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Track-Based Alignment of the Inner Detector of ATLAS AnaOvcharovaaonbehalfoftheATLASCollaboration LawrenceBerkeleyNationalLaboratory(LBNL),USA Abstract. ATLASisamultipurposeexperimentattheLHC.ThetrackingsystemofATLAS,embeddedina 2Tsolenoidalfield,iscomposedofdifferenttechnologies:siliconplanarsensors(pixelandmicrostrips)anddrift- 2 tubes.TheprocedureusedtoaligntheATLAStrackerandtheresultsofthealignmentusingdatarecordedduring 1 2010and2011usingLHCproton-protoncollisionrunsat7TeVarepresented.Validationofthealignmentis 0 2 performedbymeasuringthealignmentobservablesaswellasmanyotherphysicsobservables,notablyresonance invariantmassesinawidemassrange(KS, J/Ψ andZ).TheE/pdistributionsforelectronsfromZ → eeand n W → eν are also extensively used. The results indicate that, after the alignment with real data, the attained a precisionofthealignmentconstantsisapproximately5µm.Thesystematicerrorsduetothealignmentthatmay J affectphysicsresultsareunderstudy. 4 2 1 Introduction imizedisgivenby: ] t e (cid:88) d χ2 = r(τ,a)TV−1r(τ,a), TheATLASInnerDetector(ID),showninFig.1,iscom- s- posedofthePixel,theSemiconductorTracker(SCT)and Trks n theTransitionRadiationTracker(TRT).TheIDisdesigned whereV isthehitcovariancematrixandr(τ,a)isthevec- .i toachievethemomentum andvertexresolutionsrequired toroftrackresiduals,whichareafunctionofboththetrack s c forhigh-precisionmeasurements[1].Toensurethatthere- parameters, τ, and the alignment constants, a. ID align- i sulting requirements on track reconstruction are met, the ment implements two flavors of χ2-based algorithms: the s y position and orientation of each active detector element Global χ2 and the Local χ2. In the Global χ2 approach, h mustbeknownwithsufficientaccuracysuchthattrackpa- a simultaneous minimization with respect to all track pa- p rameterresolutionisdegradedbylessthan20%ofthede- rameters and alignment constants is done. This approach [ sign values. The following is an outline of the procedure, ensures that full correlation between alignable objects in- resultsandsomeofthechallengesofthealignmentofthe tersected by a common track is retained. In the Local χ2 1 v ID. minimization, module correlations are discarded, render- 1 ing alignment less computationally intensive. However, it 6 isnecessarytoperformmultipleiterationstoreachconver- 9 gence. The alignment uses isolated high-p tracks to re- 2 Alignment strategy T 4 ducetheimpactofpatternrecognitionambiguitiesandof . 1 multiple scattering. Both collision and cosmic ray tracks 0 The alignment is derived by minimizing track residuals are used to maximize long-distance correlations between 2 which are defined as the difference between the expected detectorelements.IDalignmentisstagedatseverallevels 1 andthemeasuredhitpositions.Theχ2functiontobemin- of granularity, corresponding to the hierarchy of its me- v: chanicalstructure.Table1showsthesubstructuresandal- i a e-mail:[email protected] gorithmsusedatdifferentlevelsintheAutumn2010align- X ment.ThenumbersintheDoFcolumnrepresenttheprod- r uctofthenumberofsubstructuresandthealloweddegrees a of freedom for each. For example, at Level 2, the Pixel halfshellswereallowedallthreerotationsandthreetrans- lations, while the endcaps only two translations and one rotation [2]. In the latest alignment, discussed in Sec. 4, the Global χ2 was used at all levels but the wire-by-wire alignment of the TRT (approximately 700,000 DoF). The latterusedtheLocalχ2approachduetocomputationalre- strictions. 3 Alignment performance TheAutumn2010alignmentwasthefirsttouse7TeVcol- Fig.1.TheATLASInnerDetector. lision data in addition to pixel module wafer deformation EPJWebofConferences Table1.OverviewofthealignmentlevelsfortheAutumn2010 ×103 m alignmentasdescribedin[2]. µ Autumn 2010 Alignment ATLAS Preliminary Level Structures #DoF Method ks / 12 100 FSFWWprHiHnMMg //2220..331550== A11l21ig48n µµmmment TsR =T 7b aTrereVl PIX:whole n trac 80 Track pT > 15 GeV Level1 SCT:barrel+2endcaps 41 Globalχ2 s o 60 TRT:barrel+2endcaps Hit 40 PIX:halfshells+disks Level2 SCT:layers+disks 852 Globalχ2 20 TRT:modules+wheels PIX:modules -1 -0.5 0 0.5 1 Level3 SCT:modules 722104 Localχ2 Residual [mm] TRT:wires Fig. 4. Improvement in resolution in the direction transverse to theTRTwiresaftertheAutumn2010alignment. ×103 m µ Autumn 2010 Alignment ATLAS Preliminary Hits on tracks / 2 345000 FSFWWprHHinMMg //2220..331550== A91l 6iµg µmnmment PTsrixa =ec kl7 b pTaTer r>Ve l15 GeV [GeV]M +µµ 999468 ZSS pu→rmin mµgµ e2 rM0 21C011 a1l iaglnigmnemnetnt DaAtaT L∫2A 0L1S d1t,P =rs e0 l=i.m7 70i n Tfaber V1y 20 92 10 90 88 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 1.05 < η < 2.5 Local x residual [mm] 86 3 2 1 0 1 2 3 Fig.2.Improvementinresolutioninthedirectionofhighestgran- Positive muon φ ularityofthePixelmodulesaftertheAutumn2010alignment. Fig. 5. An indication of a weak mode misalignment present in theendcapAregion(black)andtheeffectofusingconstrained m ×103 alignmenttoremoveit(red). µ 90 Autumn 2010 Alignment ATLAS Preliminary n tracks / 4 678000 SFFWWprHHinMMg //2220..331550== A22l58ig µµnmmment TSsrCa =Tc k 7b paTTrer >Ve l15 GeV helicalformoftracksattheexpenseofbiasingthetrackpa- o rameters.Theyarecommonlyreferredtoas“weakmodes” Hits 50 andcanbeidentifiedbyexaminingthekinematicsofreso- 40 nancedecayssuchasZ → µµ, J/Ψ → µµand K → ππ. S 30 The bias introduced in the track momenta by such mis- 20 alignments violates the symmetries inherent in these de- 10 caysandtherebyresultsinunexpecteddependencesofthe reconstructedinvariantmassonvariouskinematicobserv- -0.2 -0.1 0 0.1 0.2 ables.AstrikingexampleisthedependenceoftheZinvari- Local x residual [mm] antmassontheφtrackparameterofthepositivemuon,see Fig.3.Improvementinresolutioninthedirectionofhighestgran- Fig. 5. The approach to correct such misalignments is to ularityoftheSCTmodulesaftertheAutumn2010alignment. constrain some parameters during the alignment, thereby, minimizingthepossibilityofretainingbiases.Someexam- ples of useful constraints are: momentum measurements inputfromtheproductionsurvey.Itwasalsothefirstwire- bytheMuonSpectrometer,vertexpositionconstraintand by-wireTRTalignment.Theimpactoftheseimprovements thecalorimeterderivedconstraint.Thecalorimeterderived isevidentinthereducedwidthoftheresidualdistributions constraint,orE/pconstraint,usesthefactthatthecalorime- in the barrel sections of all sub-detectors, the Pixel, SCT terresponseforpositronsandelectronsshouldbethesame. and TRT, shown in Figs. 2, 3 and 4, respectively. Simi- Differencesbetweentheratioofenergytomomentummea- lar trends are observed in the endcap regions, where the surement between electrons and positrons in Z → ee or large track statistics used in this alignment were particu- W → eν decays can then be attributed to mismeasure- larlyadvantageous.[2] ment of the momentum in the tracker and used to obtain corrections to the reconstructed track momenta in bins of azimuthalangleandpseudorapidity.Duringalignment,the 4 Weak modes and constrained alignment trackmomentaarethenconstrainedtothecorrectedvalue. TheE/pcorrectionhasresultedinthelatestsignificantim- There exist systematic detector deformations that cannot provementinthealignmentasevidencedbytheincreasein bedetectedusingtheoutlinedapproachastheyretainthe theZinvariantmassresolutionshowninFig.6. HadronColliderPhysicsSymposium,2011,PosterSession References V Ge 3000 Spring 2011 alignment ATLAS Preliminary ates / 1 2500 ZS u→m mµµe rM 2C011 alignment Data∫ 2 L0 1d1t ,= s0 .=7 07 fTbe 1V 1.CAETRLNALSarCgoelHlaabdorroatnioCno,lTlihdeerA,JTILNASSTE3xSp0er8i0m0e3n(t2a0t08th)e. did 2000 ID tracks 2. ATLAS Collaboration, Alignment of the ATLAS In- n Z ca 1500 11..0055 << ηηµµ+ << 22..55 nperortoDnetceocltloisrioTnrsacaktin√gsS=ys7temTeVw,itAhT2L0A1S0-CLHOCNFp-r2o0to1n1-- 1000 012,https://cdsweb.cern.ch/record/1334582(2011). 500 0 60 70 80 90 100 110 120 Mµ+µ [GeV] Fig.6.ImprovementintheZmassresolutionduetousingcon- strained alignment to remove weak mode misalignment in the endcapAregion LLeevveell 11 aalliiggnnmmeenntt m] X translation [µ 105 PSSSTTTRRRiCCCxTTTeTTT l BEEBEEannannrddrddrr eeCCCCllaaaapppp ACAC AApTril L- MAaSy 20p1r1eliminary Global 0 -5 -10 Cfaoiolulirneg Pocwuter Tesctohpnic. Coooflfing Traomropid. 179711079721579801479931879931980141980151380161480401080481180611480631680661480711082281482371282421482481682511682511982721682741782781783001383021183045 Run number Fig.7.Changesinthealignmentconstantsonarun-by-runbasis. Notetheimpactofincidentssuchasmagnetrampingandcooling interruptions. 5 Run-by-run alignment monitoring Significantchangesofthedetectoralignmentoccurdueto externalfactors.Someoftheidentifiedcausesincludetem- perature changes and magnet ramping. The time-ordered globalshiftsofselectedsubstructuresinthedirectiontrans- verse to the beam pipe are shown in Fig. 7. The largest changesobservedarelessthan10µm.Tomonitorandbet- ter understand this behavior, the Level 1 alignment con- stantsarenowrecomputedonarun-by-runbasis. Additionally, as resonances have been shown to be a powerful probe in uncovering weak-mode misalignments and,thereby,momentumbiases,plotsofthereconstructed mass as a function of various kinematic variables and the massitself(asinFigs.5and6)arealsoproducedautomat- ically for every run as a part of the ATLAS data quality monitoring. 6 Conclusion and outlook The current implementation of the alignment procedure hasbeenshowntobeeffectiveandwellsuitedforthechal- lengesposedbythealignmentoftheATLASID.Thenext stepistoevaluatethesystematicscausedbyresidualmis- alignments. It has already been seen that resonances are a powerful handle for tackling this problem and ongoing studieswillsoonprovidequantitativemeasuresofanyre- mainingbiases.