Available on the CERN CDS information server CMS PAS EXO-12-048

CMS Physics Analysis Summary

Contact: cms-pag-conveners-exotica@cern.ch 2013/03/08

Search for new physics in monojet events in pp collisions at√s = 8 TeV

The CMS Collaboration

Abstract

A search has been made for events containing an energetic jet and an imbalance intransverse momentum using a data sample of pp collisions at a center-of-mass energyof 8 TeV. The data were collected by the CMS detector at the LHC and correspond toan integrated luminosity of 19.5 fb−1. The number of observed events is consistentwith the standard model expectation. Constraints on the dark matter-nucleon scat-tering cross sections are determined for both spin-independent and spin-dependentinteraction models. Limits are also placed on the Arkani-Hamed, Dimopoulos, andDvali model parameter MD as a function of the number of extra dimensions and theproduction of Unparticles.

1

1 IntroductionThis paper presents a search for new physics in events containing a jet and an imbalance intransverse momentum (Emiss

T ) using a data sample corresponding to an integrated luminosityof 19.5 fb−1. The data were collected with the Compact Muon Solenoid (CMS) detector in ppcollisions provided by the Large Hadron Collider (LHC) at a center-of-mass energy of 8 TeV.The signature has been proposed as a discovery signal for many new physics scenarios, in-cluding the pair production of dark matter particles (χ) [1, 2], large extra dimensions in theframework of the model proposed by Arkani–Hamed, Dimopoulos, and Dvali (ADD) [3–7]and Unparticle production [8].

One of the most compelling pieces of evidence for physics beyond the SM is the existence ofdark matter. Numerous astrophysical measurements, such as the rotational speed of galaxiesand gravitational lensing [9–11] point to the existence of a non-baryonic form of matter. Oneof the most popular class of candidates proposed to explain dark matter are stable weaklyinteracting massive particles (WIMPs). The direct detection experiments aim to detect the recoilfrom the scattering of a WIMP off a nucleus whilst the indirect detection experiments searchfor the products of the annihilation of dark matter particles. These particles may also be pair-produced at the LHC provided their mass is less than half the parton-parton center-of-massenergy,

√s. When accompanied by a jet from initial state radiation (ISR), these events produce

the signature of a jet plus missing transverse momentum.

The interaction between the dark matter particles and standard model (SM) particles can be as-sumed to be mediated by a particle that can be produced at the LHC or by a very heavy particlethat is not accessible to LHC energies. A heavy mediator can be integrated out of the matrixelement calculation such that the interaction is treated as a contact interaction, characterizedby a scale Λ = M/√gχgq where M is the mass of the mediator, gχ and gq are its coupling to χand to quarks, respectively [2].

In this paper, results for vector, axial-vector and scalar [12, 13] interactions between χ andquarks are presented, assuming χ is a Dirac fermion. The vector and scalar interactions can berelated to spin-independent DM-nucleon interactions whereas the axial-vector interaction canbe converted to spin-dependent DM-nucleon interactions. The results are not greatly altered ifthe DM particle is a Majorana fermion, although the vector interactions are not present in thiscase [2].

Results from previous collider searches at the Tevatron and the LHC in the monojet plus EmissT

channel [14–16] have been used to set limits on the dark matter-nucleon scattering cross section(σχN). Limits on σχN have also been determined by the CMS Collaboration in the monophotonplus Emiss

T channel [17].

Dark matter particle production results from colliders can be compared with results fromsearches for dark matter-nucleon scattering (direct detection) [18–24] and from searches fordark matter annihilation (indirect detection) [25, 26]. Indirect detection experiments assumethat the DM particle is a Majorana fermion.

The ADD model accommodates the large difference between the electroweak and Planck scalesby introducing a number δ of extra spatial dimensions, which in the simplest scenario are com-pactified over a multidimensional torus of common radius R. In this framework, the SM parti-cles and gauge interactions are confined to the ordinary 3 + 1 space-time dimensions, whereasgravity is free to propagate through the entire multidimensional space. The strength of thegravitational force in 3 + 1 dimensions is effectively diluted. The fundamental scale MD of this4+δ-dimensional theory is related to the apparent four-dimensional Planck scale MPl accord-

2 2 The CMS detector and event reconstruction

ing to MPl2 ≈ MD

δ+2Rδ. The production of gravitons is expected to be greatly enhanced bythe increased phase space available in the extra dimensions. Once produced, the graviton es-capes undetected into extra dimensions and its presence must be inferred from Emiss

T . Searchesfor large extra dimensions in monojet or monophoton channels were performed previously[15, 27–35], and no evidence of new physics was observed.

Unparticle models postulate a new scale-invariant (conformal) sector which is coupled to theSM particles through a connector sector at a high mass scale. An operator with a general non-integer scale dimension dU in a conformal sector yields a spectrum of weakly interacting par-ticles. These ‘unparticles’ leave the detector without interacting, thus manifesting themselvesas Emiss

T . In this analysis, unparticles are assumed to be sufficiently long-lived that they do notdecay in the detector. Effects of unparticles below mass scale ΛU are studied in the context ofan effective field theory. If the mass scale ΛU is assumed to be of order TeV/c2, then by using aneffective field theory below that scale one is able to study the effects of unparticles at the LHC.

2 The CMS detector and event reconstructionCMS uses a right-handed coordinate system in which the z axis points in the anticlockwisebeam direction, the x axis points towards the center of the LHC ring, and the y axis pointsup, perpendicular to the plane of the LHC ring. The azimuthal angle φ is measured in the x-yplane, and the polar angle θ is measured with respect to the z axis. A particle with energy E andmomentum ~p is characterized by transverse momentum pT = |~p| sin θ, and pseudorapidityη = − ln [tan(θ/2)].

The CMS superconducting solenoid, 12.5 m long with an internal diameter of 6 m, providesa uniform magnetic field of 3.8 T. The inner tracking system is composed of a pixel detectorwith three barrel layers at radii between 4.4 and 10.2 cm and a silicon strip tracker with 10barrel detection layers extending outwards to a radius of 1.1 m. This system is complementedby two endcaps, extending the acceptance up to |η| = 2.5. The momentum resolution forreconstructed tracks in the central region is about 1% at pT = 100 GeV/c. The calorimeters insidethe magnet coil consist of a lead tungstate crystal electromagnetic calorimeter (ECAL) and abrass-scintillator hadron calorimeter (HCAL) with coverage up to |η| = 3. The quartz/steelforward hadron calorimeters extend the calorimetry coverage up to |η| = 5. The HCAL hasan energy resolution of about 10% at 100 GeV for charged pions. Muons are measured up to|η| < 2.4 in gas-ionization detectors embedded in the flux-return yoke of the magnet. A fulldescription of the CMS detector can be found in Ref. [36].

Particles in an event are individually identified using a particle-flow reconstruction [37]. Thisalgorithm reconstructs each particle produced in a collision by using an optimised combinationof information from the tracker, the calorimeters, and the muon system, and identifies them aseither charged hadrons, neutral hadrons, photons, muons, or electrons. These particles are usedas inputs to the anti-kT jet clustering algorithm [38] with a distance parameter of 0.5. Jet energiesare corrected to particle level with pT- and η-dependent correction factors. These correctionsare derived from Monte Carlo (MC) simulation and, for data events, are supplemented bya correction, derived by measuring the pT balance in dijet events from collision data [39]. TheEmiss

T in this analysis is defined as the magnitude of the vector sum of the transverse momentumof all particles reconstructed in the event excluding muons. This definition allows the use of acontrol sample of Z(µµ) events for estimating the Z(νν) background.

Muons are reconstructed by finding compatible track segments in the silicon tracker and themuon detectors [40] and are required to be within |η| < 2.1. Electron candidates are recon-

3

structed starting from a cluster of energy deposits in the ECAL that is then matched to themomentum associated with a track in the silicon tracker. Electron candidates are required tohave |η| < 1.44 or 1.56 < |η| < 2.5 to avoid poorly instrumented regions. Muon and electroncandidates are required to originate within 2 mm of the beam axis in the transverse plane. Arelative isolation parameter is defined as the sum of the pT of the charged hadrons, neutralhadrons, and photon contributions computed in a cone of radius 0.3 around the lepton direc-tion, divided by the lepton pT. Lepton candidates with relative isolation values below 0.2 areconsidered isolated.

Hadronically decaying taus are reconstructed using the “hadron-plus-strips” (HPS) algorithm [41],which reconstructs candidates with one or three charged pions and up to two neutral pions.

3 Monte Carlo event generationThe DM signal samples are produced using the leading order (LO) matrix element event gener-ator MADGRAPH [42] interfaced with PYTHIA 6.42 [43] with tune Z2star [44] for parton shower-ing and hadronization and the CTEQ 6L1 [45] parton distribution functions (PDF). Dark matterparticles with masses Mχ =1, 10, 200, 400, 700, and 1000 GeV/c2 are generated for both vectorand axial-vector interactions. The pT of the associated parton is required to be greater than80 GeV/c. For the case of a light mediator, the mediator mass (M) is varied between 50 GeV/c2

and 3 TeV/c2 for a dark matter mass of 50 GeV/c2 and 500 GeV/c2. The widths of the mediator(Γ) considered are; Γ = M/3, M/10, M/8π.

The events for the ADD model and scalar Unparticles are generated with PYTHIA 8.153 [46, 47],using tune 4C [48] and the CTEQ 6.6M [45] PDFs. The ADD (Unparticles) model is an effectivetheory and holds only for energies well below MD (ΛU). For a parton center-of-mass energy√

s > MD, the simulated cross sections of the graviton are suppressed by a factor MD4/s2

(ΛU4/s2) [47]. Because the

√s values of the data are smaller than the current limits on MD

(ΛU), the results are not affected by this suppression. The next-to-leading-order (NLO) QCDcorrections to direct graviton production in the ADD model are sizable and depend on thepT of the recoiling parton [49]. As a simplifying assumption, we use K-factors (σNLO/σLO)corresponding to a fixed graviton pT of several hundred GeV/c; the values are 1.5 for δ = 2, 3and 1.4 for δ = 4, 5, and 6.

The Z+jets, W+jets, tt, and single-top event samples are produced using MADGRAPH interfacedwith PYTHIA 6.42, using tune Z2star and the CTEQ 6L1 PDFs. The QCD multijet sample isgenerated with PYTHIA 6.42, using tune Z2star and CTEQ 6L1 PDFs. The Z+jets and W+jetssamples are generated with a cut on the transverse momentum of the boson, pT > 100 GeV/c.All the generated signal and background events are passed through a GEANT4 [50] simulationof the CMS detector.

4 Event selectionThe data used in this analysis are recorded by two triggers, one that requires Emiss

T > 120 GeVas measured online by the trigger system, where the Emiss

T is calculated using the calorime-ter information only. The second trigger requires a jet with pT > 80 GeV/c within |η| < 2.6and for less than 95% of the jet energy in the electromagnetic calorimeter to be carried byneutral hadrons. In addition, it requires Emiss

T > 105 GeV, where the EmissT is reconstructed

using the particle-flow algorithm and excludes muons. Events are required to have at least onewell-reconstructed primary vertex [51]. To suppress the instrumental and beam-related back-

4 5 Background estimate from data

grounds, events are rejected if less than 20% of the energy of the highest pT jet is carried bycharged hadrons or more than 70% of this energy is carried by either neutral hadrons or pho-tons. Such spurious jets primarily arise from instrumental noise, where the energy depositionis limited to one sub-detector. Jets resulting from energy deposition by beam halo or cosmic-raymuons do not have associated tracks and are also rejected by these selections. The applicationof these data cleanup requirements are very effective in rejecting non-collision backgrounds.Contribution from these backgrounds are found to be negligible, based on visual inspection ofevents with very high Emiss

T .

The analysis is performed in 7 regions of EmissT ; Emiss

T > 250, 300, 350, 400, 450, 500, 550 GeV.The jet with the highest transverse momentum ( j1) is required to have pT( j1) > 110 GeV/cand |η( j1)| < 2.4. The triggers used to collect these data are fully efficient for events passingthese selection cuts. Events with more than two jets with pT above 30 GeV/c and |η| < 4.5 arediscarded. As signal events typically contain jets from initial- or final-state radiation, a secondjet ( j2) is allowed, provided ∆φ( j1, j2) < 2.5. This angular requirement suppresses QCD dijetevents.

To reduce background from Z and W production and top-quark decays, events with well re-constructed and isolated electrons with pT > 10 GeV/c and muons reconstructed with pT >10 GeV/c are rejected. Events with a well identified tau with pT > 20 GeV/c and |η| < 2.3 arealso removed. The pT(j1), η(j1), Njets and ∆φ(j1, j2) distributions are shown in Fig. 1.

The EmissT distribution from data and the expected backgrounds after all selection criteria and a

EmissT cut of 250 GeV is shown in Fig. 2. Also shown are some representative signal distributions

for dark matter, ADD and Unparticles.

Table 1 lists the number of background events obtained from the simulation at each step ofthe analysis event selection, where ’Preselection’ includes jet cleaning requirements and theminimum cuts for which the trigger is fully efficient; Emiss

T > 200 GeV, pT( j1) > 110 GeV/c and|η( j1)| < 2.4. The W+jets, Z(νν) and Z+jet processes are normalised to the LO cross sections.QCD events have been normalised to the cross section measured in dijet events and tt eventsare normalised to the measured cross section in the tt inclusive cross section measurement. Thedominant background in the signal region is Z(νν)+jets, followed by W+jets.

5 Background estimate from dataTable 1 shows that the SM backgrounds remaining after the full event selection are dominatedby the following processes: Z+jets with the Z boson decaying into a pair of neutrinos andW+jets with the W boson decaying leptonically.

These backgrounds are estimated from data utilizing a control sample of µ+jet events, whereZ(µµ) events are used to estimate the Z(νν) background and W(µν) events are used to estimatethe remaining W+jets background. The control sample is derived from the same set of triggersas those used for signal search. The full selection criteria are applied except for the leptonvetoes. A sample of Z(µµ) events is selected by requiring two muons with pT > 20 GeV/c and|η| < 2.1, with at least one muon also passing the isolation cut. The reconstructed invariantmass is required to be between 60 and 120 GeV/c2. Table 2 shows the event yields obtained forthe Z(µµ) control sample and the predicted backgrounds from MC.

The dimuon invariant mass and dimuon pT distributions in the data control sample and thesimulation for a Emiss

T cut of 250 GeV are shown in Fig. 3. The production of a Z boson in asso-ciation with jets and its subsequent decay into neutrinos has similar kinematic characteristics

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Figure 3: The dimuon invariant mass and dimuon pT distributions for data (black full pointswith error bars) and simulation (histogram) for 60 < Mµµ < 120 GeV/c2. The MC predictionhas been normalized to the data yields. There is no significant non-Z background.

to Z+jets where the Z decays to muons. By treating the pair of muons as a pair of neutrinos, thetopology of the Z(νν) process is reproduced. The number of Z(νν) events can then be predicted

7

Table 1: Number of events selected at each step of the analysis and for the following values ofEmiss

T ; EmissT > 250, 300, 350, 400, 450, 500, 550 GeV. Backgrounds are obtained from MC and

normalised as described in the text. Also shown are the number of events generated for eachprocess and the corresponding cross section used.

Selection W+jets Z+j Z(νν)+j tt QCD Single top TotalCross section (pb) 229.0 34.1 588.3 225.2 1904.8 113.5Generated 1.27e7 2.6e6 1.05e7 6.92e6 2.29e7 7.05e6 6.3e7Preselection 255647 20348 106463 50520 46076 7334 486389NJets ≤ 2 183861 15056 80792 8585 15238 2723 306254∆φ(j1, j2) < 2 166743 13798 75397 7150 585 2217 265890Muon veto 73439 800 75395 2639 562 868 153703Electron veto 54236 531 75374 1603 543 610 132898Tau veto 52098 491 74870 1506 526 573 130064Emiss

T > 250 GeV 16528 120 28818 470 177 156 46269Emiss

T > 300 GeV 6031 40 11999 175 76 52 18373Emiss

T > 350 GeV 2486 17 5469 72 23 20 8087Emiss

T > 400 GeV 1109 7 2679 32 3 7 3837Emiss

T > 450 GeV 537 4 1406 13 2 2 1964Emiss

T > 500 GeV 277 1 766 6 1 1 1053Emiss

T > 550 GeV 136 1 429 3 0 0 569

Table 2: Event yields for the Z(µµ) data control sample and the backgrounds from MC.Z+jets W+jets Z(νν) tt Single t QCD All MC Data

EmissT > 250 3405.2 0.5 0.0 27.4 10.6 0.0 3444 3626

EmissT > 300 1493.7 0.0 0.0 8.8 4.1 0.0 1507 1485

EmissT > 350 696.2 0.0 0.0 4.4 3.1 0.0 704 663

EmissT > 400 344.9 0.0 0.0 0.6 0.3 0.0 346 323

EmissT > 450 177.1 0.0 0.0 0.0 0.0 0.0 177 173

EmissT > 500 97.1 0.0 0.0 0.0 0.0 0.0 97 84

EmissT > 550 54.4 0.0 0.0 0.0 0.0 0.0 54 47

using:

N(Z(νν)) =Nobs − Nbgd

A× ε· R(

Z(νν)

Z(µµ)

)(1)

where Nobs is the number of dimuon events observed, Nbgd is the estimated number of back-ground events contributing to the dimuon sample, A is the acceptance, ε is the selection ef-ficiency for the event, and R is the ratio of branching fractions for the Z decay to a pair ofneutrinos and to a pair of muons. The acceptance A is defined as the fraction of simulatedevents that pass all signal selection requirements (except muon veto) and have two muonswith pT > 20 GeV/c and |η| < 2.1 and with an invariant mass within the Z mass window. Theselection efficiency ε is defined as the fraction of events passing acceptance cuts that have tworeconstructed muons with pT > 20 GeV/c and |η| < 2.1 and with an invariant mass within theZ mass window. The muon selection efficiency is also estimated from simulation but correctedto account for differences in the measured efficiency between data and MC.

The final prediction for the number of Z(νν) events is given in Table 3. The uncertainty on theprediction includes both statistical and systematic contributions. The sources of uncertaintyare: (i) the statistical uncertainty on the number of Z(µµ) events in the data and simulation, (ii)uncertainty from backgrounds, (ii) uncertainties on the acceptance from PDF uncertainties and

8 5 Background estimate from data

Table 3: Data-driven prediction of Z(νν) events for different EmissT regions.

EmissT ( GeV) > 250 > 300 > 350 > 400 > 450 > 500 > 550

Z(νν) 30600±1493 12119±640 5286±323 2569±188 1394±127 671±81 370±58

(iii) the uncertainty in the selection efficiency ε as determined from the difference in measuredefficiencies in data and MC simulation. Table 4 summarizes the systematic uncertainties.

Table 4: Sources of systematic uncertainty and their contributions (in %) to the total uncertaintyon the Z(νν) background.

EmissT ( GeV) > 250 > 300 > 350 > 400 > 450 > 500 > 550

Statistics (Nobs) 1.7 2.6 3.9 5.6 7.6 10.9 14.6Background (Nbgd) 0.8 0.6 0.8 0.2 0.0 0.0 0.0Acceptance (A) 2.0 2.0 2.0 2.1 2.1 2.2 2.4Selection efficiency (ε) 2.0 2.0 2.1 2.2 2.4 2.7 3.1Total 4.5 4.9 5.8 7.1 8.9 12.1 15.6

The second largest background arises from W+jets events that are not removed by the leptonveto. These events can come from W decays in which the lepton (electron or muon) is eithernot identified, not isolated, or out of the acceptance region, or events in which a τ decayshadronically. Contributions to the signal sample from these events where the lepton is ‘lost’are estimated from the W(µν)+jets control sample.

A W(µν) sample is selected by requiring an isolated muon with pT > 20 GeV/c and |η| < 2.1and the transverse mass MT to be between 50 and 100 GeV/c2. The transverse mass is definedas MT =

√2pµ

TEmissT (1− cos(∆φ)), where pµ

T is the transverse momentum of the muon and∆φ is the angle between the muon pT and the Emiss

T vectors. Table 5 shows the event yieldsobtained from the W(µν) control sample and the predicted backgrounds from MC. Figure 4shows the W transverse mass and transverse momentum distributions for data and simulationin the W(µν) control sample.

Table 5: Event yields for the W(µν) data control sample and the backgrounds from MC.W+jets Z+jets Z(νν) tt Single t QCD All MC Data

EmissT > 250 GeV 14077.6 377.7 0.0 595.0 185.6 0.0 15236 15578

EmissT > 300 GeV 6127.5 140.3 0.0 216.5 72.9 0.0 6557 6347

EmissT > 350 GeV 2873.4 61.3 0.0 79.3 31.9 0.0 3046 2893

EmissT > 400 GeV 1442.0 32.1 0.0 39.8 13.3 0.0 1527 1381

EmissT > 450 GeV 745.0 16.6 0.0 20.5 7.7 0.0 790 715

EmissT > 500 GeV 391.1 9.3 0.0 9.2 4.2 0.0 414 378

EmissT > 550 GeV 218.1 5.5 0.0 6.5 3.3 0.0 233 207

W(µν) candidate events (Nobs), after subtracting non-W contamination (Nbgd), are correctedfor the detector acceptance (A′) and selection efficiency (ε′) to obtain the total number of pro-duced events Ntot = (Nobs − Nbgd)/(A′ × ε′). This number is subsequently weighted by theinefficiency of the selection criteria used in the muon veto to predict the number of events thatare not rejected by the veto and thus remain in the signal sample.

The total background from W(µν)+jet events that are ‘lost’ because they are either out of the

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Figure 4: Distributions of the transverse mass MT (left) and the transverse momentum (right) inthe W(µν) control sample, compared with MC predictions for W(µν), tt, Z(µµ) and single-topproduction.

Table 6: Data-driven prediction of W+jets events for different EmissT regions.

EmissT ( GeV) > 250 > 300 > 350 > 400 > 450 > 500 > 550

W+jets 17625 ± 681 6042± 236 2457± 102 1044±51 516±31 269±20 128±13

acceptance or are not identified or are not isolated can be written as:

Nlost µ = Ntot × (1− Aε) (2)

where A is the acceptance, and ε is the efficiency of the muon selection used in the lepton veto.

An estimate of the ‘lost’ electron background is similarly obtained from the W(µν)+jets datasample, correcting for the muon acceptance and selection efficiency to obtain Ntot. The ratio ofthe produced W(µν) and W(eν) events passing the signal selection is taken from simulationand used to obtain Ntot for electrons. The same procedure is then applied to obtain the numberof events where the electron is either not reconstructed or not isolated or out of the acceptance.

The remaining component of the W+jets background from events where the W decays to a τlepton and the τ decays hadronically is estimated using the same method. The ratio of theproduced W(µν) and W(τν) events are used to obtain Ntot for taus. This is subsequently mul-tiplied by the inefficiency of the tau selection used in the veto to obtain the remaining W back-ground from ‘lost’ taus.

The detector acceptance for electrons, muons and taus is obtained from simulation. The selec-tion efficiency is also obtained from simulation but corrected for any difference in the efficiencymeasured in data and simulation.

The final prediction for the number of W+jets events is given in Table 6. The uncertainty onthe prediction includes both statistical and systematic contributions. The sources of this uncer-tainty are: (i) the uncertainties on the number of single-muon events in the data and simulationsamples, (ii) a 50% uncertainty on the non-W contamination obtained from simulation, (iii) un-

10 6 Results

Table 7: Summary of the contributions (in %) to the total uncertainty on the W+jets backgroundfrom the various factors used in the data-driven estimation.

EmissT ( GeV) > 250 > 300 > 350 > 400 > 450 > 500 > 550

Statistics (Nobs) 0.9 1.3 2.0 2.9 4.0 5.5 7.5Background (Nbgd) 2.5 2.3 1.9 2.1 2.1 1.9 2.4Acceptance and efficiency 2.0 2.0 2.2 2.4 2.8 3.3 4.1PDFs 2.0 2.0 2.0 2.0 2.0 2.0 2.0Total 3.9 3.9 4.1 4.9 6.0 7.6 10.1

Table 8: SM background predictions compared with data after passing the selection require-ments for various Emiss

T thresholds, corresponding to an integrated luminosity of 19.5 fb−1.The uncertainties include both statistical and systematic terms and are considered to be un-correlated. In the last two rows, expected and observed 95% confidence level upper limits onpossible contributions from new physics passing the selection requirements are given.

EmissT ( GeV)→ > 250 > 300 > 350 > 400 > 450 > 500 > 550

Z(νν)+jets 30600 ± 1493 12119 ± 640 5286 ± 323 2569 ± 188 1394 ± 127 671 ± 81 370 ± 58W+jets 17625 ± 681 6042 ± 236 2457 ± 102 1044 ± 51 516 ± 31 269 ± 20 128 ± 13tt 470 ± 235 175 ± 87.5 72 ± 36 32 ± 16 13 ± 6.5 6 ± 3.0 3 ± 1.5Z(``)+jets 127 ± 63.5 43 ± 21.5 18 ± 9.0 8 ± 4.0 4 ± 2.0 2 ± 1.0 1 ± 0.5Single t 156 ± 78.0 52 ± 26.0 20 ± 10.0 7 ± 3.5 2 ± 1.0 1 ± 0.5 0 ± 0QCD Multijets 177 ±88.5 76 ±38.0 23 ±11.5 3 ±1.5 2 ±1.0 1 ± 0.5 0 ± 0Total SM 49154 ± 1663 18506 ± 690 7875 ± 341 3663 ± 196 1931 ± 131 949 ± 83 501 ± 59Data 50419 19108 8056 3677 1772 894 508Exp. upper limit 3580 1500 773 424 229 165 125Obs. upper limit 4695 2035 882 434 157 135 131

certainties on the acceptance from PDFs, and (iv) the uncertainty in the selection efficiency ε asdetermined from the difference in measured efficiency between data and simulation. A sum-mary of the contributions of these uncertainties to the total error on the W+jets background isshown in Table 7.

Background contributions from QCD multijet events, top and Z(``)+jets production are small.QCD events are normalised to the cross section measured in dijet events, tt events are nor-malised to the measured cross section in the tt inclusive cross section measurement and Z(``)+jetsare normalised using the comparison between data and MC in the Z(µµ) control sample afterapplying the monojet selection. A 50% uncertainty is assigned to these background predictions.

6 ResultsA summary of the predictions and corresponding uncertainties for all the SM backgroundscompared to the data for different values of the Emiss

T cut are shown in Table 8. Also shown inTable 9 are the number of events from representative signal points for ADD, dark matter andUnparticles that pass the selection requirements for various Emiss

T thresholds.

The EmissT cut is optimised by using representative model points from the three signal scenarios.

The best expected limits are found to be at EmissT > 400 GeV for ADD and dark matter and

EmissT > 350 GeV for Unparticle models.

The total systematic uncertainty on the signal is found to be 20% for dark matter, ADD andUnparticles. The sources of systematic uncertainty considered are: jet energy scale, PDFs,

11

Table 9: Event yields for representative signal points from ADD, dark matter and Unparticlesafter passing the full selection criteria and various Emiss

T thresholds, corresponding to an inte-grated luminosity of 19.5 fb−1.

EmissT ( GeV)→ > 250 > 300 > 350 > 400 > 450 > 500 > 550

ADD LO MD = 3 TeV, δ = 3 4496 2888 1885 1265 881 603 422ADD LO MD = 4 TeV, δ = 3 1071 685 454 310 210 150 108DM Λ = 850 GeV, Mχ = 1 GeV 1774 1103 693 454 297 202 137DM Λ = 950 GeV, Mχ = 1 GeV 1137 707 444 291 190 129 88Unparticles dU = 1.7, ΛU = 2 TeV 4328 2220 1237 700 378 218 141Unparticles dU = 1.7, ΛU = 3 TeV 1859 905 478 247 158 103 60

δ2 3 4 5 6

)2 (

TeV

/cD

M

0

1

2

3

4

5

6

7

8

CMS Monojet (LO) 8 TeV

ATLAS Monojet (LO) 8 TeV

-1CMS Monojet (LO) 7 TeV, 5 fb

LEP

CDF

∅D

CMS Preliminary=8 TeVs, -1L dt = 19.5 fb∫

Figure 5: Comparison of lower limits on MD versus the number of extra dimensions withLEP [27–30], CDF [31], and D0 [32].

renormalization/factorization scale, uncertainty from modeling of ISR, uncertainty from thesimulation of pileup and the error on the luminosity measurement.

7 InterpretationThe consistency of the observed number of events with the background expectation is used toset limits on the production of dark matter particles, ADD model parameters and Unparticleproduction. The CLs method [52, 53] is used for calculating the upper limits on the number ofsignal events, and systematic uncertainties are modeled by log-normal distributions.

Figure 5 shows the 95% C.L. limits on MD as a function of δ from CMS, LEP and the Tevatronexperiments. Table 10 shows the expected and observed limits with and without K-factorsapplied.

For dark matter models, the observed limit on the cross section depends on the mass of thedark matter particle and the nature of its interaction with the SM particles. The limits on theeffective contact interaction scale Λ as a function of Mχ can be translated into a limit on the darkmatter-nucleon scattering cross section using the reduced mass of the χ-nucleon system [2],which can be compared with the constraints from direct and indirect detection experiments.

12 7 Interpretation

Table 10: ADD Model observed and expected limits on MD in TeV/c2 as a function of δ at LOand NLO, with K-factors of 1.5 for δ = 2,3 and 1.4 for δ = 4,5,6.

LO NLOδ Exp. Limit Obs. Limit Exp. Limit Obs. Limit2 5.12 5.10 5.70 5.673 3.96 3.94 4.31 4.294 3.46 3.44 3.72 3.715 3.11 3.10 3.32 3.316 2.95 2.94 3.13 3.12

The limits on Λ as a function of the DM mass for the vector interaction and the axial-vectorinteraction are shown in Figure 6, together with a comparison with limits from the previousCMS analysis using 5 fb−1 at 7 TeV. The observed and expected limits at the 90% CL on theDM-nucleon scattering cross section for the vector, axial-vector and scalar operators are shownin Tables 11, 12, 13 and Figures 7 and 8.

Also considered is the case in which the mediator is light enough to be accessible to the LHC.Figure 9 shows the observed limits on Λ as a function of the mass of the mediator, assumingvector interactions and a dark matter mass of 50 GeV/c2 and 500 GeV/c2. The width (Γ) of themediator is varied between M/3 and M/8π [13]. It shows the resonant enhancement in theproduction cross section once the mass of the mediator is within the kinematic range and canbe produced on-shell. At large mediator mass, the limits on Λ approximate to those obtainedin the effective theory framework [13].

]2 [GeV/cχM1 10 210 310

[GeV

]Λ

300

1000

CMS 2012 Axial Vector

CMS 2011 Axial Vector

CMS Preliminary = 8 TeVs

-1L dt = 19.5 fb∫

]2 [GeV/cχM1 10 210 310

[GeV

]Λ

300

1000

CMS 2012 Vector

CMS 2011 Vector

CMS Preliminary = 8 TeVs

-1L dt = 19.5 fb∫

Figure 6: Limits on the contact interaction scale Λ as a function of the DM mass for the currentanalysis using 19.5 fb−1 of 8 TeV data. Also shown is the result from the previous analysisusing 5 fb−1 of 7 TeV data.

The results can also be interpreted in the context of Unparticle production. Shown in Figure 10are the expected and observed 95% C.L limits on the cross-sections for S = 0 Unparticles withdU = 1.5, 1.6, 1.7, 1.8 and 1.9 as a function of ΛU for a fixed coupling constant λ = 1. Theobserved 95% C.L limit ΛU for these values of dU is shown in Table 14. This can be compared

13

Table 11: Expected and observed 90% CL limits on the dark matter-nucleon cross section andeffective contact interaction scale Λ for the vector operator.

Expected ObservedMχ (GeV) Λ (GeV) σχN (cm2) Λ (GeV) σχN (cm2)

1 897 4.04× 10−40 892 4.14× 10−40

10 907 1.21× 10−39 902 1.24× 10−39

100 897 1.49× 10−39 892 1.53× 10−39

200 868 1.71× 10−39 863 1.75× 10−39

400 783 2.60× 10−39 779 2.66× 10−39

700 600 7.54× 10−39 597 7.71× 10−39

1000 431 2.84× 10−38 428 2.90× 10−38

Table 12: Expected and observed 90% CL limits on the dark matter-nucleon cross section andeffective contact interaction scale Λ for the axial-vector operator.

Expected ObservedMχ (GeV) Λ (GeV) σχN (cm2) Λ (GeV) σχN (cm2)

1 903 1.44× 10−41 913 1.38× 10−41

10 901 4.57× 10−41 922 4.15× 10−41

100 876 6.01× 10−41 868 6.20× 10−41

200 819 7.93× 10−41 802 8.62× 10−41

400 668 1.80× 10−40 669 1.79× 10−40

700 462 7.85× 10−40 468 7.47× 10−40

1000 307 4.03× 10−39 312 3.79× 10−39

Table 13: Expected and observed 90% CL limits on the dark matter-nucleon cross section andeffective contact interaction scale Λ for the scalar operator.

Expected ObservedMχ (GeV) Λ (GeV) σχN (cm2) Λ (GeV) σχN (cm2)

1 373 3.35× 10−45 371 3.43× 10−45

10 373 1.05× 10−44 371 1.08× 10−44

100 368 1.33× 10−44 366 1.36× 10−44

200 351 1.77× 10−44 350 1.82× 10−44

400 310 3.81× 10−44 308 3.90× 10−44

700 244 1.57× 10−43 243 1.61× 10−43

1000 186 8.11× 10−43 185 8.30× 10−43

to previous limits on Unparticles from CMS [57].

8 ConclusionsA search has been performed for signatures of new physics in the monojet and Emiss

T channelusing 19.5 fb−1 of pp collisions at

√s = 8 TeV. Contributions from tt and QCD multijet

processes are reduced to a negligible level using topological selections. The dominantbackgrounds after the complete selection has been applied are from Z(νν) and W+jet events.These are estimated from data samples of Z(µµ) and W(µν) events. The data are found to bein good agreement with expected contributions from SM processes. Limits are set on the darkmatter-nucleon scattering cross section assuming vector, axial-vector and scalar operators todescribe the interaction. In addition, limits are also set on the ADD model parameter MD as a

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]2-N

ucle

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