EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN) CERN-PH-EP/2012-041 2012/03/01 CMS-EXO-11-071 Search for microscopic black holes in pp collisions at √ s = 7TeV 2 1 The CMS Collaboration∗ 0 2 b e F 8 2 ] Abstract x e - p A search for microscopic black holes in pp collisions at a center-of-mass energy of e h 7TeV is presented. The data sample corresponds to an integrated luminosity of [ 4.7fb−1 recorded by the CMS experiment at the LHC in 2011. Events with large 1 total transverse energy have been analyzed for the presence of multiple energetic v jets,leptons,andphotons,whicharetypicalsignalsofevaporatingsemiclassicaland 6 quantumblackholes,andstringballs. Agreementwiththeexpectedstandardmodel 9 3 backgrounds, which are dominated by QCD multijet production, has been observed 6 forvariouscombinedmultiplicitiesofjetsandotherreconstructedobjectsinthefinal . 2 state. Model-independent limits are set on new physics processes producing high- 0 multiplicity, energetic final states. In addition, new model-specific indicative limits 2 1 are set excluding semiclassical and quantum black holes with masses below 3.8 to : 5.3TeVandstringballswithmassesbelow4.6to4.8TeV. Theanalysishasasubstan- v i tiallyincreasedsensitivitycomparedtoprevioussearches. X r a SubmittedtotheJournalofHighEnergyPhysics ∗SeeAppendixAforthelistofcollaborationmembers 1 1 Introduction Oneofthemostspectacularpredictionsoftheorieswithlow-scalequantumgravityisthepos- sibility of microscopic black hole (BH) production in proton-proton collisions at the high en- ergies offered by the Large Hadron Collider (LHC) [1, 2]. Such models are motivated mainly bythepuzzlinglargedifferencebetweentheelectroweakscale(∼0.1TeV)andthePlanckscale (M ∼ 1016TeV), known as the hierarchy problem. In this analysis, we focus on black hole Pl production in a model with n large, flat, extra spatial dimensions (ADD model) [3, 4]. In this and in other models, the fundamental scale of new physics in n extra dimensions is given in termsofamultidimensionalPlanckscale M ,suchthat Mn+2 ∝ M2 R−n,whereRisthesizeof D D Pl extra dimensions. Some of the conclusions also apply to black holes in the Randall–Sundrum model[5,6],withasinglewarpedextradimension. This analysis extends a previous search [7] for short-lived microscopic black holes carried out by the Compact Muon Solenoid (CMS) Collaboration in 2010. The present search is based on thefull2011datasample,whichcorrespondstoanintegratedluminosityof4.7±0.2fb−1 [8,9] at a center-of-mass energy of 7TeV. The details of the analysis method and the underlying theory,aswellasthedetaileddescriptionofblackholeevaporationmodels,canbefoundinthe originalpublication[7]. Typically,microscopicblackholesarecharacterizedbytheproduction of a large number of energetic final-state particles, 75% of which are jets. Searches for black holeshavealsobeenperformedbytheATLASCollaboration[10,11]. We present our results in terms of model-independent limits on the cross section times the branching fraction into a multiparticle final state. Further, we interpret the results in terms of a set of benchmark black hole models. The analysis also extends the previous CMS search for semiclassical black holes to probe for other quantum gravity objects such as string balls [12] and quantum black holes [13]. It is commonly accepted that the semiclassical approximation is valid when the black hole mass is some 3–5 times larger than the M . The string balls are D hypothetical precursors of semiclassical black holes in an extreme quantum limit, when the mass of the object is close to the Planck scale. In cases where the semiclassical approximation no longer holds, string balls may offer a more realistic description of black hole formation and decay. String balls are described by the string scale M and string coupling g . These S S objects would evaporate similarly to black holes, except that the evaporation would occur at the Hagedorn temperature, which does not depend on the string-ball mass [12, 14], unlike the Hawking temperature [15], which decreases as the black hole mass increases. Another possibility is that a light black hole with mass close to the Planck scale may evaporate faster than it thermalizes, resulting predominantly in a nonthermal decay into a pair of jets, rather than into high-multiplicity final states [13, 16, 17]. We search for production of these objects, referred to as quantum black holes, and for their decay in both the ADD scenario and in the Randall–Sundrummodeloflow-scalegravitywithasingle(n = 1)compactextradimension. 2 The CMS detector AdetaileddescriptionoftheCMSexperimentcanbefoundelsewhere[18]. TheCMSdetector consistsofa3.8Tsuperconductingsolenoidenclosingasiliconpixelandstriptracker,acrystal electromagneticcalorimeter(ECAL),andabrass-scintillatorhadroniccalorimeter(HCAL).The finely segmented ECAL employs lead-tungstate crystals with transverse dimensions: ∆η × ∆φ = 0.0174×0.0174. The HCAL cells are grouped in projective towers, of granularity ∆η× ∆φ = 0.087×0.087 at central rapidities and increasing progressively in the forward region. Here,φandθaretheazimuthalandpolarangles,withθmeasuredwithrespecttothedirection 2 3 EventreconstructionandMonteCarlosamples of the counterclockwise beam. The pseudorapidity η is defined as −ln[tan(θ/2)]. Muons are measured in the pseudorapidity range |η| < 2.4 in gas-ionization detectors embedded in the steelreturnyoke. The CMS trigger system, used to select the most interesting events, consists of two levels. A first level (L1), composed of custom electronics, uses information from the calorimeters and muon detectors to decrease the event rate to 80kHz. A software-based High Level Trigger (HLT)furtherdecreasestheeventrateto350–400Hzfordatastorage. As in the previous analysis, we use data collected with a suite of H triggers, where H is T T defined as a scalar sum of the transverse energies (E ) of the jets above a threshold.1 There T havebeenchangesintroducedinthetriggerlogicbothatL1andHLTsince2010. Wenowuse jetscorrectedforthecalorimeterresponsetocalculatethe H variableattheHLT(uncorrected T jets are still used at L1). Also, the minimum H thresholds, as well as the minimum jet E T T requirement for a jet to be counted towards H , have been increased to account for pileup T effects and to allow for the increased instantaneous luminosity of the LHC. This minimum jet E threshold is 10GeV at L1, and 40GeV at the HLT. The minimum H threshold at the T T HLT varies between 350 and 650GeV, depending on the instantaneous luminosity. Only jets reconstructedatcentralpseudorapidities|η| < 3.0areusedinthe H calculationsatL1andat T theHLTforthe2011data-takingperiod. Thetriggerisfullyefficientforeventswith H above T 800GeV. In order to explore all possible black hole decay modes, the entire analysis was also repeated using data collected with multimuon or missing transverse energy (Emiss) triggers, T butthisyieldednoeventsconsistentwiththeexpectedblackholeproduction. 3 Event reconstruction and Monte Carlo samples Jets are reconstructed offline using energy deposits in the HCAL and ECAL, which are clus- tered using an infrared-safe anti-k algorithm with a distance parameter of 0.5 [19–21]. Qual- T ity criteria are applied to jets in order to remove calorimeter noise and noncollision back- ground [22]. We require jets to have E > 20GeV and to be reconstructed within |η| < 2.6. T Further,jetenergiesarecorrectedforcalorimeternonuniformresponsewithcorrectionfactors derivedfromMonteCarlo(MC)simulationanddijeteventsfromcollisiondata[22]. Thetrans- verse energy resolution for jets ∆E /E is better than 15% in the range considered. We recon- T T struct Emiss asthemodulusofthenegativevectorsumoftransverseenergiesintheindividual T calorimeter towers and is further corrected for the jet energy scale and for muon momenta measuredinthetrackers[23]. ElectronsandphotonsarereconstructedasisolatedenergydepositsintheECALwithashape consistent with that expected for electromagnetic showers. Electrons are required to have a track matched to the calorimeter cluster, while photons are required to have no matching hits inthesiliconlayers. Electronsandphotonsareselectedwith E > 20GeVandarerequiredto T be reconstructed in the fiducial barrel (|η| < 1.44) or endcap (1.56 < |η| < 2.4) regions. The ECALhasexcellentenergyresolution,forexamplecontributing1GeVtotheobservedwidthof theZbosonusinge+e− pairswithlowbremsstrahlungloss,measuredinthebarrelregion[24]. Muons are reconstructed as matched tracks in the muon spectrometer and the silicon tracker. Muons are selected with |η| < 2.1 and p > 20GeV, and are required to be isolated from T other tracks. Requiring the muons to have distance of the closest approach < 0.2cm helps to suppress backgrounds from cosmic-ray muons. Here, the distance of the closest approach is defined as the shortest distance between the beam line and the direction of an object in the 1Energeticelectronsandphotonsarealsoreconstructedasjetsatthetriggerlevel. 3 transverse plane. Performing a combined fit to the track segments measured in the silicon tracker and the muon system results in a transverse momentum resolution between 1% and 5%for p valuesupto1TeV. Theminimumseparationbetweenanytwoobjects(jet,lepton,or T photon)isrequiredtobe∆R = (cid:112)(∆φ)2+(∆η)2 > 0.5. Simulatedsamplesofsemiclassicalblackholeeventsareproducedusingaparton-levelBLACK- MAX [25] (v2.01) and CHARYBDIS [26, 27] (CHARYBDIS 2, v1.0.3) MC generators, followed by the parton showering simulation with PYTHIA [28] (v6.420), and a fast parametric simulation of the CMS detector [29]. The MSTW2008lo68cl [30] parton distribution functions (PDF) are usedforgeneratingthesignalsamples. The BLACKMAX and CHARYBDIS generatorscalculate the total cross section σ from geometric considerations, assuming that σ ∝ πr2, where r is S S theSchwarzschildradius[1,2]. The BLACKMAX generatorusestheapproximationofrotating black holes, which includes an additional factor that depends on the number of extra dimen- sions n. The CHARYBDIS generator incorporates a more detailed model based on Yoshino– Rychkovcorrections[31,32]tothepuregeometricalcrosssection,resultinginproductioncross sections that are lower by a factor of 1.36,1.59, and 1.78 compared to those from BLACKMAX forn = 2,4,and6,respectively. Thesescalefactorscanbeusedtointerprettheresultsobtained withoneframeworkintermsoftheother. Certain models are supported by both generators: rotating and nonrotating black holes, and black holes with mass and angular momentum loss prior to evaporation. This loss is set to be10%inthe BLACKMAX generator, whileitisestimatedintheYoshino–Rychkovmodeland variesfrom18%to30%forn = 2to6intheCHARYBDISgenerator. Inaddition,weuseCHARYB- DIS to simulate black hole evaporation resulting in a stable remnant with mass equal to the multidimensionalPlanckscale MD,oraboilingremnant(uniquetotheCHARYBDISgenerator). Both of these scenarios represent alternative descriptions of the final stage of the black hole evolution. Inthecaseofastableremnant,theterminalstageofablackholeisanoninteracting remnant with a mass of order M ; in the case of a boiling remnant, a black hole undergoes a D transformationintoastringballatamasscloseto M withsubsequentevaporationatafixed D temperature. Weproduceanumberofstring-ballsamplesusingtheBLACKMAXgenerator. Fi- nally,the QBH (version1.03)matrix-elementgenerator[33]withCTEQ6LPDFset[34]isused, followedbythepartonshoweringsimulationwithPYTHIAandfastsimulationoftheCMSde- tector, to produce quantum black hole samples. Table 1 summarizes the models used in this search. Table1: SignalMonteCarlosamplesandgeneratorsusedintheanalysis. Sampledescription BLACKMAX CHARYBDIS QBH nonrotatingBH YES YES NO RotatingBH YES YES NO RotatingBHwithmassand angularmomentumloss YES(10%loss) YES(18−30%loss) NO RotatingBH,lowmultiplicityregime NO YES NO Boilingremnant NO YES NO Stableremnant NO YES NO Stringballs YES NO NO QuantumBH NO NO YES 4 4 Analysismethod 4 Analysis method Thetotaltransverseenergyisusedtoseparateblackholecandidateeventsfrombackgrounds. A variable S is defined as a scalar sum of the transverse energy (E ) of individual objects: T T jets, electrons, photons, and muons passing the selections described above. Only objects with E > 50GeV enter into the sum for the calculation of S and count towards the final-state T T multiplicity N. This rather high minimum transverse energy requirement makes the analysis insensitivetothejetsfrompileupandreducestheSMbackgroundsbyafewordersofmagni- tude, while being fully efficient for black hole decays. We further add the measured Emiss in T the event to the S , if Emiss > 50GeV. Generalization of the S definition to include Emiss is T T T T important for testing black hole models with a significant amount of missing energy such as models with a stable noninteracting remnant. A spurious Emiss may arise in an event as the T resultofmismeasurementofthejets. However,wehavecheckedthattheconsequenteffecton S ofdoublecountingenergyinboththejetand Emiss contributionsisnegligible. Notethatby T T construction, particle misidentification does not affect the total transverse energy in the event considerably. Dependingonthedetailsoftheblackholeevaporation,alargevariationofparticlemultiplicity inthefinalstate,andalargerangeofmissingtransverseenergiesarepossible. Whileresulting in quite different signatures, these variations typically have very little effect on the value of S in the event. A recent work on quantum-gravity black holes [35] also suggests a larger T number of softer particles produced in black hole evaporation than in the semiclassical case, further emphasizing the importance of S as a largely model-independent variable for black T holesearches. The main background to black hole production arises from QCD multijet production, which dominates the event rates at large S . Smaller backgrounds come from γ/W/Z+jets and tt T production. ThesesmallerbackgroundsarenegligibleatlargevaluesofS andcontributeless T than 1% to the total background after the final selection. We estimate their contribution from MC simulation, using the MADGRAPH [36] leading-order parton-level event generator (with up to three extra partons included in the simulation) with the CTEQ6L PDF set followed by PYTHIA [28] parton showering and full CMS detector simulation via GEANT4 [37]. For the dominantQCDbackground,however,weestimatebackgroundsfromtheobserveddatausing theS multiplicityinvariancemethod[7]. Thismethodreliesontheindependenceoftheshape T oftheS spectrumonthenumberoffinal-stateobjects N;anempiricalobservationextensively T checkedbyusingvariousMCsamples(ALPGEN and PYTHIA)aswellaslow-multiplicitydata. Theoriginofthisinvarianceliesinthecollinearnatureofthefinal-stateradiation,whichtypi- callydoesnotchangethetotaltransverseenergyintheevent;hencetheindependenceoftheS T spectrum of the jet multiplicity for the QCD background. This invariance allows us to predict the shape of the S spectrum for any number of objects using the dijet data, which has been T studiedextensivelyforpresenceofnewphysicsindedicatedanalyses[38–40]. Weuselow-multiplicitydatawith N = 2and N = 3toobtainthebackgroundshapebyfitting theSTdistributionsbetween1200and2800GeVwiththeansatzfunctionP0(1+x)P1/xP2+P3log(x), which is shown in Fig. 1 as a solid line. No evidence of new physics has been observed in this region in a dedicated analysis [38]. To estimate the systematic uncertainty of the method, the same ST distributions are fitted with two additional functions, P0/(P1+P2x+x2)P3 and P0/(P1+x)P2. Thus, an envelope of functions is formed (shown as the shaded area in Fig. 1) andisusedasthesystematicuncertainty. Figure 2 shows the fit result of the background prediction for the inclusive samples with high object multiplicity events. Here, the shape of the S distribution obtained from the N = 2 T 5 eV CMS s = 7 TeV, 4.7 fb-1 a) eV CMS s = 7 TeV, 4.7 fb-1 b) 0 G106 Multiplicity, N = 2 0 G106 Multiplicity, N = 3 0 0 1 Observed Photon+Jets 1 Observed Photon+Jets s / 105 Background Wttb+aJrets s / 105 Background Wttb+aJrets nt Uncertainty Z+Jets nt Uncertainty Z+Jets e e Ev104 MD = 1.5 TeV, M BmHin = 4.5 TeV, n = 6 Ev104 MD = 1.5 TeV, M BmHin = 4.5 TeV, n = 6 M = 2.0 TeV, M min = 4.0 TeV, n = 4 M = 2.0 TeV, M min = 4.0 TeV, n = 4 D BH D BH 103 MD = 2.5 TeV, M BmHin = 3.5 TeV, n = 2 103 MD = 2.5 TeV, M BmHin = 3.5 TeV, n = 2 102 102 10 10 1 1 1500 2000 2500 3000 3500 4000 4500 1500 2000 2500 3000 3500 4000 4500 S (GeV) S (GeV) T T Figure 1: Distribution of the total transverse energy, S , for low-multiplicity events with mul- T tiplicity: a) N = 2 and b) N = 3 photons, electrons, muons, or jets in the final state. Ob- served data are depicted as points with error bars; solid line with a shaded band is the back- ground prediction and its systematic uncertainty. Non-QCD backgrounds are shown as filled histograms (not stacked). Also shown is the black hole signal for three parameter sets of the BLACKMAX nonrotating black hole model, demonstrating that signal contamination in the fit regionof1200−2800GeVwouldbesmall. sample is normalized to the observed data in the range 1800 to 2200GeV, where no signal contributionisexpected. Alsoshownaretheexpectedsemiclassicalblackholesignalsforthree parameter sets of the BLACKMAX nonrotating black hole model. The results are presented separatelyforsixdifferentvaluesoftheminimumfinalstatemultiplicity. Thedataagreewith thebackgroundshapesfromthelow-multiplicitysamplesanddonotexhibitevidencefornew physics. Figure 3 shows a similar comparison of the experimental S distribution with the T predicted signal for three parameter sets of the QBH quantum black hole model. In this case thecomparisonisshownseparatelyforjusttwovaluesoftheminimumfinalstatemultiplicity, reflecting the different decay characteristics expected for quantum black holes compared to semiclassicalblackholes. 5 Results Inordertosetexclusionlimitsonblackholeproduction,weassignsystematicuncertaintieson the background estimate varying from 3% to 300% in the S range used in this search. These T uncertainties are dominated by the uncertainties from using various fit ansatz functions (2%– 300%),whichareaddedinquadraturetothesecond-largestcontribution,whicharisefromthe normalization statistical uncertainty (2%–21%). The integrated luminosity is measured with 4.5% uncertainty [8, 9] utilizing information from the forward calorimeters. The signal uncer- tainty is dominated by the jet energy scale uncertainty of ≈ 2% [22], which translates into 2% uncertainty on the signal. An additional 2% uncertainty on the signal acceptance comes from the variation of acceptance obtained with the default MSTW2008lo68cl PDF library and PDFs withintheCTEQ61andCTEQ66errorsets[34]. Given the significant model dependence of the black hole production cross section and decay patterns,itisnotpracticaltotestalldifferentvariationsofmodelparameters,offeredbyrecent 6 5 Results eV CMS s = 7 TeV, 4.7 fb-1 a) eV CMS s = 7 TeV, 4.7 fb-1 b) 0 G105 Multiplicity, N ‡ 3 0 G105 Multiplicity, N ‡ 4 0 0 1 Observed 1 Observed nts / 104 BUancckegrtraoiunntyd nts / 104 BUancckegrtraoiunntyd e e Ev M = 1.5 TeV, M min = 4.5 TeV, n = 6 Ev M = 1.5 TeV, M min = 4.5 TeV, n = 6 103 MD = 2.0 TeV, MB mHin = 4.0 TeV, n = 4 103 MD = 2.0 TeV, MB mHin = 4.0 TeV, n = 4 D BH D BH M = 2.5 TeV, M min = 3.5 TeV, n = 2 M = 2.5 TeV, M min = 3.5 TeV, n = 2 D BH D BH 102 102 10 10 1 1 2000 2500 3000 3500 4000 4500 2000 2500 3000 3500 4000 4500 S (GeV) S (GeV) T T eV105 CMS s = 7 TeV, 4.7 fb-1 c) eV CMS s = 7 TeV, 4.7 fb-1 d) G G 0 Multiplicity, N ‡ 5 0 Multiplicity, N ‡ 6 10 Observed 10104 Observed s / 104 Background s / Background nt Uncertainty nt Uncertainty Eve103 MD = 1.5 TeV, M BmHin = 4.5 TeV, n = 6 Eve103 MD = 1.5 TeV, M BmHin = 4.5 TeV, n = 6 M = 2.0 TeV, M min = 4.0 TeV, n = 4 M = 2.0 TeV, M min = 4.0 TeV, n = 4 D BH D BH 102 MD = 2.5 TeV, M BmHin = 3.5 TeV, n = 2 102 MD = 2.5 TeV, M BmHin = 3.5 TeV, n = 2 10 10 1 1 2000 2500 3000 3500 4000 4500 2000 2500 3000 3500 4000 4500 S (GeV) S (GeV) T T eV CMS s = 7 TeV, 4.7 fb-1 e) eV CMS s = 7 TeV, 4.7 fb-1 f) 0 G104 Multiplicity, N ‡ 7 0 G Multiplicity, N ‡ 8 0 0 1 Observed 1103 Observed nts / 103 BUancckegrtraoiunntyd nts / BUancckegrtraoiunntyd e e Ev M = 1.5 TeV, M min = 4.5 TeV, n = 6 Ev M = 1.5 TeV, M min = 4.5 TeV, n = 6 D BH 102 D BH M = 2.0 TeV, M min = 4.0 TeV, n = 4 M = 2.0 TeV, M min = 4.0 TeV, n = 4 102 MD = 2.5 TeV, MB mHin = 3.5 TeV, n = 2 MD = 2.5 TeV, MB mHin = 3.5 TeV, n = 2 D BH D BH 10 10 1 1 2000 2500 3000 3500 4000 4500 2000 2500 3000 3500 4000 4500 S (GeV) S (GeV) T T Figure2: Distributionofthetotaltransverseenergy,S ,foreventswithmultiplicity: a) N ≥ 3, T b) N ≥ 4, c) N ≥ 5, d) N ≥ 6, e) N ≥ 7, and f) N ≥ 8 objects (photons, electrons, muons, or jets)inthefinalstate. Observeddataaredepictedaspointswitherrorbars;thesolidlinewith ashadedbandisthebackgroundpredictionanditssystematicuncertainty. Alsoshownarethe expectedsemiclassicalblackholesignalsforthreeparametersetsofthe BLACKMAX nonrotat- ingblackholemodel. Here,Mministheminimumblackholemass,M isthemultidimensional BH D Planckscale,andnisthenumberofextradimensions. 7 eV106 CMS s = 7 TeV, 4.7 fb-1 a) eV106 CMS s = 7 TeV, 4.7 fb-1 b) G G 0 Multiplicity, N ‡ 2 0 Multiplicity, N ‡ 3 10105 Observed 10105 Observed s / Background s / Background ent104 Uncertainty ent104 Uncertainty Ev M = 2.0 TeV, M min = 3.0 TeV, n = 1 Ev M = 2.0 TeV, M min = 3.0 TeV, n = 1 D QBH D QBH 103 MD = 3.0 TeV, M QmBinH = 3.5 TeV, n = 3 103 MD = 3.0 TeV, M QmBinH = 3.5 TeV, n = 3 M = 4.0 TeV, M min = 4.0 TeV, n = 5 M = 4.0 TeV, M min = 4.0 TeV, n = 5 D QBH D QBH 102 102 10 10 1 1 2000 2500 3000 3500 4000 4500 2000 2500 3000 3500 4000 4500 S (GeV) S (GeV) T T Figure3: Distributionofthetotaltransverseenergy, S , foreventswithmultiplicity: a) N ≥ 2 T and b) N ≥ 3 objects in the final state. Observed data are depicted as points with error bars; thesolidlinewithashadedbandisthebackgroundpredictionanditssystematicuncertainty. Alsoshownaretheexpectedquantumblackholesignalsforthreeparametersets. Here, Mmin QBH is the minimum quantum black hole mass, M is the multidimensional Planck scale, and n is D thenumberofextradimensions. black hole event generators, in a dedicated search. This study considers some 700 different signal MC samples, yet it does not come close to spanning the entire parameter space of the models; scaling the number of signal samples up and presenting the results for every model therefore becomes impractical. Hence, we first present the results of our search in a generic, model-independentway, whichwouldallowotherstoprobeadditionalmodelsusingparton- levelMCinformation, possibly augmented withaverybasicdetectorsimulation. Tofacilitate suchanapproach, weprovidemodel-independentlimits onthecrosssectiontimes theaccep- tance for new physics production in high-S inclusive final states for N ≥ 3,4,5,6,7, and 8. T ThelimitsaresetusingamodifiedfrequentistCL method[41,42]withlog-normalpriorused s tomarginalizenuisanceparametersinthelikelihoodfunction. Figure 4 shows 95% confidence level (CL) limits from a counting experiment placed on the experimentally reconstructed value S > Smin as a function of Smin, which can be used to test T T T models of new physics that result in these final states, including (but not limited to) an even broadervarietyofblackholemodelsthanwecoveredinthisanalysis. The95%CLlimitsfrom 2010data[7]arealsoshowninFig.4forcomparison. Thepresentmodel-independentlimitsare roughly0.6fbforhighvaluesofS ,representingatwoordersofmagnitudeimprovementover T the limits reported in our first publication [7]. Given the higher statistics of the 2011 sample, wearealsoabletoextendtheselimitstothe N ≥ 6,7,and8cases. For a specific subset of the black hole models [7] that are being probed, we also set dedicated limits on semiclassical and quantum black hole and string-ball production performing count- ingexperimentsusingoptimizedS and N selections. Itshouldbenotedthatthesemiclassical T approximation used for deriving the cross section within respective benchmark scenarios is expected to break down for many of the points probed, a point emphasized in a recent cri- tique[43]. Thus,theselimitsshouldbetreatedasindicative,ratherthanprecise. The si√gnal (S) significance is optimized in the presence of background (B) using a test statis- tic S/ S+B for each set of model parameters. The optimum choices of S and N for a few T 8 5 Results pb) CMS s = 7 TeV, 4.7 fb-1 a) pb) CMS s = 7 TeV, 4.7 fb-1 b) A (10 Multiplicity, N ‡ 3 A (10 Multiplicity, N ‡ 4 · min) > ST 1 OEEOxxbbppsseeeeccrrvvtteeeedddd ,–– 2 120ss10 data · min) > ST 1 OEEOxxbbppsseeeeccrrvvtteeeedddd ,–– 2 120ss10 data ST Expected, 2010 data ST Expected, 2010 data ( ( s s 10-1 10-1 2010, 35 pb-1 2010, 35 pb-1 10-2 10-2 2011, 4.7 fb-1 2011, 4.7 fb-1 10-3 10-3 2000 3000 4000 5000 2000 3000 4000 5000 S min (GeV) S min (GeV) T T pb) CMS s = 7 TeV, 4.7 fb-1 c) pb) CMS s = 7 TeV, 4.7 fb-1 d) A (10 Multiplicity, N ‡ 5 A (10 Multiplicity, N ‡ 6 · min) > ST 1 OEEOxxbbppsseeeeccrrvvtteeeedddd ,–– 2 120ss10 data · min) > ST 1 OExbpseecrvteedd – 1s ST Expected, 2010 data ST Expected – 2s ( ( s s 10-1 10-1 2010, 35 pb-1 10-2 10-2 2011, 4.7 fb-1 2011, 4.7 fb-1 10-3 10-3 2000 3000 4000 5000 2000 3000 4000 5000 S min (GeV) S min (GeV) T T pb) CMS s = 7 TeV, 4.7 fb-1 e) pb) CMS s = 7 TeV, 4.7 fb-1 f) A (10 A (10 Multiplicity, N ‡ 7 Multiplicity, N ‡ 8 · min) > ST 1 OExbpseecrvteedd – 1s · min) > ST 1 OExbpseecrvteedd – 1s ST Expected – 2s ST Expected – 2s ( ( s s 10-1 10-1 10-2 10-2 2011, 4.7 fb-1 2011, 4.7 fb-1 10-3 10-3 2000 3000 4000 5000 2000 3000 4000 5000 S min (GeV) S min (GeV) T T Figure4: Model-independent95%CLuppercrosssectionlimitsforcountingexperimentswith S > Smin as a function of Smin for events with multiplicity: a) N ≥ 3, b) N ≥ 4, c) N ≥ 5, d) T T T N ≥ 6, e) N ≥ 7, and f) N ≥ 8. The blue solid (red dotted) lines correspond to an observed (expected) limit for nominal signal acceptance uncertainty of 5%, compared to observed (ex- pected)limitsobtainedwith2010CMSdataandshownasbluedashed(reddash-dotted)line. The green and yellow bands represent one and two standard deviations from the expected limits.