 |
+ |
may differ from that of electrons and muons for two reasons. First, the $\tau$ may decay to a hadronic track plus one |
| 666 |
+ |
or two $\pi^0$'s, which may decay to $\gamma\gamma$ followed by a photon conversion. As shown in Figure~\ref{fig:absiso}, |
| 667 |
+ |
the isolation distribution for charged tracks from $\tau$ decays that are not produced in association with $\pi^0$s are |
| 668 |
+ |
consistent with that from $\E$s and $\M$s. Since events from single prong $\tau$ decays produced in association with |
| 669 |
+ |
$\pi^0$s comprise a small fraction of the total sample, and since the kinematics of $\tau$, $\pi^0$ and $\gamma\to e^+e^-$ |
| 670 |
+ |
decays are well-understood, we currently demonstrate that the isolation is well-reproduced for electrons and muons only. |
| 671 |
+ |
Second, hadronic tracks may undergo nuclear interactions and hence their tracks may not be reconstructed. |
| 672 |
+ |
As discussed above, independent studies show that the MC reproduces the hadronic tracking efficiency within 4\%, |
| 673 |
+ |
leading to a total background uncertainty of less than 0.5\% (after taking into account the fraction of the total background |
| 674 |
+ |
due to hadronic $\tau$ decays with \pt\ $>$ 10 GeV tracks), and we hence regard this effect as negligible. |
| 675 |
+ |
|
| 676 |
+ |
The tag-and-probe studies are performed in the full data sample, and compared with the DYJets madgraph sample. |
| 677 |
+ |
All events must contain a tag-probe pair (details below) with opposite-sign and satisfying the Z mass requirement 76--106 GeV. |
| 678 |
+ |
We compare the distributions of absolute track isolation for probe electrons/muons in data vs. MC. The contributions to |
| 679 |
+ |
this isolation sum are from ambient energy in the event from underlying event, pile-up and jet activitiy, and hence do |
| 680 |
+ |
not depend on the \pt\ of the probe lepton. We therefore restrict the probe \pt\ to be $>$ 30 GeV in order to suppress |
| 681 |
+ |
fake backgrounds with steeply-falling \pt\ spectra. To suppress non-Z backgrounds (in particular \ttbar) we require |
| 682 |
+ |
\met\ $<$ 30 GeV and 0 b-tagged events. |
| 683 |
+ |
The specific criteria for tags and probes for electrons and muons are: |
| 684 |
+ |
|
| 685 |
+ |
%We study the isolated track veto efficiency in bins of \njets. |
| 686 |
+ |
%We are interested in events with at least 4 jets to emulate the hadronic activity in our signal sample. However since |
| 687 |
+ |
%there are limited statistics for Z + $\geq$4 jet events, we study the isolated track performance in events with |
| 688 |
+ |
|
| 689 |
+ |
|
| 690 |
+ |
\begin{itemize} |
| 691 |
+ |
\item{Electrons} |
| 692 |
+ |
|
| 693 |
+ |
\begin{itemize} |
| 694 |
+ |
\item{Tag criteria} |
| 695 |
+ |
|
| 696 |
+ |
\begin{itemize} |
| 697 |
+ |
\item Electron passes full analysis ID/iso selection |
| 698 |
+ |
\item \pt\ $>$ 30 GeV, $|\eta|<2.1$ |
| 699 |
+ |
\item Matched to the single electron trigger \verb=HLT_Ele27_WP80_v*= |
| 700 |
+ |
\end{itemize} |
| 701 |
+ |
|
| 702 |
+ |
\item{Probe criteria} |
| 703 |
+ |
\begin{itemize} |
| 704 |
+ |
\item Electron passes full analysis ID selection |
| 705 |
+ |
\item \pt\ $>$ 30 GeV |
| 706 |
+ |
\end{itemize} |
| 707 |
+ |
\end{itemize} |
| 708 |
+ |
\item{Muons} |
| 709 |
+ |
\begin{itemize} |
| 710 |
+ |
\item{Tag criteria} |
| 711 |
+ |
\begin{itemize} |
| 712 |
+ |
\item Muon passes full analysis ID/iso selection |
| 713 |
+ |
\item \pt\ $>$ 30 GeV, $|\eta|<2.1$ |
| 714 |
+ |
\item Matched to 1 of the 2 single muon triggers |
| 715 |
+ |
\begin{itemize} |
| 716 |
+ |
\item \verb=HLT_IsoMu30_v*= |
| 717 |
+ |
\item \verb=HLT_IsoMu30_eta2p1_v*= |
| 718 |
+ |
\end{itemize} |
| 719 |
+ |
\end{itemize} |
| 720 |
+ |
\item{Probe criteria} |
| 721 |
+ |
\begin{itemize} |
| 722 |
+ |
\item Muon passes full analysis ID selection |
| 723 |
+ |
\item \pt\ $>$ 30 GeV |
| 724 |
+ |
\end{itemize} |
| 725 |
+ |
\end{itemize} |
| 726 |
+ |
\end{itemize} |
| 727 |
+ |
|
| 728 |
+ |
The absolute track isolation distributions for passing probes are displayed in Fig.~\ref{fig:tnp}. In general we observe |
| 729 |
+ |
good agreement between data and MC. To be more quantitative, we compare the data vs. MC efficiencies to satisfy |
| 730 |
+ |
absolute track isolation requirements varying from $>$ 1 GeV to $>$ 5 GeV, as summarized in Table~\ref{tab:isotrk}. |
| 731 |
+ |
In the $\geq 0$ and $\geq 1$ jet bins where the efficiencies can be tested with statistical precision, the data and MC |
| 732 |
+ |
efficiencies agree within 6\%, and we apply this as a systematic uncertainty on the isolated track veto efficiency. |
| 733 |
+ |
For the higher jet multiplicity bins the statistical precision decreases, but we do not observe any evidence for |
| 734 |
+ |
a data vs. MC discrepancy in the isolated track veto efficiency. |
| 735 |
+ |
|
| 736 |
+ |
|
| 737 |
+ |
%This is because our analysis requirement is relative track isolation $<$ 0.1, and m |
| 738 |
+ |
%This requirement is chosen because most of the tracks rejected by the isolated |
| 739 |
+ |
%track veto have a \pt\ near the 10 GeV threshold, and our analysis requirement is relative track isolation $<$ 1 GeV. |
| 740 |
+ |
|
| 741 |
+ |
\begin{figure}[hbt] |
| 742 |
+ |
\begin{center} |
| 743 |
+ |
\includegraphics[width=0.3\linewidth]{plots/el_tkiso_0j.pdf}% |
| 744 |
+ |
\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_0j.pdf} |
| 745 |
+ |
\includegraphics[width=0.3\linewidth]{plots/el_tkiso_1j.pdf}% |
| 746 |
+ |
\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_1j.pdf} |
| 747 |
+ |
\includegraphics[width=0.3\linewidth]{plots/el_tkiso_2j.pdf}% |
| 748 |
+ |
\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_2j.pdf} |
| 749 |
+ |
\includegraphics[width=0.3\linewidth]{plots/el_tkiso_3j.pdf}% |
| 750 |
+ |
\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_3j.pdf} |
| 751 |
+ |
\includegraphics[width=0.3\linewidth]{plots/el_tkiso_4j.pdf}% |
| 752 |
+ |
\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_4j.pdf} |
| 753 |
+ |
\caption{ |
| 754 |
+ |
\label{fig:tnp} Comparison of the absolute track isolation in data vs. MC for electrons (left) and muons (right) |
| 755 |
+ |
for events with the \njets\ requirement varied from \njets\ $\geq$ 0 to \njets\ $\geq$ 4. |
| 756 |
+ |
} |
| 757 |
+ |
\end{center} |
| 758 |
+ |
\end{figure} |
| 759 |
+ |
|
| 760 |
+ |
\clearpage |
| 761 |
+ |
|
| 762 |
+ |
\begin{table}[!ht] |
| 763 |
+ |
\begin{center} |
| 764 |
+ |
\begin{tabular}{l|c|c|c|c|c} |
| 765 |
+ |
|
| 766 |
+ |
%Electrons: |
| 767 |
+ |
%Selection : ((((((((((abs(tagAndProbeMass-91)<15)&&(qProbe*qTag<0))&&((eventSelection&1)==1))&&(abs(tag->eta())<2.1))&&(tag->pt()>30.0))&&(HLT_Ele27_WP80_tag > 0))&&(met<30))&&(nbl==0))&&((leptonSelection&8)==8))&&(probe->pt()>30))&&(drprobe<0.05) |
| 768 |
+ |
%Total MC yields : 2497277 |
| 769 |
+ |
%Total DATA yields : 2649453 |
| 770 |
+ |
%Muons: |
| 771 |
+ |
%Selection : ((((((((((abs(tagAndProbeMass-91)<15)&&(qProbe*qTag<0))&&((eventSelection&2)==2))&&(abs(tag->eta())<2.1))&&(tag->pt()>30.0))&&(HLT_IsoMu24_tag > 0))&&(met<30))&&(nbl==0))&&((leptonSelection&65536)==65536))&&(probe->pt()>30))&&(drprobe<0.05) |
| 772 |
+ |
%Total MC yields : 3749863 |
| 773 |
+ |
%Total DATA yields : 4210022 |
| 774 |
+ |
%Info in <TCanvas::MakeDefCanvas>: created default TCanvas with name c1 |
| 775 |
+ |
%Info in <TCanvas::Print>: pdf file plots/nvtx.pdf has been created |
| 776 |
+ |
|
| 777 |
+ |
\hline |
| 778 |
+ |
\hline |
| 779 |
+ |
e + $\geq$0 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\ |
| 780 |
+ |
\hline |
| 781 |
+ |
data & 0.098 $\pm$ 0.0002 & 0.036 $\pm$ 0.0001 & 0.016 $\pm$ 0.0001 & 0.009 $\pm$ 0.0001 & 0.006 $\pm$ 0.0000 \\ |
| 782 |
+ |
mc & 0.097 $\pm$ 0.0002 & 0.034 $\pm$ 0.0001 & 0.016 $\pm$ 0.0001 & 0.009 $\pm$ 0.0001 & 0.005 $\pm$ 0.0000 \\ |
| 783 |
+ |
data/mc & 1.00 $\pm$ 0.00 & 1.04 $\pm$ 0.00 & 1.04 $\pm$ 0.01 & 1.03 $\pm$ 0.01 & 1.02 $\pm$ 0.01 \\ |
| 784 |
+ |
|
| 785 |
+ |
\hline |
| 786 |
+ |
\hline |
| 787 |
+ |
$\mu$ + $\geq$0 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\ |
| 788 |
+ |
\hline |
| 789 |
+ |
data & 0.094 $\pm$ 0.0001 & 0.034 $\pm$ 0.0001 & 0.016 $\pm$ 0.0001 & 0.009 $\pm$ 0.0000 & 0.006 $\pm$ 0.0000 \\ |
| 790 |
+ |
mc & 0.093 $\pm$ 0.0001 & 0.033 $\pm$ 0.0001 & 0.015 $\pm$ 0.0001 & 0.009 $\pm$ 0.0000 & 0.006 $\pm$ 0.0000 \\ |
| 791 |
+ |
data/mc & 1.01 $\pm$ 0.00 & 1.03 $\pm$ 0.00 & 1.03 $\pm$ 0.01 & 1.03 $\pm$ 0.01 & 1.02 $\pm$ 0.01 \\ |
| 792 |
+ |
|
| 793 |
+ |
\hline |
| 794 |
+ |
\hline |
| 795 |
+ |
e + $\geq$1 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\ |
| 796 |
+ |
\hline |
| 797 |
+ |
data & 0.110 $\pm$ 0.0005 & 0.044 $\pm$ 0.0003 & 0.022 $\pm$ 0.0002 & 0.014 $\pm$ 0.0002 & 0.009 $\pm$ 0.0002 \\ |
| 798 |
+ |
mc & 0.110 $\pm$ 0.0005 & 0.042 $\pm$ 0.0003 & 0.021 $\pm$ 0.0002 & 0.013 $\pm$ 0.0002 & 0.009 $\pm$ 0.0001 \\ |
| 799 |
+ |
data/mc & 1.00 $\pm$ 0.01 & 1.04 $\pm$ 0.01 & 1.06 $\pm$ 0.02 & 1.08 $\pm$ 0.02 & 1.06 $\pm$ 0.03 \\ |
| 800 |
+ |
|
| 801 |
+ |
\hline |
| 802 |
+ |
\hline |
| 803 |
+ |
$\mu$ + $\geq$1 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\ |
| 804 |
+ |
\hline |
| 805 |
+ |
data & 0.106 $\pm$ 0.0004 & 0.043 $\pm$ 0.0003 & 0.023 $\pm$ 0.0002 & 0.014 $\pm$ 0.0002 & 0.010 $\pm$ 0.0001 \\ |
| 806 |
+ |
mc & 0.106 $\pm$ 0.0004 & 0.042 $\pm$ 0.0003 & 0.021 $\pm$ 0.0002 & 0.013 $\pm$ 0.0002 & 0.009 $\pm$ 0.0001 \\ |
| 807 |
+ |
data/mc & 1.00 $\pm$ 0.01 & 1.04 $\pm$ 0.01 & 1.06 $\pm$ 0.01 & 1.08 $\pm$ 0.02 & 1.07 $\pm$ 0.02 \\ |
| 808 |
+ |
|
| 809 |
+ |
\hline |
| 810 |
+ |
\hline |
| 811 |
+ |
e + $\geq$2 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\ |
| 812 |
+ |
\hline |
| 813 |
+ |
data & 0.117 $\pm$ 0.0012 & 0.050 $\pm$ 0.0008 & 0.026 $\pm$ 0.0006 & 0.017 $\pm$ 0.0005 & 0.012 $\pm$ 0.0004 \\ |
| 814 |
+ |
mc & 0.120 $\pm$ 0.0012 & 0.048 $\pm$ 0.0008 & 0.025 $\pm$ 0.0006 & 0.016 $\pm$ 0.0005 & 0.011 $\pm$ 0.0004 \\ |
| 815 |
+ |
data/mc & 0.97 $\pm$ 0.01 & 1.05 $\pm$ 0.02 & 1.05 $\pm$ 0.03 & 1.07 $\pm$ 0.04 & 1.07 $\pm$ 0.05 \\ |
| 816 |
+ |
|
| 817 |
+ |
\hline |
| 818 |
+ |
\hline |
| 819 |
+ |
$\mu$ + $\geq$2 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\ |
| 820 |
+ |
\hline |
| 821 |
+ |
data & 0.111 $\pm$ 0.0010 & 0.048 $\pm$ 0.0007 & 0.026 $\pm$ 0.0005 & 0.018 $\pm$ 0.0004 & 0.013 $\pm$ 0.0004 \\ |
| 822 |
+ |
mc & 0.115 $\pm$ 0.0010 & 0.048 $\pm$ 0.0006 & 0.025 $\pm$ 0.0005 & 0.016 $\pm$ 0.0004 & 0.012 $\pm$ 0.0003 \\ |
| 823 |
+ |
data/mc & 0.97 $\pm$ 0.01 & 1.01 $\pm$ 0.02 & 1.04 $\pm$ 0.03 & 1.09 $\pm$ 0.04 & 1.09 $\pm$ 0.04 \\ |
| 824 |
+ |
|
| 825 |
+ |
\hline |
| 826 |
+ |
\hline |
| 827 |
+ |
e + $\geq$3 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\ |
| 828 |
+ |
\hline |
| 829 |
+ |
data & 0.123 $\pm$ 0.0031 & 0.058 $\pm$ 0.0022 & 0.034 $\pm$ 0.0017 & 0.023 $\pm$ 0.0014 & 0.017 $\pm$ 0.0012 \\ |
| 830 |
+ |
mc & 0.131 $\pm$ 0.0030 & 0.055 $\pm$ 0.0020 & 0.030 $\pm$ 0.0015 & 0.020 $\pm$ 0.0013 & 0.015 $\pm$ 0.0011 \\ |
| 831 |
+ |
data/mc & 0.94 $\pm$ 0.03 & 1.06 $\pm$ 0.06 & 1.14 $\pm$ 0.08 & 1.16 $\pm$ 0.10 & 1.17 $\pm$ 0.12 \\ |
| 832 |
+ |
|
| 833 |
+ |
\hline |
| 834 |
+ |
\hline |
| 835 |
+ |
$\mu$ + $\geq$3 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\ |
| 836 |
+ |
\hline |
| 837 |
+ |
data & 0.121 $\pm$ 0.0025 & 0.055 $\pm$ 0.0018 & 0.033 $\pm$ 0.0014 & 0.022 $\pm$ 0.0011 & 0.017 $\pm$ 0.0010 \\ |
| 838 |
+ |
mc & 0.120 $\pm$ 0.0024 & 0.052 $\pm$ 0.0016 & 0.029 $\pm$ 0.0012 & 0.019 $\pm$ 0.0010 & 0.014 $\pm$ 0.0009 \\ |
| 839 |
+ |
data/mc & 1.01 $\pm$ 0.03 & 1.06 $\pm$ 0.05 & 1.14 $\pm$ 0.07 & 1.14 $\pm$ 0.08 & 1.16 $\pm$ 0.10 \\ |
| 840 |
+ |
|
| 841 |
+ |
\hline |
| 842 |
+ |
\hline |
| 843 |
+ |
e + $\geq$4 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\ |
| 844 |
+ |
\hline |
| 845 |
+ |
data & 0.129 $\pm$ 0.0080 & 0.070 $\pm$ 0.0061 & 0.044 $\pm$ 0.0049 & 0.031 $\pm$ 0.0042 & 0.021 $\pm$ 0.0034 \\ |
| 846 |
+ |
mc & 0.132 $\pm$ 0.0075 & 0.059 $\pm$ 0.0053 & 0.035 $\pm$ 0.0041 & 0.025 $\pm$ 0.0035 & 0.017 $\pm$ 0.0029 \\ |
| 847 |
+ |
data/mc & 0.98 $\pm$ 0.08 & 1.18 $\pm$ 0.15 & 1.26 $\pm$ 0.20 & 1.24 $\pm$ 0.24 & 1.18 $\pm$ 0.28 \\ |
| 848 |
+ |
|
| 849 |
+ |
\hline |
| 850 |
+ |
\hline |
| 851 |
+ |
$\mu$ + $\geq$4 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\ |
| 852 |
+ |
\hline |
| 853 |
+ |
data & 0.136 $\pm$ 0.0067 & 0.064 $\pm$ 0.0048 & 0.041 $\pm$ 0.0039 & 0.029 $\pm$ 0.0033 & 0.024 $\pm$ 0.0030 \\ |
| 854 |
+ |
mc & 0.130 $\pm$ 0.0063 & 0.065 $\pm$ 0.0046 & 0.035 $\pm$ 0.0034 & 0.020 $\pm$ 0.0026 & 0.013 $\pm$ 0.0022 \\ |
| 855 |
+ |
data/mc & 1.04 $\pm$ 0.07 & 0.99 $\pm$ 0.10 & 1.19 $\pm$ 0.16 & 1.47 $\pm$ 0.25 & 1.81 $\pm$ 0.37 \\ |
| 856 |
+ |
|
| 857 |
+ |
\hline |
| 858 |
+ |
\hline |
| 859 |
+ |
|
| 860 |
+ |
\end{tabular} |
| 861 |
+ |
\caption{\label{tab:isotrk} Comparison of the data vs. MC efficiencies to satisfy the indicated requirements |
| 862 |
+ |
on the absolute track isolation, and the ratio of these two efficiencies. Results are indicated separately for electrons and muons and for various |
| 863 |
+ |
jet multiplicity requirements.} |
| 864 |
+ |
\end{center} |
| 865 |
+ |
\end{table} |
| 866 |
+ |
|
| 867 |
+ |
\clearpage |
| 868 |
+ |
\subsection{Summary of uncertainties} |
| 869 |
+ |
\label{sec:bgunc-bottomline}. |
| 870 |
+ |
\input{uncertainties_table.tex} |
| 871 |
+ |
|
| 872 |
+ |
%Figure.~\ref{fig:reliso} compares the relative track isolation |
| 873 |
+ |
%for events with a track with $\pt > 10~\GeV$ in addition to a selected |
| 874 |
+ |
%muon for $\Z+4$ jet events and various \ttll\ components. The |
| 875 |
+ |
%isolation distributions show significant differences, particularly |
| 876 |
+ |
%between the leptons from a \W\ or \Z\ decay and the tracks arising |
| 877 |
+ |
%from $\tau$ decays. As can also be seen in the figure, the \pt\ |
| 878 |
+ |
%distribution for the various categories of tracks is different, where |
| 879 |
+ |
%the decay products from $\tau$s are significantly softer. Since the |
| 880 |
+ |
%\pt\ enters the denominator of the isolation definition and hence |
| 881 |
+ |
%alters the isolation variable... |
| 882 |
+ |
|
| 883 |
+ |
%\begin{figure}[hbt] |
| 884 |
+ |
% \begin{center} |
| 885 |
+ |
% \includegraphics[width=0.5\linewidth]{plots/pfiso_njets4_log.png}% |
| 886 |
+ |
% \includegraphics[width=0.5\linewidth]{plots/pfpt_njets4.png} |
| 887 |
+ |
% \caption{ |
| 888 |
+ |
% \label{fig:reliso}%\protect |
| 889 |
+ |
% Comparison of relative track isolation variable for PF cand probe in Z+jets and ttbar |
| 890 |
+ |
% Z+Jets and ttbar dilepton have similar isolation distributions |
| 891 |
+ |
% ttbar with leptonic and single prong taus tend to be less |
| 892 |
+ |
% isolated. The difference in the isolation can be attributed |
| 893 |
+ |
% to the different \pt\ distribution of the samples, since |
| 894 |
+ |
% $\tau$ decay products tend to be softer than leptons arising |
| 895 |
+ |
% from \W\ or \Z\ decays.} |
| 896 |
+ |
% \end{center} |
| 897 |
+ |
%\end{figure} |
| 898 |
+ |
|
| 899 |
+ |
% \includegraphics[width=0.5\linewidth]{plots/pfabsiso_njets4_log.png} |
| 900 |
+ |
|
| 901 |
+ |
|
| 902 |
+ |
%BEGIN SECTION TO WRITE OUT |
| 903 |
+ |
%In detail, the procedure to correct the dilepton background is: |
| 904 |
+ |
|
| 905 |
+ |
%\begin{itemize} |
| 906 |
+ |
%\item Using tag-and-probe studies, we plot the distribution of {\bf absolute} track isolation for identified probe electrons |
| 907 |
+ |
%and muons {\bf TODO: need to compare the e vs. $\mu$ track iso distributions, they might differ due to e$\to$e$\gamma$}. |
| 908 |
+ |
%\item We verify that the distribution of absolute track isolation does not depend on the \pt\ of the probe lepton. |
| 909 |
+ |
%This is due to the fact that this isolation is from ambient PU and jet activity in the event, which is uncorrelated with |
| 910 |
+ |
%the lepton \pt {\bf TODO: verify this in data and MC.}. |
| 911 |
+ |
%\item Our requirement is {\bf relative} track isolation $<$ 0.1. For a given \ttll\ MC event, we determine the \pt of the 2nd |
| 912 |
+ |
%lepton and translate this to find the corresponding requirement on the {\bf absolute} track isolation, which is simply $0.1\times$\pt. |
| 913 |
+ |
%\item We measure the efficiency to satisfy this requirement in data and MC, and define a scale-factor $SF_{\epsilon(trk)}$ which |
| 914 |
+ |
%is the ratio of the data-to-MC efficiencies. This scale-factor is applied to the \ttll\ MC event. |
| 915 |
+ |
%\item {\bf THING 2 we are unsure about: we can measure this SF for electrons and for muons, but we can't measure it for hadronic |
| 916 |
+ |
%tracks from $\tau$ decays. Verena has showed that the absolute track isolation distribution in hadronic $\tau$ tracks is harder due |
| 917 |
+ |
%to $\pi^0\to\gamma\gamma$ with $\gamma\to e^+e^-$.} |
| 918 |
+ |
%\end{itemize} |
| 919 |
+ |
%END SECTION TO WRITE OUT |
| 920 |
+ |
|
| 921 |
+ |
|
| 922 |
+ |
%{\bf fix me: What you have written in the next paragraph does not |
| 923 |
+ |
%explain how $\epsilon_{fake}$ is measured. |
| 924 |
+ |
%Why not measure $\epsilon_{fake}$ in the b-veto region?} |
| 925 |
+ |
|
| 926 |
+ |
%A measurement of the $\epsilon_{fake}$ in data is non-trivial. However, it is |
| 927 |
+ |
%possible to correct for differences in the $\epsilon_{fake}$ between data and MC by |
| 928 |
+ |
%applying an additional scale factor for the single lepton background |
| 929 |
+ |
%alone, using the sample in the \mt\ peak region. This scale factor is determined after applying the isolated track |
| 930 |
+ |
%veto and after subtracting the \ttll\ component, corrected for the |
| 931 |
+ |
%isolation efficiency derived previously. |
| 932 |
+ |
%As shown in Figure~\ref{fig:vetoeffcomp}, the efficiency for selecting an |
| 933 |
+ |
%isolated track in single lepton events is independent of \mt\, so the use of |
| 934 |
+ |
%an overall scale factor is justified to estimate the contribution in |
| 935 |
+ |
%the \mt\ tail. |
| 936 |
+ |
% |
| 937 |
+ |
%\begin{figure}[hbt] |
| 938 |
+ |
% \begin{center} |
| 939 |
+ |
% \includegraphics[width=0.5\linewidth]{plots/vetoeff_comp.png} |
| 940 |
+ |
% \caption{ |
| 941 |
+ |
% \label{fig:vetoeffcomp}%\protect |
| 942 |
+ |
% Efficiency for selecting an isolated track comparing |
| 943 |
+ |
% single lepton \ttlj\ and dilepton \ttll\ events in MC and |
| 944 |
+ |
% data as a function of \mt. The |
| 945 |
+ |
% efficiencies in \ttlj\ and \ttll\ exhibit no dependence on |
| 946 |
+ |
% \mt\, while the data ranges between the two. This behavior |
| 947 |
+ |
% is expected since the low \mt\ region is predominantly \ttlj, while the |
| 948 |
+ |
% high \mt\ region contains mostly \ttll\ events.} |
| 949 |
+ |
% \end{center} |
| 950 |
+ |
%\end{figure} |
| 951 |
+ |
|
| 952 |
+ |
|
| 953 |
+ |
|
| 954 |
+ |
% THIS NEEDS TO BE WRITTEN |
