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\section{Introduction}
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\label{sec:intro}
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In this Letter we describe a search for physics beyond the Standard Model (BSM)
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in a \lumi\ sample of proton-proton collisions collected by the Compact Muon
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Solenoid (CMS) detector at the Large Hadron Collider (LHC), at a center-of-mass
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energy of $\sqrt{s}=7$~TeV. We search for events with $Z \to \ell \ell$ ($\ell =
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e$ or $\mu$),
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accompanied by significant
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hadronic energy and missing transverse energy (\met). This search is motivated by
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three general considerations:
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astrophysical evidence for dark matter suggests that we concentrate on
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events with high \met, production of $Z$ bosons with high \met is
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a rare process in the SM,
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and high cross section BSM physics signals are likely to be produced
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strongly, producing significant hadronic activity in conjunction with the $Z$-boson.
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A specific BSM scenario which results in this signature is provided by
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Supersymmetric (SUSY) models in which new, heavy particles are pair-produced and subsequently
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undergo cascade decays, producing hadronic jets and, in some cases,
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$Z$-bosons~\cite{Martin:fk}. These
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cascade decays terminate in the production of a weakly-interacting massive particle (WIMP),
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which escapes detection and results in large \met.
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Our strategy is as follows. We select clean samples of $Z \to ee$ and
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$Z \to \mu \mu$ with two or more hadronic jets. We compare the \met distribution
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in these events with Standard Model (SM) expectations obtained using data-driven
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methods to minimize the dependence on Monte Carlo simulation. Having found
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no evidence for events with anomalously high \met, we proceed
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to set limits on the cross-section for the
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production of $Z$-bosons with jets and \met $> 60$ and
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$> 120$ GeV. Finally, we provide information to enable others
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to use our results for model testing.
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