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\section{Introduction}
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\label{ref:intro}
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This note presents a search for the production of supersymmetric (SUSY) stop quark pairs in events with a
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single isolated lepton, several jets, missing transverse energy, and large transverse mass. We use the full
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2011 data sample, corresponding to an integrated luminosity of \lumi.
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This search is of theoretical interest because of the critical role played
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by the stop quark in solving the hierarchy problem in SUSY models. This solution requires that the stop quark
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be light, less than a few hundred GeV and hence within reach for direct pair production. We focus on two decay modes
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$\tilde{t}\rightarrow t\chi^0_1$ and $\tilde{t}\rightarrow b \chi^+_1$ which are expected
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to have large branching fractions if they are kinematically accessible, leading to:
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\begin{itemize}
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\item $pp\rightarrow\tilde{t}\bar{\tilde{t}}\rightarrow t\bar{t}\chi^0_1\chi^0_1$, and
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\item $pp\rightarrow\tilde{t}\bar{\tilde{t}}\rightarrow b\bar{b}\chi^+_1\chi^-_1 \rightarrow b\bar{b}W^+W^-\chi^0_1\chi^0_1$.
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\end{itemize}
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Both of these signatures contain high transverse momentum (\pt) jets including two b-jets, and missing transverse
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energy (\MET) due to the invisible $\chi^0_1$ lightest SUSY particles (LSP's). In addition, the presence of
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two W bosons leads to a large branching fraction to the single lepton final state. Hence we require the presence
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of exactly one isolated, high \pt electron or muon, which provides significant suppression of several backgrounds
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that are present in the all-hadronic channel. The largest backgrounds for this signature are semi-leptonic \ttbar\
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and \wjets. These backgrounds contain a single leptonically-decaying W boson, and the transverse mass (\mt)
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of the lepton-neutrino system has a kinematic endpoint requiring \mt $<$ $M_W$. For signal stop quark events,
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the presence additional LSP's in the final states allows the \mt to exceed $M_W$. Hence we search for an excess
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of events with large \mt. The dominant background in this kinematic region is dilepton \ttbar\ where one of the
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leptons is not identified, since the presence of two neutrinos from leptonically-decaying W bosons allows the
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\mt\ to exceed $M_W$. Backgrounds are estimated from Monte Carlo (MC) simulation, with careful validation
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and determination of scale factors and corresponding uncertainties based on data control samples.
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The expected stop quark pair production cross section (see Fig.~\ref{fig:stopxsec}) varies between O(10) pb
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for $m_{\tilde{t}}=200$~GeV and O(0.01) pb for $m_{\tilde{t}}=500$~GeV. The critical challenge of this analysis
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is due to the fact that for light stop quarks with a mass close to the top quark, the production cross section is
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large but the kinematic distributions, in particular \mt, are very similar to SM \ttbar\ production, such that it becomes very
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difficult to distinguish the signal and background. For large stop quark mass the kinematic distributions differ
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from those in SM \ttbar\ production, but the cross section decreases rapidly, reducing the signal-to-background
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ratio.
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\begin{figure}[hbt]
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\begin{center}
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\includegraphics[width=0.4\linewidth]{plots/stop.pdf}
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\caption{
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\label{fig:stopxsec}\protect
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The stop quark pair production cross section in pb, as a function of the stop quark mass.}
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\end{center}
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\end{figure}
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