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\section{Search for Direct Top Squark Pair Production in the Single Lepton Final State}
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\label{sec:stop}
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This section presents the results of a dedicated search for the direct pair production of top squarks based on an integrated luminosity of 9.7~fb$^{-1}$.
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The decay of the top squark depends on the mass difference between the top squark and the LSP,
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$\Delta m = m_{\tilde{t}}-m_{\lsp}$. If $\Delta m > m_{t}$, the decay $\tilde{t}\to t\lsp$ is expected
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to have a large branching fraction. If there is a light chargino \chip, the decay
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$\tilde{t}\to b\chip\to b W \lsp$ is expected to be significant, especially in the $\Delta m < m_{t}$ region.
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The pair production of top squarks, followed be either of these decays, leads to events with 2 b-jets, 2 W bosons,
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and \met\ from the invisible LSPs. Our signal thus resembles SM $t\bar{t}$ production but with larger \met.
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The presence of two W bosons leads to a significant branching fraction to the single lepton final state,
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which we focus on here because it has smaller SM backgrounds than the all-hadronic final state.
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The analysis strategy is thus to select events with a single lepton and jets, and discriminate between
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signal and background using \met\ and the transverse mass \mt, discussed below.
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\subsection{Event Selection}
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We require the presence of exactly one well-identified and isolated lepton (e or $\mu$) with transverse
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momentum \pt\ $>$ 30 GeV and $|\eta|<1.44$ ($|\eta|<2.1$) for electrons (muons).
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We select events with at least four jets with \pt\ $>$ 30 GeV and $|\eta|<2.5$,
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which must be separated by $\Delta R \equiv \sqrt{(\Delta\eta)^2+(\Delta\phi)^2} < 0.4$ from the selected leptons.
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At least one of these jets is required to be consistent with coming from the decay of heavy flavor hadrons, as
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identified by the Combined Secondary Vertex Medium Point (CSVM) b-tagging algorithm~\cite{ref:btag}.
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The (b-)jet requirements suppress SM backgrounds from W bosons produced in association with jets from initial state
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radiation (ISR), referred to as the \wjets\ background.
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The \met\ is required to exceed 50 GeV, suppressing the background from QCD multijet production.
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\subsection{Backgrounds and Estimation Strategy}
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The SM background satisfying the above requirements is dominated by $t\bar{t}$ production where
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one W boson decays hadronically and the other leptonically (\ttljets), or where both W bosons decay leptonically (\ttll).
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There is a small contribution from \wjets, as well as a variety of SM
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processes with small cross section, including $t\bar{t}$ produced in association with a vector boson
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($t\bar{t}W$, $t\bar{t}Z$, $t\bar{t}\gamma$), processes with two (WW, WZ, ZZ) and three (WWW, WWZ, WZZ, ZZZ) elec-
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troweak vector bosons, and single top production in the tW-channel mode (these small contributions are collectively
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referred to below as the ``rare'' background).
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We define signal regions by requiring the events to have large transverse mass, defined as
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\begin{equation}
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M_T = \sqrt{ 2 p_{T}^{\ell} \met ( 1-cos(\Delta\phi))},
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\end{equation}
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where $p_{T}^{\ell}$ is the lepton transverse momentum and $\Delta\phi$ is the difference in azimuthal angles between the lepton
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and \met. This requirement strongly suppresses the background from \ttljets\ and \wjets. For both of these background sources, the lepton
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and neutrino which gives rise to the \met\ are produced together in the 2-body decay of the W, leading to the kinematic
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endpoint \mt\ $<$ $M_W$. For signal events, as well as the \ttll\ background, the presence of more than one invisible
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particle in the final state leads to events with \mt\ $>$ $M_W$. In addition to the \mt\ requirement, we make several
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\met\ requirements to achieve sensitivity to signals with different mass spectra.
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Signal regions with a large \met\ requirement are more sensitive to signals with large $\Delta m$.
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The dominant background in our signal regions is \ttll, which may produce events with large \met\ and \mt\ due to the presence of
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two invisible neutrinos. In order for \ttll\ events to pass the signal region selection, one of the two W leptons must not be identified,
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which occurs if one of the leptons is outside the acceptance, is a hadronic $\tau$ decaying to three charged particles (3-prong decay),
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is a hadronic $\tau$ decaying to a single charged particle (1-prong decay), or is an electron or muon that fails the lepton identification
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requirements. The latter two categories are suppressed by vetoing events that contain, in addition to the selected lepton, a charged particle
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with \pt\ $>$ 10 GeV that is isolated in space from other energetic charged particles. Furthermore, additional jets from initial state or
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final state radiation (ISR/FSR) are required to satisfy the jet multiplicity requirement $n_{jets}\geq4$. To validate and correct the MC modeling
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of jets from radiation, the MC is compared to data in a control dominated by \ttll, obtained by selecting events with two reconstructed leptons,
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moderate \met, and at least one b-jet. The MC distribution of $n_{jets}$ is reweighted to match the corresponding data distribution, resulting
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in correction factors of a few \%.
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The SM backgrounds are estimated from events simulated with Monte Carlo (MC) techniques, which are validated and
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(if necessary) corrected using comparisons to data in control regions. The MC expectation is normalized to data in the \mt\ peak region,
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in order to remove systematic uncertainties from integrated luminosity and $t\bar{t}$ cross section, and then extrapolated to the large \mt\ region.
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Correction factors and corresponding systematic uncertainties on the MC extrapolation factors are evaluated by comparing MC to data in dedicated
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control regions dominated by \wjets\ (obtained by vetoing events with b-jets), \ttll\ (obtained by requiring two selected leptons),
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and a mixture of \ttll\ and \ttljets\ (obtained by requiring a selected lepton and an isolated track).
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\input{results_table.tex}
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\subsection{Results}
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The results of the search are summarized in Table~\ref{tab:stop}, which displays the SM background expectations and the observed data yields
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in the signal regions. The distribution of \met\ after the requirement \mt\ $>$ 120 GeV for the SM background expectations is compared to
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data in Fig.~\ref{fig:stop}. Good agreement between the data and the expected background is observed, and we thus do not find evidence
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for the production of top squarks.
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\begin{figure}
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% Use the relevant command for your figure-insertion program
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% to insert the figure file.
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\centering
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\includegraphics[width=7cm,clip]{HCPPlots/stopmet.pdf}
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\caption{The \met\ distributions data and expected backgrounds for the top squark pair search. The data is compared to the sum of the
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expected backgrounds. The \met\ distributions expected in two example signal scenarios are indicated. The numbers in parentheses
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indicate the top squark mass, the LSP mass, and the chargino mass parameter $x$ defined in the text.}
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\label{fig:stop} % Give a unique label
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\end{figure}
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\subsection{Interpretation}
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%To interpret the results of our search, we consider two signal scenarios of top squark pair production, followed by the decays
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%$\tilde{t}\to t\lsp$ and $\tilde{t}\to b\chip\to b W \lsp$. In the first scenario, the only SUSY particles which participate
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%are the top squark and \lsp, and the model can thus be parameterized by the masses of these two particles. In the second case
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%the chargino mass is also relevant, and we introduce a third parameter $x$, defined as $m_{\chip} = x m_{\lsp} + (1-x) m_{\tilde{t}}$.
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%We consider $x=0.5$ and $x=0.75$ (we do not have sensitivity to the $x=0.25$ scenario).
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To interpret the results of our search, we consider top squark pair production where both top squarks decay according to $\tilde{t}\to t\lsp$
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(Fig.~\ref{fig:stop_interpretation}).
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The model is parameterized by the masses of the top squark ($m_{\tilde{top}}$) and \lsp ($m_{\lsp}$. We place upper limits on the signal
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production cross section using, for each model point in the 2-dimensional parameter space, the signal region with the best expected
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sensitivity. A region of the parameter space is excluded by comparing these cross section upper limits with the theoretical predictions
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for the signal cross section, computed at next-to-leading order including the resummation of soft gluon emission at next-to-leading-logarithmic
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accuracy (NLO+NLL)~\cite{ref:nlonll}. Our results probe top squarks with masses up to 430 GeV. For comparison, the requirement that SUSY
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provides a natural solution to the hierarchy problem suggests top squarks with masses not exceeding 500--700 GeV~\cite{ref:naturalsusy}.
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We also interpret our results assuming the top squark decays according to $\tilde{t}\to b\chip\to b W \lsp$, see Ref.~\cite{ref:stop}.
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The ATLAS experiment has presented a similar search for top squark pairs in the single lepton final state~\cite{ref:atlasstop}.
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The constraints from ATLAS on the top squark mass are more stringent than those presented here. The ATLAS model assumes large
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right-handed top quark polarization, while we take the top quark in the $\tilde{t}\to t\lsp$ decay to be unpolarized,
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resulting in a lower signal selection efficiency in our analysis.
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\begin{figure}
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% Use the relevant command for your figure-insertion program
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% to insert the figure file.
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\centering
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\includegraphics[width=7cm,clip]{HCPPlots/stop_interpretation.pdf}
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\caption{Interpretation of the results of the top squark pair search in the $\tilde{t}\to t\lsp$ scenario. The color scale indicates the
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cross section upper limits. The solid black contour and dashed black contours indicate the observed excluded region and variation in this
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excluded region due to the $\pm1\sigma$ uncertainties in the theoretical prediction of the signal cross section. The dashed blue
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and dotted blue contours indicate the median and $\pm1\sigma$ expected excluded regions. }
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\label{fig:stop_interpretation} % Give a unique label
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\end{figure}
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