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\section{Counting Experiments} |
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\label{sec:datadriven} |
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To look for possible BSM contributions, we define 2 signal regions that preserve about |
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To look for possible BSM contributions, we define 2 signal regions that reject all but |
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0.1\% of the dilepton $t\bar{t}$ events, by adding requirements of large \MET\ and \Ht: |
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\begin{itemize} |
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dominated by dilepton $t\bar{t}$; the expected LM1 yield is 17 (14) and the |
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expected LM3 yield is 6.4 (6.7). The signal regions are indicated in Fig.~\ref{fig:met_ht}. |
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These signal regions are tighter than the one used in our published 2010 analysis since |
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with the larger data sample they give improved sensitivity to contributions from new physics. |
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with the larger data sample they allow us to explore phase space farther from the core |
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of the SM distributions. |
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We perform counting experiments in these signal regions, and use three independent methods to estimate from data the background in the signal region. |
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The first method is a novel technique based on the ABCD method, which we used in our 2010 analysis~\cite{ref:ospaper}, |
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The first method is a novel technique which is a variation of the ABCD method, which we used in our 2010 analysis~\cite{ref:ospaper}, |
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and exploits the fact that \HT\ and $y \equiv \MET/\sqrt{H_T}$ are nearly uncorrelated for the $t\bar{t}$ background; |
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this method is referred to as the ABCD' technique. First, we extract the $y$ and \Ht\ distributions |
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$f(y)$ and $g(H_T)$ from data, using events from control regions which are dominated by background. |
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%to measure $f(y)$ and $g(H_T)$. We then |
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%multiply this ratio by the number events which fall in the control region in data |
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%to get the predicted yield, ie. $N_{pred} = R_{S/C} \times N({\rm control})$. |
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To estimate the statistical uncertainty in the predicted background, the bin contents |
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of $f(y)$ and $g(H_T)$ are smeared according to their Poisson uncertainties, the prediction is repeated 20 times |
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with these smeared distributions, and the RMS of the deviation from the nominal prediction is taken |
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as the statistical uncertainty. We have studied this technique using toy MC studies based on |
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To estimate the statistical uncertainty in the predicted background, the bin contents |
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of $f(y)$ and $g(H_T)$ are smeared according to their Poisson uncertainties. |
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We have studied this technique using toy MC studies based on |
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event samples of similar size to the expected yield in data for 1 fb$^{-1}$. |
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Based on these studies we correct the predicted background yields by factors of 1.2 $\pm$ 0.5 |
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(1.0 $\pm$ 0.5) for the high \MET\ (high \Ht) signal region. |
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Our third background estimation method is based on the fact that many models of new physics |
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produce an excess of SF with respect to OF lepton pairs, while for the \ttbar\ background the |
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rates of SF and OF lepton pairs are the same. Hence we make use of the OF subtraction technique |
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discussed in Sec.~\ref{sec:fit} in which we performed a shape analysis of the dilepton mass distribution. |
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Here we perform a counting experiment, by quantifying the the excess of SF vs. OF pairs using the |
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rates of SF and OF lepton pairs are the same, as discussed in Sec.~\ref{sec:fit}. |
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Here we perform a counting experiment, by quantifying the excess of SF vs. OF pairs using the |
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quantity |
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\begin{equation} |
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\Delta = R_{\mu e}N(ee) + \frac{1}{R_{\mu e}}N(\mu\mu) - N(e\mu). |
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\end{equation} |
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Here $R_{\mu e} = 1.13 \pm 0.05$ is the ratio of muon to electron selection efficiencies, |
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evaluated by taking the square root of the ratio of the number of |
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$Z \to \mu^+\mu^-$ to $Z \to e^+e^-$ events in data, in the mass range 76-106 GeV with no jets or |
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\met\ requirements. The quantity $\Delta$ is predicted to be 0 for processes with |
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This quantity is predicted to be 0 for processes with |
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uncorrelated lepton flavors. In order for this technique to work, the kinematic selection |
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applied to events in all dilepton flavor channels must be the same, which is not the case |
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for our default selection because the $Z$ mass veto is applied only to same-flavor channels. |
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do not know what signal may be present in the data. Having three |
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independent methods (in addition to expectations from MC) |
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adds redundancy because signal contamination can have different effects |
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in the different control regions for the two methods. |
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in the different control regions for the three methods. |
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For example, in the extreme case of a |
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BSM signal with identical distributions of $\pt(\ell \ell)$ and \MET, an excess of events might be seen |
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in the ABCD' method but not in the $\pt(\ell \ell)$ method. |
