EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN) CERN-PH-EP/2012-084 2013/01/24 CMS-EXO-11-096 Search for Dark Matter and Large Extra Dimensions in pp Collisions Yielding a Photon and Missing Transverse Energy 3 1 0 ∗ 2 The CMS Collaboration n a J 3 2 ] x e Abstract - p e h Results are presented from a search for new physics in the final state containing a [ 2 pluhmotionnos(iγty)aonfd5.0mfibs−si1ncgoltlreacntsevdeirnseppenceorlgliysi(oE/nTs).aTt√hesd=at7aTceoVrrbeysptohnedCtMoSanexipnetergimraetnedt. v 1 The observed event yield agrees with standard-model expectations for the γ+ E/ T 2 events. Using models for production of dark-matter particles (χ), we set 90% confi- 8 dencelevel(CL)upperlimitsof13.6–15.4fbonχproductionintheγ+E/ state. These 0 T . providethemostsensitiveupperlimitsforspin-dependentχ-nucleonscatteringforχ 4 0 masses(Mχ)between1and100GeV. Forspin-independentcontributions,thepresent 2 limitsareextendedtoM <3.5GeV. Formodelswith3–6largeextradimensions,our χ 1 dataexcludeextra-dimensionalPlanckscalesbetween1.65and1.71TeVat95%CL. : v i X r SubmittedtoPhysicalReviewLetters a ∗SeeAppendixAforthelistofcollaborationmembers 1 Final states in pp collisions at the Large Hadron Collider (LHC), containing a photon (γ) of large transverse momentum (p ) and missing transverse energy (E/ ), are used to investigate T T two proposals of physics beyond the standard model (SM). One involves a model for dark matter(DM),whichisnowacceptedasthedominantnon-baryoniccontributiontothematter density of the universe [1]. Direct searches for a DM candidate (χ) rely on detection through elastic χ-nucleon scattering. Indirect searches consist of observation of photons or neutrinos produced in χχ annihilations in astrophysical sources. At the LHC, DM can be produced in thereactionqq → γχχ,wherethephotonisradiatedbyoneoftheincomingquarks. Thefinal stateisahigh-p photonand E/ . Recenttheoreticalwork[2,3]caststhisprocessintermsofa T T massive mediator in the s channel that couples to a χχ pair of Dirac particles. This process is contractedintoaneffectivetheorywithacontactinteractionscaleΛ,givenbyΛ−2 = g g M−2, χ q M where M isthemediatormassand g and g areitscouplingsto χ andquarks, respectively. M χ q Themodelprovidesawaytoconnectthet-channelχ-nucleonelasticscatteringtothes-channel pair-productionmechanism. Theeffectives-channeloperatorcanbechosentorepresenteither avectororaxial-vector,spin-independentorspin-dependentinteraction,respectively. The γ+E/ final state also has sensitivity to models of extra spatial dimensions. The Arkani- T Hamed, Dimopoulos, and Dvali model (ADD) [4], in particular, provides a possible solution to the hierarchy problem, viz., the disparity between two fundamental scales of nature: the electroweakunificationscale(M ≈ 100GeV)andthePlanckscale(M ≈ 1019GeV). Inthis EW Pl framework, space-time is postulated to have n extra compact spatial dimensions with a char- acteristicscale R,leadingtoamodifiedPlanckscale, M ,givenby M2 ≈ Mn+2Rn. Assuming D Pl D M is of the same order as M , the observed large value of M can be interpreted as being D EW Pl a consequence of the “large” size of R (relative to the Planck length ≈ M−1) and the number Pl of extra dimensions in the theory. The ADD model predicts the production of gravitons that appear as Kaluza-Klein (KK) modes, where momenta in the extra dimensions appear as ob- servable massive states, except for the zero-mode of the KK excitation, which corresponds to themasslessgravitonin4+ndimensions. Theprocessqq → γG,wherethegravitonGescapes detection, motivates the search for events with single high-p isolated photons. While the in- T dividualqGcouplingsaresmall,thenumberofexpectedKKgravitonstatesislargeenoughto produceameasurablecrosssection,makingitpossibletodiscoverlargeextradimensions,orto setlowerlimitson M asafunctionofnandupperlimitsontheADDcrosssection. Thesame D physicalphenomenacanbeaccessedthroughthesingle-jet(monojet)productionchannel[5,6]. This search uses data collected with the Compact Muon Solenoid (CMS) detector [7]. The momenta of charged particles are measured using a silicon pixel and strip tracker that is im- mersed in a 3.8T superconducting solenoid, and covers the pseudorapidity range |η| < 2.5. The pseudorapidity is η = −ln[tan(θ/2)], where θ is the polar angle measured relative to the counterclockwise-beam direction. The tracker is surrounded by a crystal electromagnetic cal- orimeter (ECAL) and a brass-scintillator hadron calorimeter (HCAL). Both measure particle energy depositions and consist of a barrel assembly and two endcaps that provide coverage in the range of |η| < 3.0. A steel/quartz-fiber Cherenkov forward detector (HF) extends the calorimetric coverage to |η| < 5. Muons are measured in gas detectors embedded in the steel returnyokeoutsideofthesolenoid. Theprimarybackgroundfortheγ+E/ signalistheirreducibleSMbackgroundfromZγ → ννγ T production. ThisandotherSMbackgrounds,includingWγ,W → eν, γ+jet,multijet(referred to as QCD), and diphoton events, as well as backgrounds from beam halo and cosmic-ray muonsaretakenintoaccountintheanalysis. Events are selected from a data sample corresponding to an integrated luminosity of 5.0fb−1 2 collectedusingatwo-leveltriggersystem,withLevel-1(L1)seedingHighLevelTriggers(HLT). The single-photon triggers comprising this search are not prescaled, and are fully efficient within the selected signal region of |ηγ| < 1.44 [8] and pγ > 145GeV. To optimize the analy- T sis for single high-p photons accompanied by large E/ , photon candidates are restricted to T T be in the central barrel region, where purity is highest. To distinguish photon candidates from jets, we apply additional calorimetric selections. The ratio of energy deposited in the HCAL to that in the ECAL within a cone of ∆R = 0.15 is required to be less than 0.05, where ∆R = (cid:112)(∆φ)2+(∆η)2 is defined relative to the photon candidate and the azimuthal angle φ is measured in the plane perpendicular to the beam axis. Photon candidates must also have a showerdistributionintheECALconsistentwiththatexpectedforaphoton[8]. Isolation requirements on photon candidates impose upper limits on the energy deposited in the detector around the axis defined by the EM cluster position and the primary vertex [8]. In particular, the scalar sum of p depositions in the ECAL within a hollow cone of 0.06 < T ∆R < 0.40,excludingdepositionswithin|∆η| = 0.04oftheclustercenter,mustbe<4.2GeV+ 0.006×pγ,thesumofscalar p depositionsintheHCALwithinahollowconeof0.15 < ∆R < T T 0.40mustbe <2.2GeV+0.0025×pγ, andthescalarsumoftrack p valuesinahollowconeof T T 0.04 < ∆R < 0.40,excludingdepositionsthatareclosertotheclustercenterthan|∆η| =0.015, must be <2.0GeV + 0.001×pγ (with p in GeV units). The vetoes defined by the |∆η| cutoffs T T areneededtomaintainhighefficiencyforphotonsthatinitiateEMshowerswithinthetracker. Thetrackerisolationrequirementisbasedontracksthatoriginatefromtheprimaryvertex. SincethehighluminosityoftheLHCyieldsmultipleppinteractionsperbunchcrossing,there are several reconstructed vertices per event. The primary vertex is defined as the vertex that corresponds to the largest sum of the squares of the associated track-p values. However, to T ensurethatphotoncandidatesareisolatedfromchargedparticletracksineventswithmultiple vertices, the tracker isolation requirement must be passed by all reconstructed vertices, or the eventisrejected. The E/ is defined by the magnitude of the vector sum of the transverse energies of all of the T reconstructed objects in the event, and is computed using a particle-flow algorithm [9]. The candidateeventsarerequiredtohave E/ > 130GeV. T Alleventsarerequiredtohavetheenergydepositedinthecrystalcontainingthelargestsignal withinthephotontobewithin±3nsofthetimeexpectedforparticlesfromacollision. Thisre- quirementreducesinstrumentalbackgroundarisingfromshowersinducedbybremsstrahlung frommuonsinthebeamhaloorincosmicrays. SpurioussignalsembeddedwithinEMshow- ers that otherwise pass selection criteria are eliminated by requiring consistency among the energy deposition times for all crystals within an electromagnetic shower. Photon candidates areremovediftheyarelikelytobeelectrons, asinferredfromcharacteristicpatternsofhitsin the pixel detector, called “pixel seeds,” that are matched to the EM clusters [10]. In addition, a veto applied to events that contain muon candidates, including those that do not emanate from the collision point, prevents bremsstrahlung from muons in cosmic rays and the beam halo from being reconstructed as prompt photons balanced by E/ . Finally, events are vetoed T if they contain significant hadronic activity, defined by: (i) a track with p > 20GeV that is T ∆R > 0.04awayfromthephotoncandidate,or(ii)ajetthatisreconstructedwith p > 40GeV T using the anti-k [11] particle-flow algorithm [9], within |η| < 3.0 and ∆R < 0.5 of the axis of T thephoton. Afterapplyingalloftheselectioncriteria,75candidateeventsarefound. Backgroundsthatareoutoftimewiththecollisionsareestimatedfromdatabyexaminingthe 3 transverse distribution of energy in the EM cluster and the time-of-arrival of the signal in the crystal with the largest energy deposition. Templates for anomalous signals [12], cosmic-ray muons,andbeamhaloeventsarefittedtoacandidatesamplethathasnotimingrequirement, which reveals that the only significant residual contribution to the in-time sample arises from halomuons,withanestimated11.1±5.6events. ElectronsmisidentifiedasphotonsarisemainlyfromW → eνevents. Thematchingofelectron showerstopixelseedshasanefficiencyof(cid:101) = 0.9940±0.0025,asestimatedwithMonte-Carlo simulated events (MC) and verified with Z → ee events in data. Scaling a control sample of electron candidates by (1−(cid:101))/(cid:101) yields an estimated contribution of 3.5±1.5 W → eν events inthecandidatesample. The contamination from jets misidentified as photons is estimated by using a control sample ofEM-enrichedQCDeventstocalculatetheratioofeventsthatpassthesignalphotoncriteria relative to those that pass looser photon criteria but fail an isolation requirement. Since the EM-enriched sample also includes production of direct single photons, this additional contri- bution to the ratio is estimated by fitting templates of energy-weighted shower widths from MC-simulated γ+jets events to an independent QCD data sample, and used to subtract the γ+jets contribution. This corrected ratio is applied to a subset of the EM-enriched jet events that passes loose photon identification and additional single-photon event selection criteria, providingabackgroundcontributionof11.2±2.8jetevents. Backgrounds from (Zνν)γ, (W(cid:96)ν)γ, γ+jet, and diphoton events are estimated from MC sam- plesprocessedthroughthefullGEANT4-basedsimulationoftheCMSdetector[13,14],trigger emulationandeventreconstructionusedfordata. TheWγ → (cid:96)νγsamplesaregeneratedwith MADGRAPH5 [15], and the cross section is corrected to include next-to-leading order (NLO) effects through a K-factor calculated with MCFM [16]. The Zγ → ννγ, γ+jet, and dipho- ton samples are obtained using the PYTHIA 6.424 generator [17] at leading order (LO) and CTEQ6L1[18]partondistributionfunctions(PDF).TheZγ → ννγ sampleisalsoscaledupto reflect NLO contributions given in Ref. [19]. Good agreement between data and the rescaled MCfortheZγ → (cid:96)(cid:96)γchannelhasbeenobtainedinpreviousCMSstudies[20]. Theuncertainty onZγ → ννγandtheotherbackgroundstakesintoaccountseveralsources: theoreticaluncer- tainties on the LO cross section and K-factors; the uncertainty on the scale factor that models thedata–MCdifferenceintheefficiency;andsystematicuncertaintiesonthephoton-vertexas- signment, modeling of pile-up, and the accuracy of the energy calibration and resolution for photons,jets,andE/ . TheexpectedcontributionfromtheZγ → ννγprocesstothebackground T is 45.3±6.8 events. The combined expected background from (W(cid:96)ν)γ, γ+jet, and diphoton eventsis4.1±1.0. The 73 observed events in data agree with the total expected background of 75.1±9.4 events. Distributionsinphoton p fortheselectedcandidateeventsandforthoseestimatedfromback- T ground are shown in Fig. 1. The spectra expected from ADD for M = 1TeV and n = 3 are D superimposedforcomparison. Basedontheseresults, exclusionlimitsaresetfortheDMand ADDmodels. Thelimitsonthecrosssectionsarecalculatedbydividingthedifferencebetweenthenumberof eventsindataandthepredictednumberofbackgroundeventsbytheproductA×(cid:101)×L,where Aisthegeometricandkinematicacceptanceoftheselectioncriteria,(cid:101)istheselectionefficiency for signal, and L is the integrated luminosity. A×(cid:101) is calculated by estimating A×(cid:101) from MC the MC and multiplying it by a scale factor to account for the difference in efficiency between MCanddata. 4 VV ee CMS, s = 7 TeV DATA ents /Gents /G 111100 5.0 fb-1 T WMZoigfistfiaI Dle un-ngnn g(cQeCrtDai)nty on Bkg vv g+jets, Wg EE Beam Halo 1100--11 SM+ADD(M=1 TeV, n=3) D 1100--22 1100--33 1100--44 220000 330000 440000 550000 660000 770000 ppgg [[GGeeVV]] TT Figure 1: The photon p distribution forthe candidate sample, compared with estimated con- T tributionsfromSMbackgroundsandapredictionfromADDfor M = 1TeVandn=3. D Theefficiencyassociatedwiththeproduct A×(cid:101) forthesignalcrosssectionforbothmodels MC is determined from MC samples. For the model of DM, the MC samples are produced using asoftwarepackagefromRef.[3], requiring pγ > 125GeVand |ηγ| < 1.5. Theestimatedvalue T of A×(cid:101) for M in the range 1–100GeV is between 30.5–31.0% for vector and 29.2–31.4% MC χ for axial-vector couplings, respectively. The spectra for ADD MC events are generated using PYTHIA 8.145[21],requiring pγ > 130GeV,andscaledtoNLOusinga K-factorfromRef.[22]. T The factor A×(cid:101) for ADD is in the range of 26.5–28.5% in the parameter space spanned by MC n = 3–6and M = 1–3TeV. D SystematicuncertaintiesthatcontributetotheA×(cid:101) calculationarefromthechoiceofPDF[18, MC 23,24];theselectionoftheprimaryvertexforthephoton,modelingofpile-up,andtheenergy calibrationandresolutionforphotons[8];jets[25];andE/ [26]. Thetotalsystematicuncertainty T on A×(cid:101) is+4.8%and−4.9%. MC As mentioned above, A×(cid:101) is multiplied by a scale factor (SF) to account for the difference MC in efficiency between data and MC. The calculated SF of 0.90±0.11 combines contributions fromthetrigger,photonreconstruction,consistencyofclustertiming,andvetoes. Thephoton HLTisdeterminedtobeessentially100%efficientforourselectioncriteriaindataandinMC, butisassigneda2%uncertaintyduetosmallL1triggerinefficiencies. Sincethephotonidenti- ficationrequirementshavesimilarefficienciesforphotonsandelectrons,theelectronefficiency of 0.96±0.02, as measured in Z → ee decays is used as the SF. Corrections for photon recon- struction are described in Ref. [20]. The photon clusters in MC always have consistent timing among individual crystals, and the SF in data is found to be 0.983±0.009 based on a sample of electron events. The track and jet-veto efficiency is studied insamples of W → eν data and MC, and confirmed with Zγ → eeγ data. Since the efficiencies measured in these samples agreewithintheiruncertainties,theSFissettounityandassignedasystematicuncertaintyof ±0.10. The SF for the cosmic-ray muon veto is determined to be 0.95±0.01 by comparing its efficiencyinMCanddatainasampleofZ → eeevents. Upper limits are placed on the DM production cross sections, as a function of M , assuming χ vector and axial-vector operators, summarized in Table 2a. These are converted into the cor- Λ Λ responding lower limits on the cutoff scale , also listed in Table 2a. The values are then translatedintoupperlimitsontheχ-nucleoncrosssections,calculatedwithintheeffectivethe- ory framework. These are displayed in Fig. 2 as a function of M [2]. The 90% CL limits are χ presentedinTable2a. Superposedaretheresultsfromselectedotherexperiments. Previously inaccessible χ masses below ≈3.5GeV are excluded for a χ-nucleon cross section greater than 5 2]m (a) Spin Independent 2]m (b) CMS, s = 7 TeV n [c10-35 CCMDFS (90%CL) CCDDMMSS IIII 22001110 n [c10-35 5.0 fb-1 o o cti XENON100 CoGeNT 2011 cti e10-37 e10-37 S S s s s s o10-39 o10-39 Cr Cr n n o10-41 o10-41 cle cle Spin Dependent χ-Nu10-43 5.0 fb-1 χ-Nu10-43 CCMDFS (90%CL) CIcOeCUuPbPe 2 (0χ1χ1→W+W-) CMS, s = 7 TeV SIMPLE 2010 Super-K I+II+III (χχ→W+W-) 10-45 10-45 1 10 102 103 1 10 102 103 M [GeV] M [GeV] χ χ Figure 2: The 90% CL upper limits on the χ-nucleon cross section as a function of M for (a) χ spin-independent and (b) spin-dependent scattering. Also shown are the limits from selected experimentswithpublished[27–34]andpreliminary[35]results. Table 1: (a) Observed (expected) 90% CL upper limits on the DM production cross section σ, Λ and90%CLlowerlimitsonthecutoffscale forvectorandaxial-vectoroperatorsasafunction oftheDMmass M . (b)Expectedandobservedlowerlimitson M at95%CL,asafunctionof χ D extradimensionsn,withK-factors(andwithout,i.e.,K =1). Vector Axial-Vector M [GeV] χ σ[fb] Λ[GeV] σ[fb] Λ[GeV] 1 14.3(14.7) 572(568) 14.9(15.4) 565(561) 10 14.3(14.7) 571(567) 14.1(14.5) 573(569) 100 15.4(15.3) 558(558) 13.9(14.3) 554(550) 200 14.3(14.7) 549(545) 14.0(14.5) 508(504) 500 13.6(14.0) 442(439) 13.7(14.1) 358(356) 1000 14.1(14.5) 246(244) 13.9(14.3) 172(171) (a) 90%CLLimitsonDMmodelparameters. Expected Observed n K-factors M [TeV] M [TeV] D D 3 1.5 1.70(1.53) 1.73(1.55) 4 1.4 1.65(1.53) 1.67(1.55) 5 1.3 1.63(1.54) 1.64(1.56) 6 1.2 1.62(1.55) 1.64(1.57) (b) 95%CLLimitsonADDparameters. ≈3fb at 90% CL. For spin-dependent scattering, the upper limits surpass all previous con- straints for the mass range of 1–100GeV. The results presented are valid for mediator masses larger than the limits on Λ, assuming unity for the couplings g and g . The specific case of χ q light mediators is discussed in Ref. [3, 36]. The assumptions on χ interactions made in calcu- lating the limits vary with experiment. Further, in the case of direct and indirect searches, an astrophysicalmodelmustbeassumedforthedensityandvelocitydistributionofDM. Asetof95%confidencelevel(CL)upperlimitsarealsoplacedontheADDcrosssectionsand translatedintoexclusionsontheparameterspaceofthemodel. Theupperlimitsarecalculated 6 n [fb] CMS, s = 7 TeV TeV ] 2.5 CMS, s = 7 TeV CCMMSS NLOLO (g (+gE+E)T) ectio102 5.0 fb-1 [ MD 2 5.0 fb-1 CDD0 FL OLO (g (+gE+E)TT) s s on LEP (g +E)T Cros Limit 1.5 T 10 wer o L n=4, Theory NLO 95% CL Obs. Limit 1 n=4, Theory LO 95% CL Exp. Limit n=6, Theory NLO Exp. Limit – 68% CL n=6, Theory LO Exp. Limit – 95% CL 1 0.5 1 1.2 1.4 1.6 1.8 2 3 4 5 6 M [TeV] Number of Extra Dimensions D Figure3: (a)The95%CLupperlimitsontheLOandNLOADDcrosssectionsasafunctionof M for n = 4 and 6. (b) Limits on M as a function of n, compared to LO results from similar D D searchesattheTevatron[37,38]andLEP[39]. using a CL method [40], with uncertainties parameterized by log-normal distributions in the s fittodata. Thelimitson M ,withandwithoutK-factors,aresummarizedinTable2b. Masses D M < 1.65TeVareexcludedat95%CLfor n = 3, assumingNLOcrosssections. Theselimits, D alongwithexistingLOADDlimitsfromtheTevatron[37,38]andLEP[39],areshowninFig.3 as a function of M , for n = 4 and n = 6 extra dimensions. These results extend significantly D the limits on the ADD model in the single-photon channel beyond previous measurements at the Tevatron and LEP experiments, and set limits of M > 1.59–1.66TeV for n = 3–6 at 95% D CL. In summary, the agreement between single-photon production in pp collisions at 7TeV and standard-model expectations was used to derive significant upper limits on the vector and axial-vector contributions to the χ-nucleon scattering cross section. This search was comple- mentary to searches for elastic χ-nucleon scattering or χχ annihilation. In addition, through greater sensitivity to the ADD model, the analysis attained the most stringent limits on an effectiveextra-dimensionalPlanckscaleobtainedintheγ+E/ productionchannel. T Acknowledgements We thank R. Harnik, P. J. Fox, and J. Kopp for help in modeling dark matter production. We congratulateourcolleaguesintheCERNacceleratordepartmentsfortheexcellentperformance oftheLHCmachine. WethankthetechnicalandadministrativestaffatCERNandotherCMS institutes,andacknowledgesupportfrom: FMSR(Austria);FNRSandFWO(Belgium);CNPq, CAPES,FAPERJ,andFAPESP(Brazil);MES(Bulgaria);CERN;CAS,MoST,andNSFC(China); COLCIENCIAS (Colombia); MSES (Croatia); RPF (Cyprus); MoER, SF0690030s09 and ERDF (Estonia); Academy of Finland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF,DFG,andHGF(Germany);GSRT(Greece);OTKAandNKTH(Hungary);DAEandDST (India); IPM(Iran); SFI(Ireland); INFN(Italy); NRFandWCU(Korea); LAS(Lithuania); CIN- VESTAV, CONACYT, SEP, and UASLP-FAI (Mexico); MSI (New Zealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR (Armenia, Belarus, Georgia, Ukraine, Uzbek- istan);MON,RosAtom,RASandRFBR(Russia);MSTD(Serbia);MICINNandCPAN(Spain); Swiss Funding Agencies (Switzerland); NSC (Taipei); TUBITAK and TAEK (Turkey); STFC (UnitedKingdom);DOEandNSF(USA). 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