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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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[DESCRIBE HERE ONE BY ONE THE UNCERTAINTIES THAT ARE PRESENT IN THE SPREADSHHET |
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FROM WHICH WE CALCULATE THE TOTAL UNCERTAINTY. WE KNOW HOW TO DO THIS |
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AND |
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WE HAVE THE TECHNOLOGY FROM THE 7 TEV ANALYSIS TO PROPAGATE ALL |
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UNCERTAINTIES |
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CORRECTLY THROUGH. WE WILL DO IT ONCE WE HAVE SETTLED ON THE |
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INDIVIDUAL PIECES WHICH ARE STILL IN FLUX] |
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|
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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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region, |
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for electrons and muons separately. |
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|
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The choice to normalizing to the peak region of $M_T$ has the |
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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 $t\bar{t} \to$ 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 BG source is tabulated in |
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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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First, however, we discuss the uncertainties one-by-one and we comment |
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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 XX and XX \%, depending on the signal region |
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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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different $M_T$ regions used as control). |
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Since |
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the major BG, eg, $t\bar{t}$ are normalized to the peak regions, this |
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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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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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IN 7 TEV DATA WE HAD SOME SHAPE DIFFERENCES IN THE MTRANS REGION THAT |
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LED US TO CONSERVATIVELY INCLUDE THIS UNCERTAINTY. WE NEED TO LOOK |
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INTO THIS AGAIN |
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\subsection{Uncertainty on the Wjets cross-section and the rare MC cross-sections} |
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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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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{Scale factors for the tail-to-peak ratios for lepton + |
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\subsection{Tail-to-peak ratios for lepton + |
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jets top and W events} |
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These tail-to-peak ratios are described in Section~\ref{sec:ttp}. |
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They are studied in CR1 and CR2. The studies are described |
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in Sections~\ref{sec:cr1} and~\ref{sec:cr2}), respectively, where |
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we also give the uncertainty on the scale factors. |
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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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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 XX\% uncertainties on $K_3$ and $K_4$ |
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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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result directly in a XX\% uncertainty on the dilepton BG, which is by far |
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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\ Acceptance} |
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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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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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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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|
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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|c} |
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\hline |
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Sample & Powheg & 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 & $579 \pm 10$ & $569 \pm 16$ & $591 \pm 18$ & $610 \pm 22$ & $651 \pm 22$ & $537 \pm 16$ & $578 \pm 18$ & $570 \pm 17$ \\ |
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\hline |
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SRB & $328 \pm 7$ & $307 \pm 11$ & $329 \pm 13$ & $348 \pm 15$ & $344 \pm 15$ & $287 \pm 10$ & $313 \pm 13$ & $307 \pm 12$ \\ |
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\hline |
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SRC & $111 \pm 4$ & $99 \pm 5$ & $107 \pm 7$ & $113 \pm 8$ & $124 \pm 8$ & $95 \pm 6$ & $93 \pm 6$ & $106 \pm 6$ \\ |
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\hline |
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SRD & $39 \pm 2$ & $35 \pm 3$ & $41 \pm 4$ & $41 \pm 5$ & $47 \pm 5$ & $33 \pm 3$ & $31 \pm 3$ & $39 \pm 4$ \\ |
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\hline |
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SRE & $14 \pm 1$ & $15 \pm 2$ & $17 \pm 3$ & $12 \pm 3$ & $15 \pm 3$ & $13 \pm 2$ & $12 \pm 2$ & $16 \pm 2$ \\ |
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\hline |
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\end{tabular}} |
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\caption{ \ttdl\ predictions for alternative MC samples. The uncertainties are statistical only. |
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\label{tab:ttdlalt}} |
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\end{center} |
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\end{table} |
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\begin{figure}[hbt] |
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\begin{center} |
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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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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. 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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\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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% 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 samples. |
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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 |
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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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\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 |
| 193 |
< |
$N \sigma$ & Madgraph & Mass Up & Mass Down & Scale Up & Scale Down & |
| 194 |
< |
Match Up & Match Down \\ |
| 195 |
< |
\hline |
| 196 |
< |
\hline |
| 197 |
< |
SRA & $0.38$ & $0.42$ & $1.02$ & $2.34$ & $1.58$ & $0.01$ & $0.33$ \\ |
| 198 |
< |
\hline |
| 199 |
< |
SRB & $1.17$ & $0.07$ & $0.98$ & $0.76$ & $2.29$ & $0.78$ & $1.11$ \\ |
| 200 |
< |
\hline |
| 201 |
< |
SRC & $1.33$ & $0.37$ & $0.26$ & $1.24$ & $1.82$ & $1.97$ & $0.54$ \\ |
| 202 |
< |
\hline |
| 203 |
< |
SRD & $0.82$ & $0.46$ & $0.38$ & $1.32$ & $1.27$ & $1.47$ & $0.00$ \\ |
| 204 |
< |
\hline |
| 205 |
< |
SRE & $0.32$ & $0.75$ & $0.66$ & $0.07$ & $0.66$ & $0.83$ & $0.38$ \\ |
| 206 |
< |
\hline |
| 207 |
< |
\end{tabular}} |
| 208 |
< |
\caption{ N $\sigma$ difference in \ttdl\ predictions for alternative MC samples. |
| 209 |
< |
\label{tab:nsig}} |
| 210 |
< |
\end{center} |
| 211 |
< |
\end{table} |
| 271 |
> |
In Fig.~\ref{fig:ttllsyst} we compare the alternate MC \ttll\ background predictions |
| 272 |
> |
for regions A through E. We can make the following observations based |
| 273 |
> |
on this Figure. |
| 274 |
|
|
| 275 |
+ |
\begin{itemize} |
| 276 |
+ |
\item In the tighter signal regions we are running out of |
| 277 |
+ |
statistics. |
| 278 |
+ |
\item Within the limited statistics, there is no evidence that the |
| 279 |
+ |
situation changes as we go from signal region A to signal region E. |
| 280 |
+ |
Therefore, we assess a systematic based on the relatively high |
| 281 |
+ |
statistics |
| 282 |
+ |
test in signal region A, and apply the same systematic uncertainty |
| 283 |
+ |
to all other regions. |
| 284 |
+ |
\item In order to fully (as opposed as 1$\sigma$) cover the |
| 285 |
+ |
alternative MC variations in region A we would have to take a |
| 286 |
+ |
systematic |
| 287 |
+ |
uncertainty of $\approx 10\%$. This would be driven by the |
| 288 |
+ |
scale up/scale down variations, see Table~\ref{tab:fracdiff}. |
| 289 |
+ |
\end{itemize} |
| 290 |
|
|
| 291 |
< |
\begin{table}[!h] |
| 291 |
> |
\begin{table}[!ht] |
| 292 |
|
\begin{center} |
| 293 |
< |
\begin{tabular}{l||c|c|c|c} |
| 217 |
< |
\hline |
| 218 |
< |
Av. $\Delta$ Evt. & Alt. Gen. & $\Delta$ Mass & $\Delta$ Scale |
| 219 |
< |
& $\Delta$ Match \\ |
| 220 |
< |
\hline |
| 221 |
< |
\hline |
| 222 |
< |
SRA & $5.0$ ($1\%$) & $9.6$ ($2\%$) & $56.8$ ($10\%$) & $4.4$ ($1\%$) \\ |
| 293 |
> |
\begin{tabular}{l|c|c} |
| 294 |
|
\hline |
| 295 |
< |
SRB & $10.4$ ($3\%$) & $9.6$ ($3\%$) & $28.2$ ($9\%$) & $2.8$ ($1\%$) \\ |
| 295 |
> |
Sample |
| 296 |
> |
& K3 & K4\\ |
| 297 |
|
\hline |
| 226 |
– |
SRC & $5.7$ ($5\%$) & $3.1$ ($3\%$) & $14.5$ ($13\%$) & $6.4$ ($6\%$) \\ |
| 298 |
|
\hline |
| 299 |
< |
SRD & $1.9$ ($5\%$) & $0.1$ ($0\%$) & $6.9$ ($18\%$) & $3.6$ ($9\%$) \\ |
| 300 |
< |
\hline |
| 301 |
< |
SRE & $0.5$ ($3\%$) & $2.3$ ($16\%$) & $1.0$ ($7\%$) & $1.8$ ($12\%$) \\ |
| 299 |
> |
Powheg & $1.01 \pm 0.03$ & $0.93 \pm 0.04$ \\ |
| 300 |
> |
Madgraph & $1.01 \pm 0.04$ & $0.92 \pm 0.04$ \\ |
| 301 |
> |
Mass Up & $1.00 \pm 0.04$ & $0.92 \pm 0.04$ \\ |
| 302 |
> |
Mass Down & $1.06 \pm 0.04$ & $0.99 \pm 0.05$ \\ |
| 303 |
> |
Scale Up & $1.14 \pm 0.04$ & $1.23 \pm 0.06$ \\ |
| 304 |
> |
Scale Down & $0.89 \pm 0.03$ & $0.74 \pm 0.03$ \\ |
| 305 |
> |
Match Up & $1.02 \pm 0.04$ & $0.97 \pm 0.04$ \\ |
| 306 |
> |
Match Down & $1.02 \pm 0.04$ & $0.91 \pm 0.04$ \\ |
| 307 |
|
\hline |
| 308 |
|
\end{tabular} |
| 309 |
< |
\caption{ Av. difference in \ttdl\ events for alternative sample pairs. |
| 310 |
< |
\label{tab:devt}} |
| 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/n_dl_comp_SRA.pdf}% |
| 334 |
< |
\includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRB.pdf} |
| 335 |
< |
\includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRC.pdf}% |
| 336 |
< |
\includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRD.pdf} |
| 337 |
< |
\includegraphics[width=0.5\linewidth]{plots/n_dl_comp_SRE.pdf} |
| 338 |
< |
\caption{ |
| 339 |
< |
\label{fig:ttllsyst}\protect |
| 248 |
< |
Comparison of the \ttll\ central prediction with those using |
| 249 |
< |
alternative MC samples. The blue band corresponds to the |
| 250 |
< |
total statistical error for all data and MC samples. The |
| 251 |
< |
alternative sample predictions are indicated by the |
| 252 |
< |
datapoints. The uncertainties on the alternative predictions |
| 253 |
< |
correspond to the uncorrelated statistical uncertainty from |
| 254 |
< |
the size of the alternative sample only. |
| 255 |
< |
[TO BE UPDATED WITH THE LATEST SELECTION AND SFS]} |
| 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} |
| 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 |
|
|
| 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 1/3 (THIS WAS THE |
| 623 |
< |
7 TEV NUMBER, CHECK). The uncertainty for these events |
| 624 |
< |
is XX\% and is obtained from Tag and Probe studies of Section~\ref{sec:trkveto} |
| 625 |
< |
|
| 404 |
< |
\subsubsection{Isolated Track Veto: Tag and Probe Studies} |
| 405 |
< |
\label{sec:trkveto} |
| 406 |
< |
|
| 407 |
< |
[EVERYTHING IS 7TEV HERE, UPDATE WITH NEW RESULTS \\ |
| 408 |
< |
ADD TABLE WITH FRACTION OF EVENTS THAT HAVE A TRUE ISOLATED TRACK] |
| 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} |
| 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 predict the \ttll\ background. This study |
| 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 |
| 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 neglgigible. |
| 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 2011 data sample, and compared with the DYJets madgraph sample. |
| 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 |
| 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 |
| 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. |
| 761 |
|
|
| 762 |
|
\begin{table}[!ht] |
| 763 |
|
\begin{center} |
| 540 |
– |
\caption{\label{tab:isotrk} Comparison of the data vs. MC efficiencies to satisfy the indicated requirements |
| 541 |
– |
on the absolute track isolation, and the ratio of these two efficiencies. Results are indicated separately for electrons and muons and for various |
| 542 |
– |
jet multiplicity requirements.} |
| 764 |
|
\begin{tabular}{l|c|c|c|c|c} |
| 765 |
|
|
| 766 |
|
%Electrons: |
| 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 |
| 919 |
|
%END SECTION TO WRITE OUT |
| 920 |
|
|
| 921 |
|
|
| 922 |
< |
{\bf fix me: What you have written in the next paragraph does not explain how $\epsilon_{fake}$ is measured. |
| 923 |
< |
Why not measure $\epsilon_{fake}$ in the b-veto region?} |
| 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 |
| 949 |
|
% \end{center} |
| 950 |
|
%\end{figure} |
| 951 |
|
|
| 723 |
– |
\subsection{Summary of uncertainties} |
| 724 |
– |
\label{sec:bgunc-bottomline}. |
| 952 |
|
|
| 953 |
< |
THIS NEEDS TO BE WRITTEN |
| 953 |
> |
|
| 954 |
> |
% THIS NEEDS TO BE WRITTEN |
