We present the design and simulation of the track finding processor in the DTBX ( Drift Tube with Bunch Crossing Identification) based CMS barrel muon trigger system. The processor searches for muon tracks originating from the interaction region by joining the track segments provided by the mean timer processors of the drift chambers to track strings. It assigns transverse momenta to the reconstructed tracks using the tracks' bending angle. High speed is achieved by performing the track reconstruction fully in parallel. In this contribution the algorithms, implementation and simulation results are presented

Kluge, A

Wildschek, T

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Available on CMS information server CMS CR 1996/007CMS Conference ReportDecember 11, 1996Track Finding Processor in the DTBX BasedCMS Barrel Muon TriggerAlexander Kluge, Torsten WildschekCERN, Geneva, SwitzerlandCMS CollaborationAbstractWe present the design and simulation of the track finding processor in the DTBX (Drift Tube with BunchCrossing Identification) based CMS barrel muon trigger system. The processor searches for muon tracksoriginating from the interaction region by joining the track segments provided by the mean timer processorsof the drift chambers to track strings. It assigns transverse momenta to the reconstructed tracks using thetracks' bending angle. High speed is achieved by performing the track reconstruction fully in parallel. In thiscontribution the algorithms, implementation and simulation results are presented.Presented at First Workshop on Electronics for LHC Experiments, Lisboa, September 11-15, 19952track segment in rf  planemuon station 4muon station 3muon station 2muon station 1position of the track segment and angle 3m  f =  30 °track projected into rf planeinteraction pointmuon trackf 1f b endin g1f 2f 2 - f 1Fig 1: A sector of the CMS muon chamber system.Track Finding Processor in the DTBX Based CMS Barrel Muon TriggerAlexander Kluge, Torsten WildschekCERN, Geneva, SwitzerlandWe present the design and simulation of the track findingprocessor in the DTBX (Drift Tube with Bunch CrossingIdentification) based CMS barrel muon trigger system. Theprocessor searches for muon tracks originating from theinteraction region by joining the track segments providedby the mean timer processors of the drift chambers to trackstrings. It assigns transverse momenta to the reconstructedtracks using the tracks' bending angle. High speed isachieved by performing the track reconstruction fully inparallel. In this contribution the algorithms, implementationand simulation results are presented.INTRODUCTIONThe barrel part of the CMS muon system consists of 4muon stations, divided into 5 wheels along the z-axis andinto 12 sectors along the azimuthal angle, giving a total of60 modules per station (see fig. 9 and 1). Each modulecomprises dedicated trigger detectors (RPCs) and driftchambers [1]. The latter are used for off-line reconstructionand for triggering. Each drift chamber consists of twosuperlayers of drift tubes for measuring in the bendingprojection (R F ) and one superlayer for measuring in thenon-bending projection. Each superlayer in turn is formed offour staggered layers of drift tubes. The good spatialresolution of the drift tubes is expected to facilitatemomentum measurement with good resolution and hencethe design of a trigger with a sharp efficiency curve.INPUT TO THE TRACK FINDING PROCESSORThe chamber trigger logic, which enables theidentification of the bunch crossing, is based on a meantimer-technique [2]. The output primitive of the chamberlogic is the track segment (TS ), a triple of position,crossing angle and quality data. Those data are transferredto the trigger processor at a fixed delay after the bunchcrossing from which the muons originate. Per chamber upto two track segments (TS ) in each projection can beoutput. The position is measured with a discretization stepof 1.25 mm (or a multiple), the crossing angle with 10mrad at normal incidence; measurement range for thecrossing angle is -45o to +45o. However, this angularresolution can be achieved only if both superlayers of thatchamber contributed to the track segment. The actualresolution will thus be considerably worse than the nominalfigure suggests. It should be mentioned that what is neededfor our computations is not the position and the crossingangle with respect to the chamber, but the azimuthal angleof the hit position and the angle of the track with respect tothe radius vector. Whether the required conversion will becarried out in the chamber trigger logic or in the trackfinding processor described here is still subject todiscussion.PURPOSE OF THE TRACK FINDING PROCESSORThe task of the trigger processor is to assemble tracksegments to tracks (track finding). After checking whethera found track points to the interaction region, transversemomentum, direction values ( h , F ) and a track qualitycode are assigned.DESIGN CONSIDERATIONSThe first decision to be taken was how many tracksegments should be required in order to form a track. Thefirst approach was to demand track segments in at leastthree out of the four muon stations or in the innermost twostations to accommodate tracks with low transversemomentum. However, it turned out that this would result ina serious drop in acceptance, so the requirement wasrelaxed to require track segments in at least two muonstations only (see fig. 2).3Acceptance StudyCompare (2 out of 4) versus (3 out of 4 or innermost 2)at least 3 stations or innermost 2at least 2 stationsFig. 2: Acceptance study for two track findingconditions.TRACK FINDING ALGORITHMTwo approaches for track finding in the bending planewere considered. The template matching (or patterncomparison) technique consists in comparing the candidateagainst a predefined set of "valid" patterns obtained bysimulation and updated using the measurements. However,one of the design goals of this muon trigger is to make useof the good position resolution provided by the meantimers. Good resolution implies a large number of patternsto be stored, which results in a prohibitively high hardwareexpense. For that reason the pattern comparison methodwas rejected.The second method considered could be called pairwisematching method. Track segments are joined to trackstrings by pairwise matching. If two track segments fromdifferent stations are found to be compatible withoriginating from a single track, they form a track segmentpair, the most primitive track string; if one of those twotrack segments is compatible with a third track segmentfrom a station other than the two already belonging to thattrack string, a track segment triple is formed. A matchingfourth track segment from the remaining station wouldyield a track segment quadruple. Although the process hasbeen described in a serial way, all the forming of tracksegment pairs can be carried out in parallel.Fig. 3 illustrates the principle of the pairwise matchingmethod. After track segment pairs are found by pairwisematching these pairs may be joined to track segmentstriples or quadruples (track finding). If a valid track wasformed by the track finder a pt value is assigned (pt-assignment).AAAAAAAextrapolationresult "1/0"track found (TS1, TS2, TS3, TS4) AAAAAAAAAAAAAAAAAAAAAAAApt-assignment AAAAAAAAAATrack findingAAAAAAAAAAAAAAAAAAAAAPairwise Matching- ExtrapolationTS1, TS2, TS3, TS4ptpt assignmentAAAAAtrack selectorextrapolation windowmuon station 4muon station 3muon station 2muon station 1AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAtrack segmentAAφ2 - φ1Fig. 3: Principle of the track finding processor.The matching of two track segments will be carried outby extrapolating (recall that the angle of the track ismeasured along with the position) one of the tracksegments to the station of the second track segment andchecking that the difference between the extrapolatedposition value and the measured value of the second tracksegment is below a specific threshold. (see fig. 3)Simulations were carried out to prove that all requiredextrapolations are feasible. Due to the fact that the tracks'bending angle (angle between the track and the radiusvector in the bending plane, fig. 1) has a zero crossingwhich occurs between station 2 and station 4 nounambiguous extrapolation from station 3 to any otherstation is possible. However, all other extrapolations areunambiguous (fig. 4).A second requirement for feasibility of the extrapolationExtrapolationsfrom MS1 to MS2 from MS1 to MS3from MS1 to MS4 from MS2 to MS3from MS2 to MS4 from MS4 to MS3Fig. 4: Relation between bending angle ( f bending) in astation and the difference of the azimuthal hit coordinatesof the same and a different station.4Extrapolation deviationsfrom MS1 to MS2 from MS1 to MS3from MS1 to MS4 from MS2 to MS3from MS2 to MS4 from MS4 to MS3Fig. 5: Spread of extrapolation deviations versustransverse momentum pt.Differences of azimuthal hit coordinatesFig. 6: Differences of azimuthal hit coordinates versuspt.Fig. 7: Bending angle determined by single anglemeasurement versus pt.method is that the spread of the extrapolation deviation(defined as the difference of the extrapolated and themeasured value) is small compared to the chamberdimensions (one chamber spans about 0.5 rad in F ). Fig. 5shows that the deviation of the extrapolation is found to bebelow the required limit. The pairwise matching methodwas thus adopted.PT ASSIGNMENTFor assigning a transverse momentum one can exploiteither the bending angle or the sagitta of the track in themuon system. The drawback of the sagitta method is highercomplexity of the hardware implementation: To determinea sagitta either two measured angles or three measuredpositions can be used. The poor resolution of the angularmeasurement would force us to use three positions whichimplies more data transfer and more expense for look up-tables.Determining the bending angle can be done via a singleangular measurement (with poor momentum resolution) orusing a difference of two azimuthal position measurements.The bending angle measurement was chosen to determinept. Fig. 6 shows the relation between pt and the differencesof azimuthal hit coordinates from two track segments. Fig.7 displays the relation between pt and the track bendingangle obtained from only one track segment.PERFORMANCEEfficiency curves for several values of pt-threshold areshown in figure 8.Efficiency curvesFig. 8: Efficiency curves for the whole DTBX drift tubetrigger system for the thresholds 50, 70 and 100 GeV.5HARDWARE REQUIREMENTS OF THE TRACKFINDING PROCESSORThe majority of the previously implemented hardwaretriggers for muon identification in large scale high energyphysics experiments are based on pattern comparisonmethods. Most of the systems only count the number ofmuons crossing the muon system and do not measure anyparticle properties like pt or track location. All previouslyimplemented muon triggers have in common that thenumber of channels, i.e. the size of the detector, is 10 to100 times smaller than the size of CMS and the requiredmaximum calculation time is at least 10 times higher.The design of the data acquisition system of CMS [1]requires a maximum latency for the track finder system of400 ns. The pt information of muons which crossed themuon system must be given to the global trigger each 25ns. Processing must therefore be deadtimeless. This impliesa low possible number of calculation steps and a quite welladapted projection of the chamber geometry to thehardware system. Due to the high magnetic field and thenon-projective chamber system the particles cross segmentboundaries often. This poses a major challenge to thesystem design of the track finder since all data exchangebetween processing units contribute to the latency.For reasons of calculation speed the trigger processorhas to be designed in a hardwired way. Each triggerdecision must be made after a fixed time, independent ofthe data. This implies design restrictions that have to bemade in order to render hardware complexity andcalculation time reasonable. The impact of theserestrictions were examined using a VHDL-model of thesystem. The VHDL-model of the design was used tooptimize the system parameters with respect to thehardware extent and system performance.A very important property of the trigger is itsprogrammability. Of course, hardwired design and a largefreedom in programmability are contradictory. There are,however, some aspects in the overall design of the systemwhich require easy and automated reprogrammability. Anexample is the possibility of chamber misalignment.Extrapolation values would have to be adapted to the newenvironmental settings in a convenient fast way.Special focus was given to the modularity of the design.It ensures independence of the design from globalparameters like the maximum number of track segmentsgiven by the mean timer electronics.OVERALL DESIGN OF THE TRACK FINDINGPROCESSORThis system is divided into five ring trigger sorters ( D hx D f  = 0.35 x 2 p ,  see fig. 9). Each ring trigger sorter issubdivided into twelve sector processors (track finders)with a segmentation D h  x D f  = 0.35 x 0.52. A sectorprocessor matches the track segments identified by themeantimer logic and tries to form complete tracks. If thesector processor succeeds, it assigns a pt value to eachtrack, tests if the track extrapolates to the interaction pointand then forwards up to two tracks to the ring trigger sorter.Of the 12 x 2 possible tracks identified by the sectorprocessors only the four tracks with the highest pt areretained by the ring trigger sorter. All the information onthese tracks - pt, charge, h , f , quality - is then forwardedto the global muon trigger.η=0.35MS 1 to 4} sectorprocessor}5 x5 x 125 xring trigger sortermean timerandchamber logic60 xη-φ segmenttrigger ringφ=0.52global muon trigger1xFig. 9: Track Finding (or Sector-) ProcessorSegmentation and Logic Block Diagram.The Sector Processor (SP)In fig. 10 the block diagram of the track finder system isdisplayed. The sector processor (SP) is divided in threeparts - the extrapolator (EU), the track finder (TF) and thept-, h - and f -assignment units (PAU, h AU, f AU), see alsofig. 3. The extrapolation units attempt to match tracksegment pairs of distinct stations using the extrapolationcriteria described above. When track segment pairs meetthese criteria this information is forwarded to the trackfinder unit (TF). It evaluates all extrapolation results inorder to find up to two complete tracks. The track finderconditions mentioned earlier are applied. The output of thetrack finder unit are the addresses of the track segments foreach found track. The track router (TR) - a multiplexerarray - forwards the corresponding track segment data tothe pt-, h - and f -assignment units (PAU, h AU, f AU).6EU43TFTRfI_ 1..4aI_ 1..4fII_ 1..4aII_ 1..4f AUpt1, f1,h1 , q1pt2, f2,h2 , q2RSDT ring sortersector proc. SP SP sector proc.f = 12f = 11f = 10f = 9f = 8f = 7f = 6f = 5f = 4f = 3f = 2ring trigger cell RTC1RTC2RTC3RTC4RTC5pt1, f1,h1 , q1pt2, f2,h2 , q2IV-IIIII-IVII-IIII-IIII-IIff -1 f +1hh -1hh -1hh -1hhEU24 EU24EU24EU23EU23EU13EU12f = 12 x 14EU from neighbouring hf  segmentspt3, f3,h3 , q3pt4, f4,h4 , q4EU43EU43 SP sector proc. SP sector proc. SP sector proc. SP sector proc. SP sector proc. SP sector proc. SP sector proc. SP sector proc. SP sector proc. SP sector proc.EU14 I-IVhEU23Track Finder and  Track Routerh AUPAUpt,f,h-Assignment Units global muon triggerFig. 10: Block Diagram of the Track Finding Processor System.On-line test facilitySince the performance of the trigger will directlyinfluence the data quality and thus the performance of thewhole experiment, special attention has to be given to thecapability of trigger monitoring and hardware errordetection. An on-line test feature for the system wasdesigned. It is able to test the functionality at all times -even during data taking. It is particularly important to beable to monitor the system remotely and automatically fortwo reasons: Firstly it will not be possible to access thesystem during data taking and secondly the complexity ofthe system makes any 'conventional' test featureimpracticable. Each sector processor will contain severalmonitoring units capable of being triggered and read out bya central monitoring unit. A monitoring processor will beresponsible for recalculating of the trigger decisions madeby the trigger processor. In case of errors this is an efficientway to detect damaged parts in the system.REFERENCES[1] CMS, The Compact Muon Solenoid, Technical Proposal,CERN/LHCC 94-38, LHCC/P1, 15 December 1994[2] M. De Giorgi et al., Design and Simulations of the TriggerElectronics for the CMS Muon Barrel Chambers, CMSTN/95-01, CERN, 12 January 1995andthe talk by R. Martinelli at this workshop

Track finding processor in the DTBX based CMS barrel muon trigger

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