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Measurement of muon momentum resolution of the ATLAS detector AntonioSalvucci1,aonbehalfoftheATLASCollaboration RadboudUniversityNijmegenandNikhef Abstract. TheATLASdetectorhasbeendesignedtohavegoodmuonmomentumresolutionuptomomenta in the TeV range. The muon momentum resolution of the ATLAS spectrometer has been measured with p-p 2 collision data recorded in 2011. The measurement combines the di-muon mass resolution in J/ψ → µµ and 1 Z → µµ decays with measurements of the alignment accuracy of the detector based on straight muon tracks, 0 2 whichareacquiredwithspecialrunswithoutmagneticfieldintheATLASdetector. n a 1 Introduction 2 Parametrization of the momentum J resolution as a function of p and η 3 T 2 Therelativemomentumresolution,σ(p)/p,originatesfrom ] The physics programme of the ATLAS Experiment [1] at differenteffects[3,4].TheATLASMSisdesignedtopro- t e theLHCincludesinvestigationsofmanyprocesseswithfi- videamomentumresolutionasafunctionoftheηandφ. d nal state muons. The ATLAS detector is equipped with a Foragivenvalueofη,theresolutioncanbeparametrized - MuonSpectrometer(MS)optimizedtoprovideamomen- asafunctionof p : s T n tummeasurementwitharelativeresolutionbetterthan3% i over a wide p range and 10% at p =1 TeV, where p σ(p) pMS . T T T = 0 ⊕pMS ⊕pMS ·p (1) s isthemuonmomentumcomponentintheplanetransverse p p 1 2 T c T to the beam axis. The momentum in the MS is measured si fromthedeflectionofthemuontrajectoryinthemagnetic wherepMS,pMS,pMS arecoefficientsrelatedtotheenergy 0 1 2 y field generated by a system of air-core toroid coils. The lossinthecalorimetermaterial,multiplescatteringandin- h MS track is reconstructed using three layers of precision trinsicresolutionterms,respectively. p drift tube (MDT) chambers in the pseudorapidity1 range FortheID,thecurvaturemeasurementdependsonthe [ |η|<2,andtwolayersofMDTchambersbehindonelayer track length of the muon in the active material, which is 1 ofcathodestripchambers(CSC)for2≤|η|<2.7. reducedclosetotheedgeoftheTRTfiducialvolume.This v resultsinauniformresponseinthecentralpartandarapid 4 An additional determination of the muon momentum worseningbeyondthisregion.Theapproximateparametriza- 0 isprovidedbytheInnerDetector(ID)for|η|<2.5.TheID tionoftheresolutionis 7 iscomposedofthreedetectorsprovidingcoordinatemea- 4 surementsfortrackreconstructioninsideasolenoidalmag- σ(p) = pID⊕pID·p for|η|<1.9 (2) 1. neticfieldof2T.Closetotheinteractionpointitfeaturesa p 1 2 T 0 siliconpixeldetector,surroundedbyasiliconstripdetector σ(p) 1 2 (SCT).Intheoutermostpartthereisatransitionradiation p = p1ID⊕p2ID·pTtan2(θ) for|η|>1.9 (3) 1 strawtubetracker(TRT)withacoverageof|η|<1.9. v: Muons entering in this analysis are reconstructed as where p1ID, p2IDarethemultiplescatteringandtheintrinsic Xi combined muons. The underlying muon identification is resolutionterms,respectively. Inthisstudy,fourregionsinpseudorapidityaredistin- described in [2] and relies on the principle that first sep- r guished: a arate tracks are measured in ID and MS before they are reconstructed as a single trajectory. This yields a higher - Barrel:covering0<|η|<1.05; momentumresolutionthancouldbeachievedusingthein- - Transition:covering1.05<|η|<1.7; dividualtracks. - End-caps:covering1.7<|η|<2.0; - CSC/No-TRT:covering2.0<|η|<2.5. Thispaperdocumentsthemuonmomentumresolution inthefirstpassofreconstructionof p-pcollisiondatacol- ThesefourregionsarestudiedusingZ →µµdecays. lectedin2011correspondingtoanintegratedluminosityof 2.54fb−1.Thefirstpassofreconstructionusespreliminary calibrationandalignment. 3 Combined fit to the muon resolution components a e-mail:[email protected] TheprocessZ →µµisusedtostudythemomentumreso- 1 Thepseudorapidityisη=−ln(tan(θ/2)),whereθisthepolar lutionandtodeterminethecorrectionsneededforsimula- anglewithrespecttothebeamline. tionineachηregionofthedetector.Weusetwoquantities: EPJWebofConferences i) thewidthofthereconstructeddi-muoninvariantmass Table1.Constraintsontheintrinsicresolutionterm peak at the Z pole, which is a convolution of the nat- ηregion Constrainton∆pMS (TeV−1) ural width of the Z boson and the muon momentum 2 resolution; barrel 0.143±0.030 ii) thedifferencebetweentheindependentmomentummea- transition 0.312±0.050 surementsoftheIDandMSforcombinedmuons,which end-caps 0.200±0.050 issensitivetothequadraticsumoftheIDandMSmo- CSC/No-TRT 0.408±0.050 mentumresolutions.Thisdifferenceisweightedbythe muon electric charge (q/pID −q/pMS): this disentan- T T gles systematic effects of the curvature due to local 4 Combined fit results misalignements from the overall intrinsic resolution, reducing the bias on the estimation of the resolution The constraints on the ∆p parameters are applied in the i andcorrectionparameters. combined fit by adding a penalty term (cid:80) (cid:18)∆pi−ai(cid:19)2 to the i σai totalχ2beingminimized,wherea istheexpectationvalue 3.1 Globalfitprocedure i and σ the associated uncertainty for each of the con- ai strained∆p parameters.Thefittedcorrectionsparameters Using the previous inputs, the measurements of the MS i are provided in Table 2 together with their statistical and andIDmomentumresolutionareobtainedusingaMonte systematicuncertainties. Figure1showsanexampleofZ Carlotemplatetechnique,basedona“global”fitprocedure with: i) atemplatefittoreconstructedZlineshape: Table2.Setofcorrectionstobeappliedonthe p parametriza- T weallowformomentumresolutionsmearinginthefit tion of thesimulated resolution in theMS and IDto reproduce to the Z lineshape obtained from MS and ID tracks theoneindata.Systematicerrorsonthetransitionregionaredue and a combined fit with events with muons in differ- toadifferentdefinitionoftheregionitself(1.2<|η|<1.7) ent detector regions. In this case we are sensitive to σ ⊕σ ηregion ∆pMS (%) ∆pMS (TeV−1) mult.scatt. intrinsic 1 2 ii) theabove,plustemplatefitto(q/pID−q/pMS)distri- T T barrel 1.80±0.05 0.095±0.016 bution: we allow for momentum resolution smearing transition 3.17±0.15±0.22 0.250±0.026±0.067 inthefit,thatcomputeseveralbinsof pT ,keepingre- end-caps 1.23±0.11 0.169±0.069 gionsseparated.ThiscaseissensitivetoσID⊕σMS CSC/No-TRT 0.52±0.58 0.453±0.028 iii) externalconstraintsonMSalignmentandmultiplescat- ηregion ∆pID(%) ∆pID(TeV−1) teringinIDandMS(see3.2) 1 2 Concerningthesmearing,forboththeMSandtheID,the barrel 0 0.283±0.011 transformationof p is transition 0 0.736±0.022±0.567 T end-caps 0 0.871±0.017 (cid:16) (cid:17) p(cid:48) = p 1+g∆pID,MS +g∆pID,MSp (4) CSC/No-TRT 0 0.050±0.001 T T 1 2 T where p(cid:48) indicatesthesimulatedmuon p afterapplying T T the correction ∆pID,MS, while g is a normally distributed i randomnumberwithmean0andwidth1. 3.2 Externalconstraintstothecombinedfit Inthefittingprocedure,additionalknowledgeisintroduced fromindependentstudies,bothfortheIDandtheMS.This reducesthecorrelationamongthemultiplescatteringand thedetectorresolutiontermsinthefit,resultinginsmaller uncertaintiesonthefittedparameters. For the ID, the correction to the multiple scattering term in the ID, ∆pID, is fixed to a value of zero, due to 1 Fig. 1. Examples of Z lineshape fit for MS tracks in the barrel aknowledgeoftheIDmaterialof0.05%. region,before(ontheleft)andafterfit(ontheright). For the MS, the multiple scattering term, ∆pMS, is a 1 freeparameterofthefit.Theenergylossofmuonsismainly concentratedinthecalorimeterandhasbeenmeasuredin lineshapefitforMStracksinthebarrelregion,before(left) [6].ItscontributiontotheoverallMSresolutioninthe pT andafter(right)thefit. rangefrom20GeVto100GeVisnegligibleandsonoad- The values of the correction parameters quantify the ditionalcontributionfortheenergyloss,∆pMS,isincluded. increase in momentum resolution in data when compared 0 For the intrinsic resolution term, ∆pMS, the best estimate tosimulation.Thefullparametrizationoftheexperimental 2 of the alignment accuracy is applied. This is the result of momentumresolutionisobtainedbyquadraticallyadding studiesfromsamplesofstraighttracksobtainedinperiods theuncorrectedsimulatedresolutiontermsofequations1- ofcollisiondatatakenwithnomagneticfieldinthemuon 3andthecorrespondingparametersfromTable2.There- system.Theconstraintson∆pMS arereportedonTable1. sultsforthefullparametrizationarelistedinTable3. 2 2011HadronColliderPhysicssymposium(HCP-2011) Table3.Resolutionparametrizationasdefinedinequations1-3 intheMSandID. ηregion pMS (TeV) pMS (%) pMS (TeV−1) 0 1 2 barrel 0.25±0.01 3.27±0.05 0.168±0.016 transition 0 6.49±0.26 0.336±0.072 end-caps 0 3.79±0.11 0.196±0.069 CSC/No-TRT 0.15±0.01 2.82±0.58 0.469±0.028 ηregion pID(TeV) pID(%) pID(TeV−1) 0 1 2 barrel n.a 1.55±0.01 0.417±0.011 transition n.a 2.55±0.01 0.801±0.567 end-caps n.a 3.32±0.02 0.985±0.019 CSC/No-TRT n.a 4.86±0.22 0.069±0.003 5 Measured resolutions as a function of p T The parametrized resolution as a function of p for the T barrelregion,obtainedusingthevaluesoftheparameters from the combined fits, are shown in figure 2 for the MS Fig.3.Di-muoninvariantmasscomparisonintheZbosonmass and the ID. The resolution curves for experimental data range between collision data (dots) and simulation (full his- (in blue) are compared to those from uncorrected param- togram),aftercorrectingthesimulatedmuonp ,inthefullrange T eters obtained for the simulation (in red). To indicate the ofη.Fromtoplefttobottom:MS,IDandcombinedmeasurea- mentsareshown. 6 Conclusions Adeterminationofthemuonmomentumresolutionispre- sented for the integrated luminosity of 2.54 fb−1collision datacollectedin2011withtheATLASdetector.Z → µµ decayshavebeenusedtoevaluatetheresolutionasafunc- tion of the muon p and η, for both the MS and the ID. T Themomentumresolutionsweremeasuredontheexperi- mentaldataandcomparedwiththesimulation.Resultsob- tained present an improvement of the resolution and the alignment with respect to those obtained with 2010 data [7]. References 1. ATLAS Collaboration, The ATLAS Experiment at the CERNLargeHadronCollider,JINST3(2008)S08003 2. ATLAS Collaboration, Determination of the muon re- construction efficiency in ATLAS at the Z resonance in √ p-pcollisionsat s = 7TeV,ATLAS-CONF-2011-008 (2011). 3. ATLAS Collaboration, Commissioning of the ATLAS MuonSpectrometerwithCosmicRays,Eur.Phys.J.C70, (2010)875. 4. ATLASCollaboration,TheATLASInnerDetectorcom- missioning and calibration, Eur.Phys.J. C 70, (2010) Fig.2.Resolutioncurvefromthefittedparametervaluesonthe 787. MS(top)andtheID(bottom)incollisiondataandsimulationasa 5. ATLASCollaboration,StudyoftheMaterialBudgetin functionofthemuonpT ,forthebarrelregion.Thesolidblueline the ATLAS Inner Detector with K0 decays in collision √ S showsdeterminationsbasedondata,thedashedbluelineshows dataat s=900GeV,ATLAS-CONF-2010-019(2010). theextrapolationto p rangenotaccessibleinthisanalysisand T 6. ATLAS Collaboration, Studies of the perfomance of thedashedredlineshowsthedeterminationsfromsimulation. theATLASdetectorusingcosmic-raymuonsEur.Phys.J. C71(2011)1593. goodnessofthesimulationcorrectionprovidedinsection 7. ATLAS Collaboration, ATLAS Muon Momentum Res- 4,figure3showsthedistributionofthedi-muoninvariant olutionintheFirstPassReconstructionofthe2010 p-p √ massintheZregionafterapplyingthecorrections,forMS, CollisionDataat s=7TeV,ATLAS-CONF-2011-046 IDandcombinedtracks. (2011).