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\section{Systematics Uncertainties in the Background Prediction} |
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\label{sec:systematics} |
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%\section{Systematics Uncertainties on the Background Prediction} |
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%\label{sec:systematics} |
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|
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The methodology for determining the systematics on the background |
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predictions has not changed with respect to the nominal analysis. |
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Because the template method has not changed, the same |
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systematic uncertainty is assessed on this prediction (32\%). |
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The 50\% uncertainty on the WZ and ZZ background is also unchanged. |
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The systematic uncertainty in the OF background prediction based on |
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e$\mu$ events has changed, due to the different composition of this |
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sample after vetoing events containing b-tagged jets. |
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|
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As in the nominal analysis, we do not require the e$\mu$ events |
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to satisfy the dilepton mass requirement and apply a scaling factor K, |
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extracted from MC, to account for the fraction of e$\mu$ events |
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which satisfy the dilepton mass requirement. This procedure is used |
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in order to improve the statistical precision of the OF background estimate. |
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|
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For the selection used in the nominal analysis, |
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the e$\mu$ sample is completely dominated by $t\bar{t}$ |
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events, and we observe that K is statistically consistent with constant with |
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respect to the \MET\ requirement. However, in this analysis, the $t\bar{t}$ |
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background is strongly suppressed by the b-veto, and hence the non-$t\bar{t}$ |
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backgrounds (specifically, $Z\to\tau\tau$ and VV) become more relevant. |
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At low \MET, the $Z\to\tau\tau$ background is pronounced, while $t\bar{t}$ |
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and VV dominate at high \MET\ (see App.~\ref{app:kinemu}). |
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Therefore, the sample composition changes |
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as the \MET\ requirement is varied, and as a result K depends |
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on the \MET\ requirement. |
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|
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We thus measure K in MC separately for each |
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\MET\ requirement, as displayed in Fig.~\ref{fig:kvmet} (left). |
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%The systematic uncertainty on K is determined separately for each \MET\ |
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%requirement by comparing the relative difference in K in data vs. MC. |
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The values of K used are the MC predictions |
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%and the total systematic uncertainty on the OF prediction |
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%as shown in |
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(Table \ref{fig:kvmettable}). |
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The contribution to the total OF prediction systematic uncertainty |
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from K is assessed from the ratio of K in data and MC, |
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shown in Fig.~\ref{fig:kvmet} (right). |
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The ratio is consistent with unity to roughly 17\%, |
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so we take this value as the systematic from K. |
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17\% added in quadrature with 7\% from |
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the electron to muon efficieny ratio |
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(as assessed in the inclusive analysis) |
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yields a total systematic of $\sim$18\% |
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which we round up to 20\%. |
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For \MET\ $>$ 150, there are no OF events in data inside the Z mass window |
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so we take a systematic based on the statistical uncertainty |
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of the MC prediction for K. |
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This value is 25\% for \MET\ $>$ 150 GeV and 60\% for \MET\ $>$ 200 GeV. |
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%Although we cannot check the value of K in data for \MET\ $>$ 150 |
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%because we find no OF events inside the Z mass window for this \MET\ |
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%cut, the overall OF yields with no dilepton mass requirement |
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%agree to roughly 20\% (9 data vs 7.0 $\pm$ 1.1 MC). |
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|
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|
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%Below Old |
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|
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%In reevaluating the systematics on the OF prediction, however, |
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%we observed a different behavior of K as a function of \MET\ |
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%as was seen in the inclusive analysis. |
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|
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%Recall that K is the ratio of the number of \emu\ events |
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%inside the Z window to the total number of \emu\ events. |
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%In the inclusive analysis, it is taken from \ttbar\ MC |
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%and used to scale the inclusive \emu\ yield in data. |
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%The yield scaled by K is then corrected for |
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%the $e$ vs $\mu$ efficiency difference to obtain the |
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%final OF prediction. |
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|
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%Based on the plot in figure \ref{fig:kvmet}, |
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%we choose to use a different |
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%K for each \MET\ cut and assess a systematic uncertainty |
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%on the OF prediction based on the difference between |
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%K in data and MC. |
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%The variation of K as a function of \MET\ is caused |
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%by a change in sample composition with increasing \MET. |
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%At \MET\ $<$ 60 GeV, the contribution of Z plus jets is |
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%not negligible (as it was in the inclusive analysis) |
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%because of the b veto. (See appendix \ref{app:kinemu}.) |
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%At higher \MET, \ttbar\ and diboson backgrounds dominate. |
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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 |
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uncertainty is given in Table~\ref{tab:cr1yields}. |
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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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\label{sec:ttdilbkgunc} |
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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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\clearpage |
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\subsubsection{Check of the impact of Signal Contamination} |
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|
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We examine the contribution of possible signal events in the \ttll\ |
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control regions (CR4 and CR5). It should be emphasized that these |
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regions are not used to apply data/MC SFs. They are used to quantify |
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the level of data/MC agreement and assign a corresponding uncertainty. |
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|
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To illustrate how much signal is expected to populate these control |
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regions, we examine signal points near the edge of the analysis' |
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sensitivity (m(stop) = 450 m($\chi^0$) = 0 for T2tt, m(stop) = 450 |
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m($\chi^0$) = 0 for T2bw with x=0.75 and m(stop) = 350 |
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m($\chi^0$) = 0 for T2bw with x=0.5). |
| 194 |
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Table~\ref{tab:signalcontamination} compares the expected signal |
| 195 |
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yields and the raw total MC background prediction in the control |
| 196 |
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regions with the \met\ and \mt\ requirements corresponding to SRB, SRC |
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and SRD (these are the signal regions that dominate the |
| 198 |
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sensitivity). The signal contamination is smaller than the uncertainty |
| 199 |
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on the dilepton background and smaller than the signal/background in |
| 200 |
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the signal regions, with the exception of the T2bw scenario with x=0.5. |
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However, based on the fact that the CR4 and CR5 are not used to extract |
| 202 |
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data/MC SFs and that CR4 shows a slight deficit of data compared to |
| 203 |
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the MC prediction, indicating that we do not observe evidence of |
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signal contamination, we do not assign an additional uncertainty. |
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|
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\begin{table}[!h] |
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\begin{center} |
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{\small |
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\begin{tabular}{l l||c|c|c} |
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\hline |
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\multicolumn{2}{c||}{Sample} & CR B & CR C & CR D \\ |
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\hline |
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\hline |
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\multirow{4}{*}{CR4} & Raw MC & $168.2 \pm 4.5$& $51.5 \pm 2.5$& $19.6 \pm 1.5$ \\ |
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%\hline |
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& T2tt m(stop) = 450 m($\chi^0$) = 0 & $2.6 \pm 0.3$ $(2\%)$ & $2.0 \pm 0.2$ $(4\%)$ & $1.4 \pm 0.2$ $(7\%)$ \\ |
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& T2bw x=0.75 m(stop) = 450 m($\chi^0$) = 0 & $10.5 \pm 0.4$ $(6\%)$ &$6.1 \pm 0.3$ $(12\%)$ & $3.1 \pm 0.2$ $(16\%)$ \\ |
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& T2bw x=0.5 m(stop) = 350 m($\chi^0$) = 0 & $32.1 \pm 1.5$ $(19\%)$ & $14.7 \pm 1.0$ $(29\%)$ & $5.5 \pm 0.6$ $(28\%)$ \\ |
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\hline |
| 220 |
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\hline |
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\multirow{4}{*}{CR5} & Raw MC & $306.5 \pm 6.2$& $101.8 \pm 3.6$& $38.0 \pm 2.2$ \\ |
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%\hline |
| 223 |
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& T2tt m(stop) = 450 m($\chi^0$) = 0 & $10.6 \pm 0.6$ $(3\%)$ & $7.8 \pm 0.5$ $(8\%)$ & $5.4 \pm 0.4$ $(14\%)$ \\ |
| 224 |
+ |
& T2bw x=0.75 m(stop) = 450 m($\chi^0$) = 0 & $17.3 \pm 0.5$ $(6\%)$ &$11.3 \pm 0.4$ $(11\%)$ & $6.2 \pm 0.3$ $(16\%)$\\ |
| 225 |
+ |
& T2bw x=0.5 m(stop) = 350 m($\chi^0$) = 0 & $33.0 \pm 1.5$ $(11\%)$& $14.4 \pm 1.0$ $(14\%)$& $5.7 \pm 0.6$ $(15\%)$ \\ |
| 226 |
+ |
\hline |
| 227 |
+ |
\hline |
| 228 |
+ |
\hline |
| 229 |
+ |
\multirow{4}{*}{SIGNAL} & Raw MC & $486.3 \pm 7.8$& $164.3 \pm 4.5$& $61.5 \pm 2.8$ \\ |
| 230 |
+ |
& T2tt m(stop) = 450 m($\chi^0$) = 0 & $65.3 \pm 1.4$ $(13\%)$& $48.8 \pm 1.2$ $(30\%)$& $32.9 \pm 1.0$ $(53\%)$ \\ |
| 231 |
+ |
& T2bw x=0.75 m(stop) = 450 m($\chi^0$) = 0 & $69.3 \pm 1.0$ $(14\%)$& $47.3 \pm 0.8$ $(29\%)$& $27.3 \pm 0.6$ $(44\%)$ \\ |
| 232 |
+ |
& T2bw x=0.5 m(stop) = 350 m($\chi^0$) = 0 & $105.5 \pm 2.8$ $(22\%)$& $44.6 \pm 1.8$ $(27\%)$& $15.9 \pm 1.1$ $(26\%)$ \\ |
| 233 |
+ |
\hline |
| 234 |
+ |
\end{tabular}} |
| 235 |
+ |
\caption{ Yields in \mt\ tail comparing the raw SM MC prediction to the |
| 236 |
+ |
yields for a few signal points on the edge of our sensitivity in the \ttll\ |
| 237 |
+ |
control regions CR4, CR5 and in the corresponding signal region. |
| 238 |
+ |
The numbers in parenthesis are the expected signal yield divided by |
| 239 |
+ |
the total background. The uncertainties are statistical only. |
| 240 |
+ |
\label{tab:signalcontamination}} |
| 241 |
+ |
\end{center} |
| 242 |
+ |
\end{table} |
| 243 |
+ |
|
| 244 |
+ |
%CR5 DUMP |
| 245 |
+ |
%Total & $880.3 \pm 10.4$& $560.0 \pm 8.3$& $306.5 \pm 6.2$& $101.8 \pm 3.6$& $38.0 \pm 2.2$& $16.4 \pm 1.4$& $8.2 \pm 1.0$& $4.6 \pm 0.8$ \\ |
| 246 |
+ |
%\hline |
| 247 |
+ |
%\hline |
| 248 |
+ |
%Data & $941$& $559$& $287$& $95$& $26$& $8$& $5$& $3$ \\ |
| 249 |
+ |
%\hline |
| 250 |
+ |
%T2tt m(stop) = 250 m($\chi^0$) = 0 & $84.3 \pm 9.2$& $61.9 \pm 7.9$& $35.7 \pm 6.0$& $5.9 \pm 2.4$& $1.0 \pm 1.0$& $1.0 \pm 1.0$& $0.0 \pm 0.0$& $0.0 \pm 0.0$ \\ |
| 251 |
+ |
%\hline |
| 252 |
+ |
%T2tt m(stop) = 300 m($\chi^0$) = 50 & $61.4 \pm 4.7$& $53.6 \pm 4.4$& $42.0 \pm 3.9$& $14.3 \pm 2.3$& $7.2 \pm 1.6$& $1.8 \pm 0.8$& $0.7 \pm 0.5$& $0.0 \pm 0.0$ \\ |
| 253 |
+ |
%\hline |
| 254 |
+ |
%T2tt m(stop) = 300 m($\chi^0$) = 100 & $33.3 \pm 3.5$& $28.6 \pm 3.2$& $19.2 \pm 2.6$& $6.1 \pm 1.5$& $1.8 \pm 0.8$& $0.4 \pm 0.4$& $0.4 \pm 0.4$& $0.4 \pm 0.4$ \\ |
| 255 |
+ |
%\hline |
| 256 |
+ |
%T2tt m(stop) = 350 m($\chi^0$) = 0 & $33.4 \pm 2.2$& $29.8 \pm 2.1$& $27.3 \pm 2.0$& $15.3 \pm 1.5$& $5.6 \pm 0.9$& $1.9 \pm 0.5$& $0.3 \pm 0.2$& $0.0 \pm 0.0$ \\ |
| 257 |
+ |
%\hline |
| 258 |
+ |
%T2tt m(stop) = 450 m($\chi^0$) = 0 & $12.0 \pm 0.6$& $11.3 \pm 0.6$& $10.6 \pm 0.6$& $7.8 \pm 0.5$& $5.4 \pm 0.4$& $3.1 \pm 0.3$& $1.8 \pm 0.2$& $0.6 \pm 0.1$ \\ |
| 259 |
+ |
%\hline |
| 260 |
+ |
%T2bw m(stop) = 350 x=0.5 m($\chi^0$) = 0 & $48.5 \pm 1.9$& $40.2 \pm 1.7$& $33.0 \pm 1.5$& $14.4 \pm 1.0$& $5.7 \pm 0.6$& $2.7 \pm 0.4$& $1.3 \pm 0.3$& $0.5 \pm 0.2$ \\ |
| 261 |
+ |
%\hline |
| 262 |
+ |
%T2bw m(stop) = 450 x=0.75 m($\chi^0$) = 0 & $22.3 \pm 0.6$& $20.2 \pm 0.6$& $17.3 \pm 0.5$& $11.3 \pm 0.4$& $6.2 \pm 0.3$& $3.1 \pm 0.2$& $1.3 \pm 0.1$& $0.7 \pm 0.1$ \\ |
| 263 |
+ |
%\hline |
| 264 |
+ |
|
| 265 |
+ |
%CR4 DUMP |
| 266 |
+ |
%\hline |
| 267 |
+ |
%Total & $510.1 \pm 8.0$& $324.2 \pm 6.3$& $168.2 \pm 4.5$& $51.5 \pm 2.5$& $19.6 \pm 1.5$& $7.8 \pm 1.0$& $2.6 \pm 0.6$& $1.1 \pm 0.3$ \\ |
| 268 |
+ |
%\hline |
| 269 |
+ |
%\hline |
| 270 |
+ |
%Data & $462$& $289$& $169$& $45$& $10$& $7$& $5$& $3$ \\ |
| 271 |
+ |
%\hline |
| 272 |
+ |
%T2tt m(stop) = 250 m($\chi^0$) = 0 & $37.7 \pm 6.1$& $30.9 \pm 5.5$& $18.0 \pm 4.2$& $6.0 \pm 2.5$& $2.0 \pm 1.4$& $0.0 \pm 0.0$& $0.0 \pm 0.0$& $0.0 \pm 0.0$ \\ |
| 273 |
+ |
%\hline |
| 274 |
+ |
%T2tt m(stop) = 300 m($\chi^0$) = 50 & $16.6 \pm 2.4$& $14.4 \pm 2.3$& $11.3 \pm 2.0$& $5.6 \pm 1.4$& $3.2 \pm 1.1$& $1.8 \pm 0.8$& $0.0 \pm 0.0$& $0.0 \pm 0.0$ \\ |
| 275 |
+ |
%\hline |
| 276 |
+ |
%T2tt m(stop) = 300 m($\chi^0$) = 100 & $9.6 \pm 1.8$& $6.4 \pm 1.5$& $4.6 \pm 1.3$& $0.7 \pm 0.5$& $0.4 \pm 0.4$& $0.0 \pm 0.0$& $0.0 \pm 0.0$& $0.0 \pm 0.0$ \\ |
| 277 |
+ |
%\hline |
| 278 |
+ |
%T2tt m(stop) = 350 m($\chi^0$) = 0 & $8.2 \pm 1.1$& $7.6 \pm 1.0$& $5.7 \pm 0.9$& $3.4 \pm 0.7$& $1.9 \pm 0.5$& $0.6 \pm 0.3$& $0.3 \pm 0.2$& $0.1 \pm 0.1$ \\ |
| 279 |
+ |
%\hline |
| 280 |
+ |
%T2tt m(stop) = 450 m($\chi^0$) = 0 & $3.1 \pm 0.3$& $2.9 \pm 0.3$& $2.6 \pm 0.3$& $2.0 \pm 0.2$& $1.4 \pm 0.2$& $1.0 \pm 0.2$& $0.4 \pm 0.1$& $0.2 \pm 0.1$ \\ |
| 281 |
+ |
%\hline |
| 282 |
+ |
%T2bw m(stop) = 350 x=0.5 m($\chi^0$) = 0 & $52.6 \pm 1.9$& $42.6 \pm 1.7$& $32.1 \pm 1.5$& $14.7 \pm 1.0$& $5.5 \pm 0.6$& $1.9 \pm 0.4$& $0.6 \pm 0.2$& $0.3 \pm 0.1$ \\ |
| 283 |
+ |
%\hline |
| 284 |
+ |
%T2bw m(stop) = 450 x=0.75 m($\chi^0$) = 0 & $16.9 \pm 0.5$& $14.9 \pm 0.5$& $10.5 \pm 0.4$& $6.1 \pm 0.3$& $3.1 \pm 0.2$& $1.5 \pm 0.1$& $0.6 \pm 0.1$& $0.3 \pm 0.1$ \\ |
| 285 |
+ |
%\hline |
| 286 |
+ |
|
| 287 |
+ |
|
| 288 |
+ |
\subsubsection{Check of the uncertainty on the \ttll\ Background} |
| 289 |
+ |
|
| 290 |
+ |
We check that the systematic uncertainty assigned to the \ttll\ background prediction |
| 291 |
+ |
covers the uncertainty associated with |
| 292 |
+ |
the theoretical modeling of the \ttbar\ production and decay |
| 293 |
+ |
by comparing the background predictions obtained using |
| 294 |
+ |
alternative MC samples. It should be noted that the full analysis is |
| 295 |
+ |
performed with the alternative samples under consideration, |
| 296 |
+ |
including the derivation of the various data-to-MC scale factors. |
| 297 |
+ |
The variations considered are |
| 298 |
+ |
|
| 299 |
+ |
\begin{itemize} |
| 300 |
+ |
\item Top mass: The alternative values for the top mass differ |
| 301 |
+ |
from the central value by $6~\GeV$: $m_{\mathrm{top}} = 178.5~\GeV$ and $m_{\mathrm{top}} |
| 302 |
+ |
= 166.5~\GeV$. |
| 303 |
+ |
\item Jet-parton matching scale: This corresponds to variations in the |
| 304 |
+ |
scale at which the Matrix Element partons from Madgraph are matched |
| 305 |
+ |
to Parton Shower partons from Pythia. The nominal value is |
| 306 |
+ |
$x_q>20~\GeV$. The alternative values used are $x_q>10~\GeV$ and |
| 307 |
+ |
$x_q>40~\GeV$. |
| 308 |
+ |
\item Renormalization and factorization scale: The alternative samples |
| 309 |
+ |
correspond to variations in the scale $\times 2$ and $\times 0.5$. The nominal |
| 310 |
+ |
value for the scale used is $Q^2 = m_{\mathrm{top}}^2 + |
| 311 |
+ |
\sum_{\mathrm{jets}} \pt^2$. |
| 312 |
+ |
\item Alternative generators: Samples produced with different |
| 313 |
+ |
generators, Powheg (our default) and Madgraph. |
| 314 |
+ |
\item Modeling of taus: The alternative sample does not include |
| 315 |
+ |
Tauola and is otherwise identical to the Powheg sample. |
| 316 |
+ |
This effect was studied earlier using 7~TeV samples and found to be negligible. |
| 317 |
+ |
\item The PDF uncertainty is estimated following the PDF4LHC |
| 318 |
+ |
recommendations. The events are reweighted using alternative |
| 319 |
+ |
PDF sets for CT10 and MSTW2008 and the uncertainties for each are derived using the |
| 320 |
+ |
alternative eigenvector variations and the ``master equation''. |
| 321 |
+ |
The NNPDF2.1 set with 100 replicas is also used. The central value is |
| 322 |
+ |
determined from the mean and the uncertainty is derived from the |
| 323 |
+ |
$1\sigma$ range. The overall uncertainty is derived from the envelope of the |
| 324 |
+ |
alternative predictions and their uncertainties. |
| 325 |
+ |
This effect was studied earlier using 7~TeV samples and found to be negligible. |
| 326 |
+ |
\end{itemize} |
| 327 |
|
|
| 328 |
|
\begin{figure}[hbt] |
| 329 |
|
\begin{center} |
| 330 |
< |
\includegraphics[width=0.48\linewidth]{plots/kvmet_data_ttbm.pdf} |
| 331 |
< |
\includegraphics[width=0.48\linewidth]{plots/kvmet_ratio.pdf} |
| 330 |
> |
\includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRA.pdf}% |
| 331 |
> |
\includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRB.pdf} |
| 332 |
> |
\includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRC.pdf}% |
| 333 |
> |
\includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRD.pdf} |
| 334 |
> |
\includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRE.pdf} |
| 335 |
|
\caption{ |
| 336 |
< |
\label{fig:kvmet}\protect |
| 337 |
< |
The left plot shows |
| 338 |
< |
K as a function of \MET\ in MC (red) and data (black). |
| 339 |
< |
The bin low edge corresponds to the \MET\ cut, and the |
| 340 |
< |
bins are inclusive. |
| 341 |
< |
The MC used is a sum of all SM MC used in the yield table of |
| 342 |
< |
section \ref{sec:yields}. |
| 343 |
< |
The right plot is the ratio of K in data to MC. |
| 344 |
< |
The ratio is fit to a line whose slope is consistent with zero |
| 345 |
< |
(the fit parameters are |
| 346 |
< |
0.9 $\pm$ 0.4 for the intercept and |
| 347 |
< |
0.001 $\pm$ 0.005 for the slope). |
| 348 |
< |
} |
| 349 |
< |
\end{center} |
| 336 |
> |
\label{fig:ttllsyst}\protect |
| 337 |
> |
Comparison of the \ttll\ central prediction with those using |
| 338 |
> |
alternative MC samples. The blue band corresponds to the |
| 339 |
> |
total statistical error for all data and MC samples. The |
| 340 |
> |
alternative sample predictions are indicated by the |
| 341 |
> |
datapoints. The uncertainties on the alternative predictions |
| 342 |
> |
correspond to the uncorrelated statistical uncertainty from |
| 343 |
> |
the size of the alternative sample only. Note the |
| 344 |
> |
suppressed vertical scales.} |
| 345 |
> |
\end{center} |
| 346 |
> |
\end{figure} |
| 347 |
> |
|
| 348 |
> |
|
| 349 |
> |
\begin{table}[!h] |
| 350 |
> |
\begin{center} |
| 351 |
> |
{\footnotesize |
| 352 |
> |
\begin{tabular}{l||c|c|c|c|c|c|c} |
| 353 |
> |
\hline |
| 354 |
> |
$\Delta/N$ [\%] & Madgraph & Mass Up & Mass Down & Scale Up & Scale Down & |
| 355 |
> |
Match Up & Match Down \\ |
| 356 |
> |
\hline |
| 357 |
> |
\hline |
| 358 |
> |
SRA & $2$ & $2$ & $5$ & $12$ & $7$ & $0$ & $2$ \\ |
| 359 |
> |
\hline |
| 360 |
> |
SRB & $6$ & $0$ & $6$ & $5$ & $12$ & $5$ & $6$ \\ |
| 361 |
> |
\hline |
| 362 |
> |
% SRC & $10$ & $3$ & $2$ & $12$ & $14$ & $16$ & $4$ \\ |
| 363 |
> |
% \hline |
| 364 |
> |
% SRD & $10$ & $6$ & $6$ & $21$ & $15$ & $19$ & $0$ \\ |
| 365 |
> |
% \hline |
| 366 |
> |
% SRE & $6$ & $17$ & $15$ & $2$ & $12$ & $17$ & $8$ \\ |
| 367 |
> |
\hline |
| 368 |
> |
\end{tabular}} |
| 369 |
> |
\caption{ Relative difference in \ttdl\ predictions for alternative MC |
| 370 |
> |
samples in |
| 371 |
> |
the higher statistics regions SRA and SRB. These differences |
| 372 |
> |
are based on the central values of the predictions. For a fuller |
| 373 |
> |
picture |
| 374 |
> |
of the situation, including statistical uncertainites, see Fig.~\ref{fig:ttllsyst}. |
| 375 |
> |
\label{tab:fracdiff}} |
| 376 |
> |
\end{center} |
| 377 |
> |
\end{table} |
| 378 |
> |
|
| 379 |
> |
|
| 380 |
> |
In Fig.~\ref{fig:ttllsyst} we compare the alternate MC \ttll\ background predictions |
| 381 |
> |
for regions A through E. We can make the following observations based |
| 382 |
> |
on this Figure. |
| 383 |
> |
|
| 384 |
> |
\begin{itemize} |
| 385 |
> |
\item In the tighter signal regions we are running out of |
| 386 |
> |
statistics. |
| 387 |
> |
\item Within the limited statistics, there is no evidence that the |
| 388 |
> |
situation changes as we go from signal region A to signal region E. |
| 389 |
> |
%Therefore, we assess a systematic based on the relatively high |
| 390 |
> |
%statistics |
| 391 |
> |
%test in signal region A, and apply the same systematic uncertainty |
| 392 |
> |
%to all other regions. |
| 393 |
> |
\item In signal regions B and above, the uncertainties assigned in Section~\ref{sec:ttdilbkgunc} |
| 394 |
> |
fully cover the alternative MC variations. |
| 395 |
> |
\item In order to fully (as opposed as 1$\sigma$) cover the |
| 396 |
> |
alternative MC variations in region A we would have to take a |
| 397 |
> |
systematic |
| 398 |
> |
uncertainty of $\approx 10\%$ instead of $5\%$. This would be driven by the |
| 399 |
> |
scale up/scale down variations, see Table~\ref{tab:fracdiff}. |
| 400 |
> |
\end{itemize} |
| 401 |
> |
|
| 402 |
> |
\begin{table}[!ht] |
| 403 |
> |
\begin{center} |
| 404 |
> |
\begin{tabular}{l|c|c} |
| 405 |
> |
\hline |
| 406 |
> |
Sample |
| 407 |
> |
& K3 & K4\\ |
| 408 |
> |
\hline |
| 409 |
> |
\hline |
| 410 |
> |
Powheg & $1.01 \pm 0.03$ & $0.93 \pm 0.04$ \\ |
| 411 |
> |
Madgraph & $1.01 \pm 0.04$ & $0.92 \pm 0.04$ \\ |
| 412 |
> |
Mass Up & $1.00 \pm 0.04$ & $0.92 \pm 0.04$ \\ |
| 413 |
> |
Mass Down & $1.06 \pm 0.04$ & $0.99 \pm 0.05$ \\ |
| 414 |
> |
Scale Up & $1.14 \pm 0.04$ & $1.23 \pm 0.06$ \\ |
| 415 |
> |
Scale Down & $0.89 \pm 0.03$ & $0.74 \pm 0.03$ \\ |
| 416 |
> |
Match Up & $1.02 \pm 0.04$ & $0.97 \pm 0.04$ \\ |
| 417 |
> |
Match Down & $1.02 \pm 0.04$ & $0.91 \pm 0.04$ \\ |
| 418 |
> |
\hline |
| 419 |
> |
\end{tabular} |
| 420 |
> |
\caption{$\met>100$ GeV: Data/MC scale factors used to account for differences in the |
| 421 |
> |
fraction of events with additional hard jets from radiation in |
| 422 |
> |
\ttll\ events. \label{tab:njetskfactors_met100}} |
| 423 |
> |
\end{center} |
| 424 |
> |
\end{table} |
| 425 |
> |
|
| 426 |
> |
|
| 427 |
> |
However, we have two pieces of information indicating that the |
| 428 |
> |
scale up/scale down variations are inconsistent with the data. |
| 429 |
> |
These are described below. |
| 430 |
> |
|
| 431 |
> |
The first piece of information is that the jet multiplicity in the scale |
| 432 |
> |
up/scale down sample is the most inconsistent with the data. This is shown |
| 433 |
> |
in Table~\ref{tab:njetskfactors_met100}, where we tabulate the |
| 434 |
> |
$K_3$ and $K_4$ factors of Section~\ref{sec:jetmultiplicity} for |
| 435 |
> |
different \ttbar\ MC samples. The data/MC disagreement in the $N_{jets}$ |
| 436 |
> |
distribution |
| 437 |
> |
for the scale up/scale down samples is also shown in Fig.~\ref{fig:dileptonnjets_scaleup} |
| 438 |
> |
and~\ref{fig:dileptonnjets_scaledw}. This should be compared with the |
| 439 |
> |
equivalent $N_{jets}$ plots for the default Powheg MC, see |
| 440 |
> |
Fig.~\ref{fig:dileptonnjets}, which agrees much better with data. |
| 441 |
> |
|
| 442 |
> |
\begin{figure}[hbt] |
| 443 |
> |
\begin{center} |
| 444 |
> |
\includegraphics[width=0.5\linewidth]{plots/njets_all_met50_mueg_scaleup.pdf} |
| 445 |
> |
\includegraphics[width=0.5\linewidth]{plots/njets_all_met50_diel_scaleup.pdf}% |
| 446 |
> |
\includegraphics[width=0.5\linewidth]{plots/njets_all_met50_dimu_scaleup.pdf} |
| 447 |
> |
\caption{ |
| 448 |
> |
\label{fig:dileptonnjets_scaleup}%\protect |
| 449 |
> |
SCALE UP: Comparison of the jet multiplicity distribution in data and MC for dilepton events in the \E-\M\ |
| 450 |
> |
(top), \E-\E\ (bottom left) and \M-\M\ (bottom right) channels.} |
| 451 |
> |
\end{center} |
| 452 |
> |
\end{figure} |
| 453 |
> |
|
| 454 |
> |
\begin{figure}[hbt] |
| 455 |
> |
\begin{center} |
| 456 |
> |
\includegraphics[width=0.5\linewidth]{plots/njets_all_met50_mueg_scaledw.pdf} |
| 457 |
> |
\includegraphics[width=0.5\linewidth]{plots/njets_all_met50_diel_scaledw.pdf}% |
| 458 |
> |
\includegraphics[width=0.5\linewidth]{plots/njets_all_met50_dimu_scaledw.pdf} |
| 459 |
> |
\caption{ |
| 460 |
> |
\label{fig:dileptonnjets_scaledw}%\protect |
| 461 |
> |
SCALE DOWN: Comparison of the jet multiplicity distribution in data and MC for dilepton events in the \E-\M\ |
| 462 |
> |
(top), \E-\E\ (bottom left) and \M-\M\ (bottom right) channels.} |
| 463 |
> |
\end{center} |
| 464 |
|
\end{figure} |
| 465 |
|
|
| 466 |
|
|
| 467 |
+ |
\clearpage |
| 468 |
+ |
|
| 469 |
+ |
The second piece of information is that we have performed closure |
| 470 |
+ |
tests in CR5 using the alternative MC samples. These are exactly |
| 471 |
+ |
the same tests as the one performed in Section~\ref{sec:CR5} on the |
| 472 |
+ |
Powheg sample. As we argued previously, this is a very powerful |
| 473 |
+ |
test of the background calculation. |
| 474 |
+ |
The results of this test are summarized in Table~\ref{tab:hugecr5yields}. |
| 475 |
+ |
Concentrating on the relatively high statistics CR5A region, we see |
| 476 |
+ |
for all \ttbar\ MC samples except scale up/scale down we obtain |
| 477 |
+ |
closure within 1$\sigma$. The scale up/scale down tests closes |
| 478 |
+ |
worse, only within 2$\sigma$. This again is evidence that the |
| 479 |
+ |
scale up/scale down variations are in disagreement with the data. |
| 480 |
+ |
|
| 481 |
+ |
\input{hugeCR5Table.tex} |
| 482 |
+ |
|
| 483 |
+ |
Based on the two observations above, we argue that the MC |
| 484 |
+ |
scale up/scale down variations are too extreme. We feel that |
| 485 |
+ |
a reasonable choice would be to take one-half of the scale up/scale |
| 486 |
+ |
down variations in our MC. This factor of 1/2 would then bring |
| 487 |
+ |
the discrepancy in the closure test of |
| 488 |
+ |
Table~\ref{tab:hugecr5yields} for the scale up/scale down variations |
| 489 |
+ |
from about 2$\sigma$ to about 1$\sigma$. |
| 490 |
+ |
|
| 491 |
+ |
Then, going back to Table~\ref{tab:fracdiff}, and reducing the scale |
| 492 |
+ |
up/scale |
| 493 |
+ |
down variations by a factor 2, we can see that a systematic |
| 494 |
+ |
uncertainty |
| 495 |
+ |
of 5\% covers the range of reasonable variations from different MC |
| 496 |
+ |
models in SRA and SRB. |
| 497 |
+ |
%The alternative MC models indicate that a 6\% systematic uncertainty |
| 498 |
+ |
%covers the range of reasonable variations. |
| 499 |
+ |
Note that this 5\% is also consistent with the level at which we are |
| 500 |
+ |
able to test the closure of the method with alternative samples in CR5 for the high statistics |
| 501 |
+ |
regions (Table~\ref{tab:hugecr5yields}). |
| 502 |
+ |
The range of reasonable variations obtained with the alternative |
| 503 |
+ |
samples are consistent with the uncertainties assigned for |
| 504 |
+ |
the \ttll\ background based on the closure of the background |
| 505 |
+ |
predictions and data in CR4 and CR5. |
| 506 |
+ |
|
| 507 |
+ |
|
| 508 |
+ |
|
| 509 |
+ |
|
| 510 |
+ |
|
| 511 |
+ |
%\begin{table}[!h] |
| 512 |
+ |
%\begin{center} |
| 513 |
+ |
%{\footnotesize |
| 514 |
+ |
%\begin{tabular}{l||c||c|c|c|c|c|c|c} |
| 515 |
+ |
%\hline |
| 516 |
+ |
%Sample & Powheg & Madgraph & Mass Up & Mass Down & Scale |
| 517 |
+ |
%Up & Scale Down & |
| 518 |
+ |
%Match Up & Match Down \\ |
| 519 |
+ |
%\hline |
| 520 |
+ |
%\hline |
| 521 |
+ |
%SRA & $579 \pm 10$ & $569 \pm 16$ & $591 \pm 18$ & $610 \pm 22$ & $651 \pm 22$ & $537 \pm 16$ & $578 \pm 18$ & $570 \pm 17$ \\ |
| 522 |
+ |
%\hline |
| 523 |
+ |
%SRB & $328 \pm 7$ & $307 \pm 11$ & $329 \pm 13$ & $348 \pm 15$ & $344 \pm 15$ & $287 \pm 10$ & $313 \pm 13$ & $307 \pm 12$ \\ |
| 524 |
+ |
%\hline |
| 525 |
+ |
%SRC & $111 \pm 4$ & $99 \pm 5$ & $107 \pm 7$ & $113 \pm 8$ & $124 \pm 8$ & $95 \pm 6$ & $93 \pm 6$ & $106 \pm 6$ \\ |
| 526 |
+ |
%\hline |
| 527 |
+ |
%SRD & $39 \pm 2$ & $35 \pm 3$ & $41 \pm 4$ & $41 \pm 5$ & $47 \pm 5$ & $33 \pm 3$ & $31 \pm 3$ & $39 \pm 4$ \\ |
| 528 |
+ |
%\hline |
| 529 |
+ |
%SRE & $14 \pm 1$ & $15 \pm 2$ & $17 \pm 3$ & $12 \pm 3$ & $15 \pm 3$ & $13 \pm 2$ & $12 \pm 2$ & $16 \pm 2$ \\ |
| 530 |
+ |
%\hline |
| 531 |
+ |
%\end{tabular}} |
| 532 |
+ |
%\caption{ \ttdl\ predictions for alternative MC samples. The uncertainties are statistical only. |
| 533 |
+ |
%\label{tab:ttdlalt}} |
| 534 |
+ |
%\end{center} |
| 535 |
+ |
%\end{table} |
| 536 |
+ |
|
| 537 |
+ |
|
| 538 |
+ |
|
| 539 |
|
|
| 540 |
< |
\begin{table}[htb] |
| 540 |
> |
%\begin{table}[!h] |
| 541 |
> |
%\begin{center} |
| 542 |
> |
%{\footnotesize |
| 543 |
> |
%\begin{tabular}{l||c|c|c|c|c|c|c} |
| 544 |
> |
%\hline |
| 545 |
> |
%$N \sigma$ & Madgraph & Mass Up & Mass Down & Scale Up & Scale Down & |
| 546 |
> |
%Match Up & Match Down \\ |
| 547 |
> |
%\hline |
| 548 |
> |
%\hline |
| 549 |
> |
%SRA & $0.38$ & $0.42$ & $1.02$ & $2.34$ & $1.58$ & $0.01$ & $0.33$ \\ |
| 550 |
> |
%\hline |
| 551 |
> |
%SRB & $1.17$ & $0.07$ & $0.98$ & $0.76$ & $2.29$ & $0.78$ & $1.11$ \\ |
| 552 |
> |
%\hline |
| 553 |
> |
%SRC & $1.33$ & $0.37$ & $0.26$ & $1.24$ & $1.82$ & $1.97$ & $0.54$ \\ |
| 554 |
> |
%\hline |
| 555 |
> |
%SRD & $0.82$ & $0.46$ & $0.38$ & $1.32$ & $1.27$ & $1.47$ & $0.00$ \\ |
| 556 |
> |
%\hline |
| 557 |
> |
%SRE & $0.32$ & $0.75$ & $0.66$ & $0.07$ & $0.66$ & $0.83$ & $0.38$ \\ |
| 558 |
> |
%\hline |
| 559 |
> |
%\end{tabular}} |
| 560 |
> |
%\caption{ N $\sigma$ difference in \ttdl\ predictions for alternative MC samples. |
| 561 |
> |
%\label{tab:nsig}} |
| 562 |
> |
%\end{center} |
| 563 |
> |
%\end{table} |
| 564 |
> |
|
| 565 |
> |
|
| 566 |
> |
%\begin{table}[!h] |
| 567 |
> |
%\begin{center} |
| 568 |
> |
%\begin{tabular}{l||c|c|c|c} |
| 569 |
> |
%\hline |
| 570 |
> |
%Av. $\Delta$ Evt. & Alt. Gen. & $\Delta$ Mass & $\Delta$ Scale |
| 571 |
> |
%& $\Delta$ Match \\ |
| 572 |
> |
%\hline |
| 573 |
> |
%\hline |
| 574 |
> |
%SRA & $5.0$ ($1\%$) & $9.6$ ($2\%$) & $56.8$ ($10\%$) & $4.4$ ($1\%$) \\ |
| 575 |
> |
%\hline |
| 576 |
> |
%SRB & $10.4$ ($3\%$) & $9.6$ ($3\%$) & $28.2$ ($9\%$) & $2.8$ ($1\%$) \\ |
| 577 |
> |
%\hline |
| 578 |
> |
%SRC & $5.7$ ($5\%$) & $3.1$ ($3\%$) & $14.5$ ($13\%$) & $6.4$ ($6\%$) \\ |
| 579 |
> |
%\hline |
| 580 |
> |
%SRD & $1.9$ ($5\%$) & $0.1$ ($0\%$) & $6.9$ ($18\%$) & $3.6$ ($9\%$) \\ |
| 581 |
> |
%\hline |
| 582 |
> |
%SRE & $0.5$ ($3\%$) & $2.3$ ($16\%$) & $1.0$ ($7\%$) & $1.8$ ($12\%$) \\ |
| 583 |
> |
%\hline |
| 584 |
> |
%\end{tabular} |
| 585 |
> |
%\caption{ Av. difference in \ttdl\ events for alternative sample pairs. |
| 586 |
> |
%\label{tab:devt}} |
| 587 |
> |
%\end{center} |
| 588 |
> |
%\end{table} |
| 589 |
> |
|
| 590 |
> |
|
| 591 |
> |
|
| 592 |
> |
\clearpage |
| 593 |
> |
|
| 594 |
> |
% |
| 595 |
> |
% |
| 596 |
> |
%The methodology for determining the systematics on the background |
| 597 |
> |
%predictions has not changed with respect to the nominal analysis. |
| 598 |
> |
%Because the template method has not changed, the same |
| 599 |
> |
%systematic uncertainty is assessed on this prediction (32\%). |
| 600 |
> |
%The 50\% uncertainty on the WZ and ZZ background is also unchanged. |
| 601 |
> |
%The systematic uncertainty in the OF background prediction based on |
| 602 |
> |
%e$\mu$ events has changed, due to the different composition of this |
| 603 |
> |
%sample after vetoing events containing b-tagged jets. |
| 604 |
> |
% |
| 605 |
> |
%As in the nominal analysis, we do not require the e$\mu$ events |
| 606 |
> |
%to satisfy the dilepton mass requirement and apply a scaling factor K, |
| 607 |
> |
%extracted from MC, to account for the fraction of e$\mu$ events |
| 608 |
> |
%which satisfy the dilepton mass requirement. This procedure is used |
| 609 |
> |
%in order to improve the statistical precision of the OF background estimate. |
| 610 |
> |
% |
| 611 |
> |
%For the selection used in the nominal analysis, |
| 612 |
> |
%the e$\mu$ sample is completely dominated by $t\bar{t}$ |
| 613 |
> |
%events, and we observe that K is statistically consistent with constant with |
| 614 |
> |
%respect to the \MET\ requirement. However, in this analysis, the $t\bar{t}$ |
| 615 |
> |
%background is strongly suppressed by the b-veto, and hence the non-$t\bar{t}$ |
| 616 |
> |
%backgrounds (specifically, $Z\to\tau\tau$ and VV) become more relevant. |
| 617 |
> |
%At low \MET, the $Z\to\tau\tau$ background is pronounced, while $t\bar{t}$ |
| 618 |
> |
%and VV dominate at high \MET\ (see App.~\ref{app:kinemu}). |
| 619 |
> |
%Therefore, the sample composition changes |
| 620 |
> |
%as the \MET\ requirement is varied, and as a result K depends |
| 621 |
> |
%on the \MET\ requirement. |
| 622 |
> |
% |
| 623 |
> |
%We thus measure K in MC separately for each |
| 624 |
> |
%\MET\ requirement, as displayed in Fig.~\ref{fig:kvmet} (left). |
| 625 |
> |
%%The systematic uncertainty on K is determined separately for each \MET\ |
| 626 |
> |
%%requirement by comparing the relative difference in K in data vs. MC. |
| 627 |
> |
%The values of K used are the MC predictions |
| 628 |
> |
%%and the total systematic uncertainty on the OF prediction |
| 629 |
> |
%%as shown in |
| 630 |
> |
%(Table \ref{fig:kvmettable}). |
| 631 |
> |
%The contribution to the total OF prediction systematic uncertainty |
| 632 |
> |
%from K is assessed from the ratio of K in data and MC, |
| 633 |
> |
%shown in Fig.~\ref{fig:kvmet} (right). |
| 634 |
> |
%The ratio is consistent with unity to roughly 17\%, |
| 635 |
> |
%so we take this value as the systematic from K. |
| 636 |
> |
%17\% added in quadrature with 7\% from |
| 637 |
> |
%the electron to muon efficieny ratio |
| 638 |
> |
%(as assessed in the inclusive analysis) |
| 639 |
> |
%yields a total systematic of $\sim$18\% |
| 640 |
> |
%which we round up to 20\%. |
| 641 |
> |
%For \MET\ $>$ 150, there are no OF events in data inside the Z mass window |
| 642 |
> |
%so we take a systematic based on the statistical uncertainty |
| 643 |
> |
%of the MC prediction for K. |
| 644 |
> |
%This value is 25\% for \MET\ $>$ 150 GeV and 60\% for \MET\ $>$ 200 GeV. |
| 645 |
> |
%%Although we cannot check the value of K in data for \MET\ $>$ 150 |
| 646 |
> |
%%because we find no OF events inside the Z mass window for this \MET\ |
| 647 |
> |
%%cut, the overall OF yields with no dilepton mass requirement |
| 648 |
> |
%%agree to roughly 20\% (9 data vs 7.0 $\pm$ 1.1 MC). |
| 649 |
> |
% |
| 650 |
> |
% |
| 651 |
> |
%%Below Old |
| 652 |
> |
% |
| 653 |
> |
%%In reevaluating the systematics on the OF prediction, however, |
| 654 |
> |
%%we observed a different behavior of K as a function of \MET\ |
| 655 |
> |
%%as was seen in the inclusive analysis. |
| 656 |
> |
% |
| 657 |
> |
%%Recall that K is the ratio of the number of \emu\ events |
| 658 |
> |
%%inside the Z window to the total number of \emu\ events. |
| 659 |
> |
%%In the inclusive analysis, it is taken from \ttbar\ MC |
| 660 |
> |
%%and used to scale the inclusive \emu\ yield in data. |
| 661 |
> |
%%The yield scaled by K is then corrected for |
| 662 |
> |
%%the $e$ vs $\mu$ efficiency difference to obtain the |
| 663 |
> |
%%final OF prediction. |
| 664 |
> |
% |
| 665 |
> |
%%Based on the plot in figure \ref{fig:kvmet}, |
| 666 |
> |
%%we choose to use a different |
| 667 |
> |
%%K for each \MET\ cut and assess a systematic uncertainty |
| 668 |
> |
%%on the OF prediction based on the difference between |
| 669 |
> |
%%K in data and MC. |
| 670 |
> |
%%The variation of K as a function of \MET\ is caused |
| 671 |
> |
%%by a change in sample composition with increasing \MET. |
| 672 |
> |
%%At \MET\ $<$ 60 GeV, the contribution of Z plus jets is |
| 673 |
> |
%%not negligible (as it was in the inclusive analysis) |
| 674 |
> |
%%because of the b veto. (See appendix \ref{app:kinemu}.) |
| 675 |
> |
%%At higher \MET, \ttbar\ and diboson backgrounds dominate. |
| 676 |
> |
% |
| 677 |
> |
% |
| 678 |
> |
% |
| 679 |
> |
% |
| 680 |
> |
%\begin{figure}[hbt] |
| 681 |
> |
% \begin{center} |
| 682 |
> |
% \includegraphics[width=0.48\linewidth]{plots/kvmet_data_ttbm.pdf} |
| 683 |
> |
% \includegraphics[width=0.48\linewidth]{plots/kvmet_ratio.pdf} |
| 684 |
> |
% \caption{ |
| 685 |
> |
% \label{fig:kvmet}\protect |
| 686 |
> |
% The left plot shows |
| 687 |
> |
% K as a function of \MET\ in MC (red) and data (black). |
| 688 |
> |
% The bin low edge corresponds to the \MET\ cut, and the |
| 689 |
> |
% bins are inclusive. |
| 690 |
> |
% The MC used is a sum of all SM MC used in the yield table of |
| 691 |
> |
% section \ref{sec:yields}. |
| 692 |
> |
% The right plot is the ratio of K in data to MC. |
| 693 |
> |
% The ratio is fit to a line whose slope is consistent with zero |
| 694 |
> |
% (the fit parameters are |
| 695 |
> |
% 0.9 $\pm$ 0.4 for the intercept and |
| 696 |
> |
% 0.001 $\pm$ 0.005 for the slope). |
| 697 |
> |
% } |
| 698 |
> |
% \end{center} |
| 699 |
> |
%\end{figure} |
| 700 |
> |
% |
| 701 |
> |
% |
| 702 |
> |
% |
| 703 |
> |
%\begin{table}[htb] |
| 704 |
> |
%\begin{center} |
| 705 |
> |
%\caption{\label{fig:kvmettable} The values of K used in the OF background prediction. |
| 706 |
> |
%The uncertainties shown are the total relative systematic used for the OF prediction, |
| 707 |
> |
%which is the systematic uncertainty from K added in quadrature with |
| 708 |
> |
%a 7\% uncertainty from the electron to muon efficieny ratio as assessed in the |
| 709 |
> |
%inclusive analysis. |
| 710 |
> |
%} |
| 711 |
> |
%\begin{tabular}{lcc} |
| 712 |
> |
%\hline |
| 713 |
> |
%\MET\ Cut & K & Relative Systematic \\ |
| 714 |
> |
%\hline |
| 715 |
> |
%%the met zero row is used only for normalization of the money plot. |
| 716 |
> |
%%0 & 0.1 & \\ |
| 717 |
> |
%30 & 0.12 & 20\% \\ |
| 718 |
> |
%60 & 0.13 & 20\% \\ |
| 719 |
> |
%80 & 0.12 & 20\% \\ |
| 720 |
> |
%100 & 0.12 & 20\% \\ |
| 721 |
> |
%150 & 0.09 & 25\% \\ |
| 722 |
> |
%200 & 0.06 & 60\% \\ |
| 723 |
> |
%\hline |
| 724 |
> |
%\end{tabular} |
| 725 |
> |
%\end{center} |
| 726 |
> |
%\end{table} |
| 727 |
> |
|
| 728 |
> |
\subsection{Uncertainty from the isolated track veto} |
| 729 |
> |
This is the uncertainty associated with how well the isolated track |
| 730 |
> |
veto performance is modeled by the Monte Carlo. This uncertainty |
| 731 |
> |
only applies to the fraction of dilepton BG events that have |
| 732 |
> |
a second e/$\mu$ or a one prong $\tau \to h$, with |
| 733 |
> |
$P_T > 10$ GeV in $|\eta| < 2.4$. This fraction is about 1/3, see |
| 734 |
> |
Table~\ref{tab:trueisotrk}. |
| 735 |
> |
The uncertainty for these events |
| 736 |
> |
is 6\% and is obtained from tag-and-probe studies, see Section~\ref{sec:trkveto}. |
| 737 |
> |
|
| 738 |
> |
\begin{table}[!h] |
| 739 |
|
\begin{center} |
| 740 |
< |
\caption{\label{fig:kvmettable} The values of K used in the OF background prediction. |
| 741 |
< |
The uncertainties shown are the total relative systematic used for the OF prediction, |
| 742 |
< |
which is the systematic uncertainty from K added in quadrature with |
| 743 |
< |
a 7\% uncertainty from the electron to muon efficieny ratio as assessed in the |
| 744 |
< |
inclusive analysis. |
| 745 |
< |
} |
| 746 |
< |
\begin{tabular}{lcc} |
| 747 |
< |
\hline |
| 748 |
< |
\MET\ Cut & K & Relative Systematic \\ |
| 749 |
< |
\hline |
| 750 |
< |
%the met zero row is used only for normalization of the money plot. |
| 751 |
< |
%0 & 0.1 & \\ |
| 752 |
< |
30 & 0.12 & 20\% \\ |
| 753 |
< |
60 & 0.13 & 20\% \\ |
| 754 |
< |
80 & 0.12 & 20\% \\ |
| 755 |
< |
100 & 0.12 & 20\% \\ |
| 756 |
< |
150 & 0.09 & 25\% \\ |
| 757 |
< |
200 & 0.06 & 60\% \\ |
| 740 |
> |
{\footnotesize |
| 741 |
> |
\begin{tabular}{l||c|c|c|c|c|c|c} |
| 742 |
> |
\hline |
| 743 |
> |
Sample & SRA & SRB & SRC & SRD & SRE & SRF & SRG \\ |
| 744 |
> |
\hline |
| 745 |
> |
\hline |
| 746 |
> |
$\mu$ Frac. \ttdl\ with true iso. trk. & $0.32 \pm 0.03$ & $0.30 \pm 0.03$ & $0.32 \pm 0.06$ & $0.34 \pm 0.10$ & $0.35 \pm 0.16$ & $0.40 \pm 0.24$ & $0.50 \pm 0.32$ \\ |
| 747 |
> |
\hline |
| 748 |
> |
\hline |
| 749 |
> |
e Frac. \ttdl\ with true iso. trk. & $0.32 \pm 0.03$ & $0.31 \pm 0.04$ & $0.33 \pm 0.06$ & $0.38 \pm 0.11$ & $0.38 \pm 0.19$ & $0.60 \pm 0.31$ & $0.61 \pm 0.45$ \\ |
| 750 |
> |
\hline |
| 751 |
> |
\end{tabular}} |
| 752 |
> |
\caption{ Fraction of \ttdl\ events with a true isolated track. |
| 753 |
> |
\label{tab:trueisotrk}} |
| 754 |
> |
\end{center} |
| 755 |
> |
\end{table} |
| 756 |
> |
|
| 757 |
> |
\subsubsection{Isolated Track Veto: Tag and Probe Studies} |
| 758 |
> |
\label{sec:trkveto} |
| 759 |
> |
|
| 760 |
> |
|
| 761 |
> |
In this section we compare the performance of the isolated track veto in data and MC using tag-and-probe studies |
| 762 |
> |
with samples of Z$\to$ee and Z$\to\mu\mu$. The purpose of these studies is to demonstrate that the efficiency |
| 763 |
> |
to satisfy the isolated track veto requirements is well-reproduced in the MC, since if this were not the case |
| 764 |
> |
we would need to apply a data-to-MC scale factor in order to correctly |
| 765 |
> |
predict the \ttll\ background. |
| 766 |
> |
|
| 767 |
> |
This study |
| 768 |
> |
addresses possible data vs. MC discrepancies for the {\bf efficiency} to identify (and reject) events with a |
| 769 |
> |
second {\bf genuine} lepton (e, $\mu$, or $\tau\to$1-prong). It does not address possible data vs. MC discrepancies |
| 770 |
> |
in the fake rate for rejecting events without a second genuine lepton; this is handled separately in the top normalization |
| 771 |
> |
procedure by scaling the \ttlj\ contribution to match the data in the \mt\ peak after applying the isolated track veto. |
| 772 |
> |
|
| 773 |
> |
Furthermore, we test the data and MC |
| 774 |
> |
isolated track veto efficiencies for electrons and muons since we are using a Z tag-and-probe technique, but we do not |
| 775 |
> |
directly test the performance for hadronic tracks from $\tau$ decays. The performance for hadronic $\tau$ decay products |
| 776 |
> |
may differ from that of electrons and muons for two reasons. First, the $\tau$ may decay to a hadronic track plus one |
| 777 |
> |
or two $\pi^0$'s, which may decay to $\gamma\gamma$ followed by a photon conversion. As shown in Figure~\ref{fig:absiso}, |
| 778 |
> |
the isolation distribution for charged tracks from $\tau$ decays that are not produced in association with $\pi^0$s are |
| 779 |
> |
consistent with that from $\E$s and $\M$s. Since events from single prong $\tau$ decays produced in association with |
| 780 |
> |
$\pi^0$s comprise a small fraction of the total sample, and since the kinematics of $\tau$, $\pi^0$ and $\gamma\to e^+e^-$ |
| 781 |
> |
decays are well-understood, we currently demonstrate that the isolation is well-reproduced for electrons and muons only. |
| 782 |
> |
Second, hadronic tracks may undergo nuclear interactions and hence their tracks may not be reconstructed. |
| 783 |
> |
As discussed above, independent studies show that the MC reproduces the hadronic tracking efficiency within 4\%, |
| 784 |
> |
leading to a total background uncertainty of less than 0.5\% (after taking into account the fraction of the total background |
| 785 |
> |
due to hadronic $\tau$ decays with \pt\ $>$ 10 GeV tracks), and we hence regard this effect as negligible. |
| 786 |
> |
|
| 787 |
> |
The tag-and-probe studies are performed in the full data sample, and compared with the DYJets madgraph sample. |
| 788 |
> |
All events must contain a tag-probe pair (details below) with opposite-sign and satisfying the Z mass requirement 76--106 GeV. |
| 789 |
> |
We compare the distributions of absolute track isolation for probe electrons/muons in data vs. MC. The contributions to |
| 790 |
> |
this isolation sum are from ambient energy in the event from underlying event, pile-up and jet activitiy, and hence do |
| 791 |
> |
not depend on the \pt\ of the probe lepton. We therefore restrict the probe \pt\ to be $>$ 30 GeV in order to suppress |
| 792 |
> |
fake backgrounds with steeply-falling \pt\ spectra. To suppress non-Z backgrounds (in particular \ttbar) we require |
| 793 |
> |
\met\ $<$ 30 GeV and 0 b-tagged events. |
| 794 |
> |
The specific criteria for tags and probes for electrons and muons are: |
| 795 |
> |
|
| 796 |
> |
%We study the isolated track veto efficiency in bins of \njets. |
| 797 |
> |
%We are interested in events with at least 4 jets to emulate the hadronic activity in our signal sample. However since |
| 798 |
> |
%there are limited statistics for Z + $\geq$4 jet events, we study the isolated track performance in events with |
| 799 |
> |
|
| 800 |
> |
|
| 801 |
> |
\begin{itemize} |
| 802 |
> |
\item{Electrons} |
| 803 |
> |
|
| 804 |
> |
\begin{itemize} |
| 805 |
> |
\item{Tag criteria} |
| 806 |
> |
|
| 807 |
> |
\begin{itemize} |
| 808 |
> |
\item Electron passes full analysis ID/iso selection |
| 809 |
> |
\item \pt\ $>$ 30 GeV, $|\eta|<2.1$ |
| 810 |
> |
\item Matched to the single electron trigger \verb=HLT_Ele27_WP80_v*= |
| 811 |
> |
\end{itemize} |
| 812 |
> |
|
| 813 |
> |
\item{Probe criteria} |
| 814 |
> |
\begin{itemize} |
| 815 |
> |
\item Electron passes full analysis ID selection |
| 816 |
> |
\item \pt\ $>$ 30 GeV |
| 817 |
> |
\end{itemize} |
| 818 |
> |
\end{itemize} |
| 819 |
> |
\item{Muons} |
| 820 |
> |
\begin{itemize} |
| 821 |
> |
\item{Tag criteria} |
| 822 |
> |
\begin{itemize} |
| 823 |
> |
\item Muon passes full analysis ID/iso selection |
| 824 |
> |
\item \pt\ $>$ 30 GeV, $|\eta|<2.1$ |
| 825 |
> |
\item Matched to 1 of the 2 single muon triggers |
| 826 |
> |
\begin{itemize} |
| 827 |
> |
\item \verb=HLT_IsoMu30_v*= |
| 828 |
> |
\item \verb=HLT_IsoMu30_eta2p1_v*= |
| 829 |
> |
\end{itemize} |
| 830 |
> |
\end{itemize} |
| 831 |
> |
\item{Probe criteria} |
| 832 |
> |
\begin{itemize} |
| 833 |
> |
\item Muon passes full analysis ID selection |
| 834 |
> |
\item \pt\ $>$ 30 GeV |
| 835 |
> |
\end{itemize} |
| 836 |
> |
\end{itemize} |
| 837 |
> |
\end{itemize} |
| 838 |
> |
|
| 839 |
> |
The absolute track isolation distributions for passing probes are displayed in Fig.~\ref{fig:tnp}. In general we observe |
| 840 |
> |
good agreement between data and MC. To be more quantitative, we compare the data vs. MC efficiencies to satisfy |
| 841 |
> |
absolute track isolation requirements varying from $>$ 1 GeV to $>$ 5 GeV, as summarized in Table~\ref{tab:isotrk}. |
| 842 |
> |
In the $\geq 0$ and $\geq 1$ jet bins where the efficiencies can be tested with statistical precision, the data and MC |
| 843 |
> |
efficiencies agree within 6\%, and we apply this as a systematic uncertainty on the isolated track veto efficiency. |
| 844 |
> |
For the higher jet multiplicity bins the statistical precision decreases, but we do not observe any evidence for |
| 845 |
> |
a data vs. MC discrepancy in the isolated track veto efficiency. |
| 846 |
> |
|
| 847 |
> |
|
| 848 |
> |
%This is because our analysis requirement is relative track isolation $<$ 0.1, and m |
| 849 |
> |
%This requirement is chosen because most of the tracks rejected by the isolated |
| 850 |
> |
%track veto have a \pt\ near the 10 GeV threshold, and our analysis requirement is relative track isolation $<$ 1 GeV. |
| 851 |
> |
|
| 852 |
> |
\begin{figure}[hbt] |
| 853 |
> |
\begin{center} |
| 854 |
> |
\includegraphics[width=0.3\linewidth]{plots/el_tkiso_0j.pdf}% |
| 855 |
> |
\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_0j.pdf} |
| 856 |
> |
\includegraphics[width=0.3\linewidth]{plots/el_tkiso_1j.pdf}% |
| 857 |
> |
\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_1j.pdf} |
| 858 |
> |
\includegraphics[width=0.3\linewidth]{plots/el_tkiso_2j.pdf}% |
| 859 |
> |
\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_2j.pdf} |
| 860 |
> |
\includegraphics[width=0.3\linewidth]{plots/el_tkiso_3j.pdf}% |
| 861 |
> |
\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_3j.pdf} |
| 862 |
> |
\includegraphics[width=0.3\linewidth]{plots/el_tkiso_4j.pdf}% |
| 863 |
> |
\includegraphics[width=0.3\linewidth]{plots/mu_tkiso_4j.pdf} |
| 864 |
> |
\caption{ |
| 865 |
> |
\label{fig:tnp} Comparison of the absolute track isolation in data vs. MC for electrons (left) and muons (right) |
| 866 |
> |
for events with the \njets\ requirement varied from \njets\ $\geq$ 0 to \njets\ $\geq$ 4. |
| 867 |
> |
} |
| 868 |
> |
\end{center} |
| 869 |
> |
\end{figure} |
| 870 |
> |
|
| 871 |
> |
\clearpage |
| 872 |
> |
|
| 873 |
> |
\begin{table}[!ht] |
| 874 |
> |
\begin{center} |
| 875 |
> |
\begin{tabular}{l|c|c|c|c|c} |
| 876 |
> |
|
| 877 |
> |
%Electrons: |
| 878 |
> |
%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) |
| 879 |
> |
%Total MC yields : 2497277 |
| 880 |
> |
%Total DATA yields : 2649453 |
| 881 |
> |
%Muons: |
| 882 |
> |
%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) |
| 883 |
> |
%Total MC yields : 3749863 |
| 884 |
> |
%Total DATA yields : 4210022 |
| 885 |
> |
%Info in <TCanvas::MakeDefCanvas>: created default TCanvas with name c1 |
| 886 |
> |
%Info in <TCanvas::Print>: pdf file plots/nvtx.pdf has been created |
| 887 |
> |
|
| 888 |
> |
\hline |
| 889 |
> |
\hline |
| 890 |
> |
e + $\geq$0 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\ |
| 891 |
> |
\hline |
| 892 |
> |
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 \\ |
| 893 |
> |
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 \\ |
| 894 |
> |
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 \\ |
| 895 |
> |
|
| 896 |
> |
\hline |
| 897 |
> |
\hline |
| 898 |
> |
$\mu$ + $\geq$0 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\ |
| 899 |
> |
\hline |
| 900 |
> |
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 \\ |
| 901 |
> |
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 \\ |
| 902 |
> |
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 \\ |
| 903 |
> |
|
| 904 |
> |
\hline |
| 905 |
> |
\hline |
| 906 |
> |
e + $\geq$1 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\ |
| 907 |
|
\hline |
| 908 |
+ |
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 \\ |
| 909 |
+ |
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 \\ |
| 910 |
+ |
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 \\ |
| 911 |
+ |
|
| 912 |
+ |
\hline |
| 913 |
+ |
\hline |
| 914 |
+ |
$\mu$ + $\geq$1 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\ |
| 915 |
+ |
\hline |
| 916 |
+ |
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 \\ |
| 917 |
+ |
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 \\ |
| 918 |
+ |
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 \\ |
| 919 |
+ |
|
| 920 |
+ |
\hline |
| 921 |
+ |
\hline |
| 922 |
+ |
e + $\geq$2 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\ |
| 923 |
+ |
\hline |
| 924 |
+ |
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 \\ |
| 925 |
+ |
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 \\ |
| 926 |
+ |
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 \\ |
| 927 |
+ |
|
| 928 |
+ |
\hline |
| 929 |
+ |
\hline |
| 930 |
+ |
$\mu$ + $\geq$2 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\ |
| 931 |
+ |
\hline |
| 932 |
+ |
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 \\ |
| 933 |
+ |
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 \\ |
| 934 |
+ |
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 \\ |
| 935 |
+ |
|
| 936 |
+ |
\hline |
| 937 |
+ |
\hline |
| 938 |
+ |
e + $\geq$3 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\ |
| 939 |
+ |
\hline |
| 940 |
+ |
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 \\ |
| 941 |
+ |
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 \\ |
| 942 |
+ |
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 \\ |
| 943 |
+ |
|
| 944 |
+ |
\hline |
| 945 |
+ |
\hline |
| 946 |
+ |
$\mu$ + $\geq$3 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\ |
| 947 |
+ |
\hline |
| 948 |
+ |
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 \\ |
| 949 |
+ |
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 \\ |
| 950 |
+ |
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 \\ |
| 951 |
+ |
|
| 952 |
+ |
\hline |
| 953 |
+ |
\hline |
| 954 |
+ |
e + $\geq$4 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\ |
| 955 |
+ |
\hline |
| 956 |
+ |
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 \\ |
| 957 |
+ |
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 \\ |
| 958 |
+ |
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 \\ |
| 959 |
+ |
|
| 960 |
+ |
\hline |
| 961 |
+ |
\hline |
| 962 |
+ |
$\mu$ + $\geq$4 jets & $>$ 1 GeV & $>$ 2 GeV & $>$ 3 GeV & $>$ 4 GeV & $>$ 5 GeV \\ |
| 963 |
+ |
\hline |
| 964 |
+ |
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 \\ |
| 965 |
+ |
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 \\ |
| 966 |
+ |
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 \\ |
| 967 |
+ |
|
| 968 |
+ |
\hline |
| 969 |
+ |
\hline |
| 970 |
+ |
|
| 971 |
|
\end{tabular} |
| 972 |
+ |
\caption{\label{tab:isotrk} Comparison of the data vs. MC efficiencies to satisfy the indicated requirements |
| 973 |
+ |
on the absolute track isolation, and the ratio of these two efficiencies. Results are indicated separately for electrons and muons and for various |
| 974 |
+ |
jet multiplicity requirements.} |
| 975 |
|
\end{center} |
| 976 |
|
\end{table} |
| 977 |
+ |
|
| 978 |
+ |
\clearpage |
| 979 |
+ |
\subsection{Summary of uncertainties} |
| 980 |
+ |
\label{sec:bgunc-bottomline} |
| 981 |
+ |
|
| 982 |
+ |
The contribution from each source to the total uncertainty on the background yield is given in Tables~\ref{tab:relativeuncertaintycomponents} and~\ref{tab:uncertaintycomponents} for the relative and absolute uncertainties, respectively. In the low-\met\ regions the dominant uncertainty comes from the top tail-to-peak ratio, $R_{top}$ (Section~\ref{sec:ttp}), while in the high-\met\ regions the \ttll\ systematic uncertainty dominates (Section~\ref{sec:ttdilbkgunc}). |
| 983 |
+ |
|
| 984 |
+ |
\input{uncertainties_table.tex} |
| 985 |
+ |
|
| 986 |
+ |
|
| 987 |
+ |
|
| 988 |
+ |
|
| 989 |
+ |
|
| 990 |
+ |
%Figure.~\ref{fig:reliso} compares the relative track isolation |
| 991 |
+ |
%for events with a track with $\pt > 10~\GeV$ in addition to a selected |
| 992 |
+ |
%muon for $\Z+4$ jet events and various \ttll\ components. The |
| 993 |
+ |
%isolation distributions show significant differences, particularly |
| 994 |
+ |
%between the leptons from a \W\ or \Z\ decay and the tracks arising |
| 995 |
+ |
%from $\tau$ decays. As can also be seen in the figure, the \pt\ |
| 996 |
+ |
%distribution for the various categories of tracks is different, where |
| 997 |
+ |
%the decay products from $\tau$s are significantly softer. Since the |
| 998 |
+ |
%\pt\ enters the denominator of the isolation definition and hence |
| 999 |
+ |
%alters the isolation variable... |
| 1000 |
+ |
|
| 1001 |
+ |
%\begin{figure}[hbt] |
| 1002 |
+ |
% \begin{center} |
| 1003 |
+ |
% \includegraphics[width=0.5\linewidth]{plots/pfiso_njets4_log.png}% |
| 1004 |
+ |
% \includegraphics[width=0.5\linewidth]{plots/pfpt_njets4.png} |
| 1005 |
+ |
% \caption{ |
| 1006 |
+ |
% \label{fig:reliso}%\protect |
| 1007 |
+ |
% Comparison of relative track isolation variable for PF cand probe in Z+jets and ttbar |
| 1008 |
+ |
% Z+Jets and ttbar dilepton have similar isolation distributions |
| 1009 |
+ |
% ttbar with leptonic and single prong taus tend to be less |
| 1010 |
+ |
% isolated. The difference in the isolation can be attributed |
| 1011 |
+ |
% to the different \pt\ distribution of the samples, since |
| 1012 |
+ |
% $\tau$ decay products tend to be softer than leptons arising |
| 1013 |
+ |
% from \W\ or \Z\ decays.} |
| 1014 |
+ |
% \end{center} |
| 1015 |
+ |
%\end{figure} |
| 1016 |
+ |
|
| 1017 |
+ |
% \includegraphics[width=0.5\linewidth]{plots/pfabsiso_njets4_log.png} |
| 1018 |
+ |
|
| 1019 |
+ |
|
| 1020 |
+ |
%BEGIN SECTION TO WRITE OUT |
| 1021 |
+ |
%In detail, the procedure to correct the dilepton background is: |
| 1022 |
+ |
|
| 1023 |
+ |
%\begin{itemize} |
| 1024 |
+ |
%\item Using tag-and-probe studies, we plot the distribution of {\bf absolute} track isolation for identified probe electrons |
| 1025 |
+ |
%and muons {\bf TODO: need to compare the e vs. $\mu$ track iso distributions, they might differ due to e$\to$e$\gamma$}. |
| 1026 |
+ |
%\item We verify that the distribution of absolute track isolation does not depend on the \pt\ of the probe lepton. |
| 1027 |
+ |
%This is due to the fact that this isolation is from ambient PU and jet activity in the event, which is uncorrelated with |
| 1028 |
+ |
%the lepton \pt {\bf TODO: verify this in data and MC.}. |
| 1029 |
+ |
%\item Our requirement is {\bf relative} track isolation $<$ 0.1. For a given \ttll\ MC event, we determine the \pt of the 2nd |
| 1030 |
+ |
%lepton and translate this to find the corresponding requirement on the {\bf absolute} track isolation, which is simply $0.1\times$\pt. |
| 1031 |
+ |
%\item We measure the efficiency to satisfy this requirement in data and MC, and define a scale-factor $SF_{\epsilon(trk)}$ which |
| 1032 |
+ |
%is the ratio of the data-to-MC efficiencies. This scale-factor is applied to the \ttll\ MC event. |
| 1033 |
+ |
%\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 |
| 1034 |
+ |
%tracks from $\tau$ decays. Verena has showed that the absolute track isolation distribution in hadronic $\tau$ tracks is harder due |
| 1035 |
+ |
%to $\pi^0\to\gamma\gamma$ with $\gamma\to e^+e^-$.} |
| 1036 |
+ |
%\end{itemize} |
| 1037 |
+ |
%END SECTION TO WRITE OUT |
| 1038 |
+ |
|
| 1039 |
+ |
|
| 1040 |
+ |
%{\bf fix me: What you have written in the next paragraph does not |
| 1041 |
+ |
%explain how $\epsilon_{fake}$ is measured. |
| 1042 |
+ |
%Why not measure $\epsilon_{fake}$ in the b-veto region?} |
| 1043 |
+ |
|
| 1044 |
+ |
%A measurement of the $\epsilon_{fake}$ in data is non-trivial. However, it is |
| 1045 |
+ |
%possible to correct for differences in the $\epsilon_{fake}$ between data and MC by |
| 1046 |
+ |
%applying an additional scale factor for the single lepton background |
| 1047 |
+ |
%alone, using the sample in the \mt\ peak region. This scale factor is determined after applying the isolated track |
| 1048 |
+ |
%veto and after subtracting the \ttll\ component, corrected for the |
| 1049 |
+ |
%isolation efficiency derived previously. |
| 1050 |
+ |
%As shown in Figure~\ref{fig:vetoeffcomp}, the efficiency for selecting an |
| 1051 |
+ |
%isolated track in single lepton events is independent of \mt\, so the use of |
| 1052 |
+ |
%an overall scale factor is justified to estimate the contribution in |
| 1053 |
+ |
%the \mt\ tail. |
| 1054 |
+ |
% |
| 1055 |
+ |
%\begin{figure}[hbt] |
| 1056 |
+ |
% \begin{center} |
| 1057 |
+ |
% \includegraphics[width=0.5\linewidth]{plots/vetoeff_comp.png} |
| 1058 |
+ |
% \caption{ |
| 1059 |
+ |
% \label{fig:vetoeffcomp}%\protect |
| 1060 |
+ |
% Efficiency for selecting an isolated track comparing |
| 1061 |
+ |
% single lepton \ttlj\ and dilepton \ttll\ events in MC and |
| 1062 |
+ |
% data as a function of \mt. The |
| 1063 |
+ |
% efficiencies in \ttlj\ and \ttll\ exhibit no dependence on |
| 1064 |
+ |
% \mt\, while the data ranges between the two. This behavior |
| 1065 |
+ |
% is expected since the low \mt\ region is predominantly \ttlj, while the |
| 1066 |
+ |
% high \mt\ region contains mostly \ttll\ events.} |
| 1067 |
+ |
% \end{center} |
| 1068 |
+ |
%\end{figure} |
| 1069 |
+ |
|
| 1070 |
+ |
|
| 1071 |
+ |
|
| 1072 |
+ |
% THIS NEEDS TO BE WRITTEN |
