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\section{Limits on New Physics}
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\label{sec:limit}
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%As discussed in Section~\ref{sec:results}, we see one event
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%in the signal region.
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%The background prediction from the SM MC is
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%1.3 events.
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%The data driven background predictions from the ABCD method
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%and the $\pt(\ell\ell)$ method are $1.3 \pm 0.8({\rm stat}) \pm 0.3({\rm syst})$ and
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%$2.1 \pm 2.1({\rm stat}) \pm 0.6({\rm syst})$ events, respectively.
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%These three predictions are in good agreement with each other
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%and with the observation of one event in the signal region.
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%We calculate a Bayesian 95\% CL upper limit~\cite{ref:cl95cms}
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%on the number of non SM events in the signal region to be 4.1,
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%using a background prediction of $N_\textrm{BG}=1.4 \pm 0.8$
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%events and a Gaussian model of nuissance parameter integration.
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%The upper limit is not very sensitive to $N_\textrm{BG}$ and its uncertainty.
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The three background predictions for the high-\pt\ lepton trigger search
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discussed in Section~\ref{sec:results} are in good agreement with each other and
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with the observation of one event in the signal region.
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A Bayesian 95\%~confidence level (CL) upper limit~\cite{ref:cl95cms} on the number of
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non-SM events in the signal region is determined to be 4.0,
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using a background prediction of $N_\textrm{BG} = 1.4 \pm 0.8$
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events and a log-normal model of nuisance parameter integration.
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The upper limit is not very sensitive to $N_\textrm{BG}$ and its uncertainty.
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This generic upper limit is not corrected for the possibility
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of signal contamination in the control regions. This is justified because
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the two independent background estimation methods based on data agree
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and are also consistent with the SM MC prediction.
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Moreover, no evidence for non-SM contributions in
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the control regions is observed (Table~\ref{tab:datayield} and Figure~\ref{fig:victory}).
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This bound rules out the benchmark SUSY scenario LM0, for which the
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number of expected signal events is $8.6 \pm 1.6$, while the LM1 scenario predicts
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$3.6 \pm 0.5$ events.
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The uncertainties in the LM0 and LM1 event yields arise from energy scale, luminosity,
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and lepton efficiency, as discussed in Section~\ref{sec:systematics}.
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For the same-flavour search using hadronic activity triggers discussed in Section~\ref{sec:HT},
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no same-flavour events are observed and the corresponding Bayesian 95\% CL upper limit on the
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non-SM yield is 3.0 events.
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This bound rules out the benchmark SUSY scenarios LM0 and LM1, for which the
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numbers of expected signal events are $7.3 \pm 1.6$ and $3.6 \pm 0.7$, respectively.
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%As an example of the sensitivity of this search, we
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%remind the reader that the number of expected signal events in the benchmark
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%SUSY scenarios LM0 and LM1 are $8.6 \pm 1.6$ and $3.6 \pm 0.5$, respectively,
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%where the uncertainties are from energy scale, luminosity, and lepton efficiency.
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%Following text on CMSSM scan taken from RA1 paper
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We also quote the result more generally in the context of the CMSSM.
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The Bayesian 95\% CL limit in the $(m_0,m_{1/2})$ plane, for $\tan\beta=3$,
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$A_0 = 0$ and $\mu > 0$ is shown in Figure~\ref{fig:msugra}.
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The high-\pt\ lepton and hadronic trigger searches have similar sensitivity to the CMSSM;
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here we choose to show results based on the high-\pt\ lepton trigger search. The
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SUSY particle spectrum is calculated using SoftSUSY~\cite{Allanach:2002uq}, and the
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signal events are generated at leading order (LO) with \PYTHIA6.4.22.
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NLO cross sections, obtained with the
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program Prospino~\cite{Beenakker:1997kx}, are used to calculate the observed
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exclusion contour.
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At each point in the $(m_0,m_{1/2})$ plane, the acceptance uncertainty is calculated by
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summing in quadrature the uncertainties from jet and \MET\ energy scale using the
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procedure discussed in Section~\ref{sec:systematics}, the uncertainty in the
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NLO cross section due to the choice of factorization and renormalization scale,
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and the uncertainty from the parton distribution function (PDF) for CTEQ6.6~\cite{Nadolsky:2008fk},
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estimated from the envelope provided by the CTEQ6.6 error sets.
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The luminosity uncertainty and dilepton
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selection efficiency uncertainty are also included, giving a total relative acceptance uncertainty which varies
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in the range 0.2--0.3.
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%We consider a point excluded if the NLO yield exceeds the 95\% CL Bayesian upper limit
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%calculated with this acceptance uncertainty, using a log-normal model for the nuisance
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%parameter integration.
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A point is considered to be excluded if the NLO yield exceeds the 95\% CL
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Bayesian upper limit calculated with this acceptance uncertainty, using
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a log-normal model for the nuisance parameter integration.
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The limit curves do not include the effect of signal
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contamination in the control regions. We have verified that this
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has a negligible impact on the excluded regions in Figure~\ref{fig:msugra}.
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\begin{figure}[tbh]
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\begin{center}
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\includegraphics[width=1\linewidth]{plots_final/RA6_ExclusionLimit_tanb3_LO.pdf}
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\caption{\label{fig:msugra}\protect
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%Text taken from RA1 paper
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The observed 95\% CL exclusion contour at NLO (solid red line) and LO (dashed blue line)
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in the CMSSM $(m_0,m_{1/2})$ plane for $\tan\beta=3$, $A_0 = 0$ and $\mu > 0$.
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The area below the curve is excluded by this measurement. Exclusion limits obtained from
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previous experiments are presented as filled areas in the plot. Thin grey lines correspond to
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constant squark and gluino masses.
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%The plot also shows the two benchmark points LM0 and LM1 for comparison.
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%Exclusion curve in the CMSSM parameter space,
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%assuming $\tan\beta=3$, sign of $\mu = +$ and $A_{0}=0\GeVcc$.
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}
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\end{center}
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\end{figure}
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The excluded regions for the CDF
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search for jets + missing energy final states~\cite{PhysRevLett.102.121801} were
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obtained for $\tan\beta=5$, while those from D0~\cite{Abazov2008449} were obtained for
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$\tan\beta=3$, each with approximately 2~fb$^{-1}$ of data and for $\mu < 0$.
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The LEP-excluded
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regions are based on searches for sleptons and charginos~\cite{LEPSUSY}.
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%A comparison of the exclusion limit for tan b = 3 to that for tan b = 10
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%for fixed values of A0 = 0 and sign(m) > 0 indicates that
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%the exclusion reach is only weakly dependent on the value of tan b;
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%the limit shifts by less than 20\GeV in m0 and by less than 10\GeV in
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%m1/2.
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The D0 exclusion limit, valid for $\tan\beta=3$ and obtained from
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a search for associated production of charginos $\chi_{1}^{\pm}$ and
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neutralinos $\chi_2^0$ in trilepton final states~\cite{Abazov200934}, is also
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included in Figure~\ref{fig:msugra}. In contrast to the other limits presented in
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Figure~\ref{fig:msugra}, the results of our search and of the trilepton search are strongly dependent on
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the choice of $\tan\beta$ and they reach the highest sensitivity in the
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CMSSM for $\tan\beta$ values below 10.
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%We also performed a scan of the CMSSM parameter space. We set $\tan\beta=3$,
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%sign of $\mu = +$, $A_{0}=0\GeVcc$, and scan the $m_{0}$ and $m_{1/2}$ parameters
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%in steps of 10\GeVcc. At each point we calculate the acceptance uncertainty by
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%summing in quadrature the uncertainties from jet and \MET\ energy scale using the
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%procedure discussed in Section~\ref{sec:systematics} ($2-21$\%), the uncertainty in the
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%NLO cross-section assessed by varying the factorization and renormalization scale
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%by a factor of 2 ($12-15$\%), and the uncertainty from the parton density function (PDF)
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%assessed by () ($X-X$\%). We also include the luminosity uncertainty (11\%) and dilepton
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%selection efficiency uncertainty (5\%), giving a total acceptance uncertainty of $X-X$\%.
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%For each scan point, we calculate a 95\% CL upper limit using a Bayesian technique
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%using the observed signal yield (1 event), the acceptance uncertainty as calculated above, and
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%the predicted background yield and uncertainty $N_\textrm{BG}=1.4 \pm 0.8$. The point is considered
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%excluded if the NLO event yield exceeds this upper limit. The results are shown in Figure~\ref{fig:msugra}.
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