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\section{Background Estimates from Data} |
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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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For the high \MET\ (high \Ht) signal region, the MC predicts 2.6 (2.5) SM events, |
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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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We use three independent methods to estimate from data the background in the signal region. |
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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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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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Because $y$ and \Ht\ are weakly-correlated, the distribution of events in the $y$ vs. \Ht\ plane is described by: |
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\begin{equation} |
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\label{eq:abcdprime} |
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\frac{\partial^2 N}{\partial y \partial H_T} = f(y)g(H_T), |
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\end{equation} |
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allowing us to deduce the number of events falling in any region of this plane. In particular, |
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we can deduce the number of events falling in our signal regions defined by requirements on \MET\ and \Ht. |
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We measure the $f(y)$ and $g(H_T)$ distributions using events in the regions indicated in Fig.~\ref{fig:abcdprimedata} |
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Next, we randomly sample values of $y$ and \Ht\ from these distributions; each pair of $y$ and \Ht\ values is a pseudo-event. |
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We generate a large ensemble of pseudo-events, and find the ratio $R_{S/C}$, the ratio of the |
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number of pseudo-events falling in the signal region to the number of pseudo-events |
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falling in a control region defined by the same requirements used to select events |
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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, we smear the bin contents |
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of $f(y)$ and $g(H_T)$ according to their uncertainties. We repeat the prediction 20 times |
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with these smeared distributions, and take the RMS of the deviation from the nominal prediction |
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We measure the $f(y)$ and $g(H_T)$ distributions using events in the regions indicated in Fig.~\ref{fig:abcdprimedata}, |
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and predict the background yields in the signal regions using Eq.~\ref{eq:abcdprime}. |
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%Next, we randomly sample values of $y$ and \Ht\ from these distributions; each pair of $y$ and \Ht\ values is a pseudo-event. |
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%We generate a large ensemble of pseudo-events, and find the ratio $R_{S/C}$, the ratio of the |
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%number of pseudo-events falling in the signal region to the number of pseudo-events |
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%falling in a control region defined by the same requirements used to select events |
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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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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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$\pt(\ell\ell)$ distribution to model the $\pt(\nu\nu)$ distribution, |
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which is identified with \MET. Thus, we use the number of observed |
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events with $\HT > 300\GeV$ and $\pt(\ell\ell) > 275\GeV$ |
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($\HT > 600\GeV$ and $\pt(\ell\ell) > 200\GeV^{1/2}$ ) |
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($\HT > 600\GeV$ and $\pt(\ell\ell) > 200\GeV$ ) |
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to predict the number of background events with |
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$\HT > 300\GeV$ and $\MET > 275\GeV$ ($\HT > 600\GeV$ and $\MET > 200\GeV$). |
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In practice, two corrections must be applied to this prediction, as described below. |
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% |
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% Now describe the corrections |
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% |
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The first correction accounts for the $\MET > 50\GeV$ requirement in the |
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preselection, which is needed to reduce the DY background. We |
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rescale the prediction by a factor equal to the inverse of the |
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fraction of events passing the preselection which also satisfy the |
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requirement $\pt(\ell\ell) > 50\GeVc$. |
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For the \Ht\ $>$ 300 GeV requirement corresponding to the high \MET\ signal region, |
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we determine this correction from data and find $K_{50}=1.5 \pm 0.3$. |
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For the \Ht\ $>$ 600 GeV requirement corresponding to the high \Ht\ signal region, |
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we do not have enough events in data to determine this correction with statistical |
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precision, so we instead extract it from MC and find $K_{50}=1.3 \pm 0.2$. |
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The second correction ($K_C$) is associated with the known polarization of the $W$, which |
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introduces a difference between the $\pt(\ell\ell)$ and $\pt(\nu\nu)$ |
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distributions. The correction $K_C$ also takes into account detector effects such as the hadronic energy |
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scale and resolution which affect the \MET\ but not $\pt(\ell\ell)$. |
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The total correction factor is $K_{50} \times K_C = 2.2 \pm 0.9$ ($1.7 \pm 0.6$) for the |
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high \MET (high \Ht) signal regions, where the uncertainty includes the statistical uncertainty |
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in the extraction of $K$ and $K_C$ and the 5\% uncertainty in the hadronic energy scale~\cite{ref:jes}. |
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In practice, we apply two corrections to this prediction, following the same procedure as in Ref.~\cite{ref:ospaper}. |
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The first correction is $K_{50}=1.5 \pm 0.3$ ($1.3 \pm 0.2$) for the high \MET\ (high \Ht) signal region. |
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The second correction factor is $K_C = 1.5 \pm 0.5$ ($1.3 \pm 0.4$) for the |
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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. In SUSY, such an excess may be produced |
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in the decay $\chi_2^0 \to \chi_1^0 \ell^+\ell^-$ or in the decay of $Z$ bosons produced in |
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the cascade decays of heavy, colored objects. In contrast, for the \ttbar\ background the |
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rates of SF and OF lepton pairs are the same, as is also the case for other SM backgrounds |
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such as $W^+W^-$ or DY$\to\tau^+\tau^-$. We quantify the excess of SF vs. OF pairs using the |
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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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quantity |
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\begin{equation} |
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\label{eq:ofhighpt} |
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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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\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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where $R_{\mu e} = 1.13 \pm 0.05$ is the ratio of muon to electron selection efficiencies, |
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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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in the control regions, which tends to decrease the significance of a signal |
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which may be present in the data by increasing the background prediction. |
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In general, it is difficult to quantify these effects because we |
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do not know what signal may be present in the data. Having two |
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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. |
