Feasibility study of the CMS first-level muon trigger track finder

*Correspondence address. DESY, ZEUS Wisconsin Group,Notkestrasse 85, 22607 Hamburg, Germany. Tel.: #49-40-8998-2489; fax: #49-40-8998-3092.

E-mail address: [email protected] (T. Wildschek).

Nuclear Instruments and Methods in Physics Research A 452 (2000) 505}517

Feasibility study of the CMS "rst-levelmuon trigger track "nder

Alexander Kluge, Torsten Wildschek*

EP Division, CERN, 1211 Gene% ve 23, Switzerland

Received 22 March 1999; received in revised form 15 November 1999; accepted 3 April 2000

Abstract

We describe a feasibility study for a fast, pipelined "rst-level muon trigger based on measurements from drift tubechambers for the CMS experiment at LHC. The algorithm, hardware implementation and simulation results for theperformance are presented. ( 2000 Elsevier Science B.V. All rights reserved.

Keywords: First-level muon trigger; Fast track "nder

1. Introduction

The muon trigger track "nder receives its inputfrom the barrel muon chambers of the CMS de-tector [1]. These chambers are Drift Tubes withBunch Crossing Identi"cation (DTBX) [2] and areequipped with chamber trigger logic, which per-forms local pattern recognition and generates trig-ger primitives.

Fig. 1 shows the trigger chain of the "rst leveltrigger all the way from the chamber trigger logic tothe global trigger. The chamber trigger logic acts asTrigger Primitive Generator (TPG), the muon trig-ger track "nder described in this paper as regionalmuon trigger.

Fig. 2 shows a perspective view of the muonchambers in the barrel region. The Barrel MuonSystem consists of four stations (MS1}MS4) em-bedded into the iron yoke, which returns the mag-netic #ux of the solenoid. The stations aresegmented into planar rectangular chambers: Thereare "ve wheels along the z-axis, each approximately2.5 m long. Along azimuth /, each wheel is dividedinto 12 sectors, so one sector covers approximately303 [1,2]. Each of the 12 sectors comprisesone chamber per station, except for two sectorsthat consist of two chambers in the outermoststation MS4, but for the "rst-level trigger thesetwo chambers are treated as a single logicalchamber. There is thus a total of 240 (logical)chambers in the barrel region. It is intended toapply a similar algorithm in the endcap muonchambers (Fig. 3), but this paper will treat thebarrel only. The magnetic "eld inside the solenoidis 4 T, in the yoke 2 T.

0168-9002/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved.PII: S 0 1 6 8 - 9 0 0 2 ( 0 0 ) 0 0 4 4 7 - 2

Fig. 1. The trigger chain: from chamber data to global trigger.

Fig. 2. Perspective view of the barrel muon detector.

Fig. 3. Longitudinal view of one octant of CMS, with straightmuon tracks showing the pseudorapidity-coverage of the muonstations. The chamber geometry in this (z,R)-view is non-projec-tive, and tracks cross wheel boundaries.

2. Speci5cation

2.1. Input quantities

The chamber trigger logic employs a mean-timermethod [3}5] to determine the bunch crossingfrom which the measured particles originate. Foreach bunch crossing (at an LHC clock rate of 40MHz) it outputs up to two trigger primitives, calledtrack segments, per chamber. This track segment is(Fig. 4):

f Position. Azimuthal angle of the hit relative tothe axis of the /-sector of the chamber.

f Bend angle. The angle between the track and theradius vector at the crossing point in the bendingplane projection.

f Quality. Indicates how many of the drift celllayers and superlayers in the chamber contrib-uted to the track segment.

Fig. 4 shows the de"nition of the quantities posi-tion and bend angle. Table 1 gives an overview ofthe input quantities.

2.2. Task of the trigger processor

The muon trigger track "nder accepts input fromthe chamber trigger logic, joins track segments totracks and assigns track parameters to the foundtracks. Then it performs sorting and selection topass on only the tracks of highest transverse mo-mentum p

5to the global muon trigger, which com-

bines the information from barrel and endcapmuon chambers with calorimeter information.

The track "nding criteria are as follows:

f A track should be recognized if it gives a tracksegment in at least two of the four muon stations.This criterion is based on a study of track "ndinge$ciency [6].

f A track should point back to the interactionregion.

f One track segment should not belong to morethan one track.

The next stage after "nding tracks, is measuringthe properties of those tracks. These properties willbe described in the following section on outputquantities.

506 A. Kluge, T. Wildschek / Nuclear Instruments and Methods in Physics Research A 452 (2000) 505}517

Fig. 4. De"nition of the input quantities position and bendangle. This "gure also shows the bending of the track due to themagnetic "eld of the CMS solenoid coil.

Table 1Input quantities to the muon trigger track "nder

Quantity No. of bits Resolution

Position 12 0.2 mrad(1.25}2.5) mm

Bend angle 49 10 mradQuality 3 *

Table 2Output quantities

Quantity No. of bits

Transverse momentum p5

5Charge sign q 1Pseudo-rapidity g 2Azimuth / 8Quality 4

Selection steps are required to restrict theamount of data to transfer to the next stage; theyserve to get rid of ghosts and background. Themain backgrounds are due to d-rays or electro-magnetic showers initiated by the muon and topunch-through from the calorimeter. The selectioncriteria are based on track quality and transverse

momentum. After selection, up to four tracks per z-wheel can be output to the global muon trigger.

2.3. Output quantities

After processing the data that it received fromthe chamber trigger logic, the muon trigger track"nder transfers its output for up to four tracks perz-wheel to the global muon trigger [7].

The track parameters measured by the muontrigger track "nder are the transverse momentump5, track direction (pseudorapidity g and azimuth

/) and quality. The quality tag indicates how manyand which stations contributed to the track andwhat the qualities of the contributing track seg-ments were. Due to constraints on the amount ofdata transferred, the quality is compressed to 4 bitsfrom 12 bits (4 stations ] 3 bits/station). It tells theglobal muon trigger how con"dent it can be thatthe found track is really a muon track and nota ghost created by the trigger primitive generationand/or track "nding. Moreover, it indicates theresolution that can be expected from the p

5-

measurement: A track that has track segments instations 1 and 2 will have a much "ner momentumresolution than a track with track segments instations 3 and 4 only.

Table 2 gives an overview of the output quantit-ies and the number of bits required/desired by theglobal muon trigger.

The muon trigger track "nder can transfer up tofour tracks per z-wheel to the global muon trigger.For each track the wheel identi"er is known, so thenumber of 2 bits for g in the above table refers toa relative pseudo-rapidity with respect to the wheelto which the track belongs.

A. Kluge, T. Wildschek / Nuclear Instruments and Methods in Physics Research A 452 (2000) 505}517 507

2.4. Requirements and design issues

The muon trigger track "nder must ful"ll thefollowing basic requirements, derived from the gen-eral requirements to the CMS muon trigger [1]:

f Performance. The trigger processor should befully e$cient down to the lowest p

5-muons that

reach the muon chambers (4 GeV/c at g"0,decreasing down to 2 GeV/c in the endcaps). Theperformance at low momenta is relevant fordimuon triggers at an initial low luminosity op-eration of LHC.

f Latency. The maximum latency of the track "n-der is 14 bunch crossings (0.35 ls) [8].

f Deadtime. The "rst level trigger is required byCMS to be deadtime-free.

f Flexibility. An important design issue is #exibil-ity: The trigger must be able to adapt to unex-pected e!ects, such as higher than expected ratesand changes in experimental conditions. Itshould have the capability to deal with noisy anddead channels.

Particular challenges are:

f The non-projective geometry in the (z,R)-projec-tion (Fig. 3) resulting in muons changing wheelsduring their journey through the muon system.

f The high magnetic "eld leading to a strong be-nding of the tracks. Tracks, particularly at lowmomenta, are likely to change /-sectors in themuon system due to magnetic bending and mul-tiple scattering.

This means that individual sector processorshave to communicate with each other and ex-change data, posing a serious interconnectionproblem.

3. Algorithm

The processing of the track "nder can be logi-cally divided into three stages. The "rst stage con-sists of track "nding, the second stage of measuringthe properties of tracks found in the "rst stage, andthe third stage sorts and selects to pass on only thehighest-p

5tracks to the global muon trigger.

3.1. Track xnding

The input to the trigger consists of track seg-ments in the individual chambers of the muonsystem. The "rst task of the trigger is to assemblethese local track segments to full tracks.

3.1.1. Pairwise matching methodTrack segments are joined to tracks by pairwise

matching. If two track segments from di!erent sta-tions are found to be compatible with originatingfrom a single track, they form a track segment pair.If one of these two track segments is in turn com-patible with a third track segment from a stationdi!erent than the two, a track segment triple isformed. A compatible fourth track segment yieldsa track segment quadruple. In short, a string ofmatching track segments forms a track.

A track segment pair already forms a valid track,there is thus a total of (4

4)#(4

3)#(4

2)"11 track

classes: tracks with track segments in all 4 muonstations (track class 1234), in 3 muon stations (trackclass 123 with the 3 innermost stations etc.), or inonly 2 muon stations (track class 12 with the 2 in-nermost stations, etc.).

This algorithm has a high degree of intrinsicparallelism: All the comparisons required to estab-lish compatibility of track segments can be carriedout in parallel.

The station pairings required depend on thetrack selection criteria: Two track segments fromtwo di!erent stations already form a valid track, soin total (4

2) station pairings have to be examined:

1-2, 1-3, 1-4, 2-3, 2-4, 3-4.

3.1.2. Pairwise matching by extrapolationThe pairwise matching of track segments can be

carried out by extrapolation. The principle of theextrapolation method is shown in Fig. 5. In thefollowing discussion, the track segment which isextrapolated will be called source track segment.The track segment to whose chamber the sourcetrack segment is extrapolated will be called targettrack segment.

The procedure is to extrapolate the source tracksegment to the station of the target track segment,using the former's measured bend angle. The bendangle is a function of transverse momentum, so the


Fig. 5. Principle of the extrapolation method: The track seg-ment's measured bend angle in muon station 1 (MS1) is used toextrapolate to the target station (MS2). The di!erence betweenextrapolated (/

%95) and measured (/

2) position in MS2 must be

below the threshold D5)3

for a match.

extrapolation takes the track's curvature into ac-count. In principle, one could use a simpler extra-polation, such as a zeroth-order extrapolation,where the extrapolated azimuthal position is sim-ply the same as the source track segment's mea-sured position. That approach, however, whilesimplifying the algorithm, would have a lower ac-ceptance for strongly bent low p

5tracks and hence

violate one of the basic requirements put down forthe trigger processor in Section 2.4.

The second step is to check that the di!erencebetween extrapolated position and measured posi-tion of the target track segment is below a speci"cthreshold. That threshold should depend on trans-verse momentum p

5, because the stochastic e!ects

that smear the particle's trajectory on its way fromone station to the next depend on transverse mo-mentum. The e!ects are multiple scattering andenergy loss #uctuations. Again, the bend angle isrelated to p

5, so that p

5-dependence can be taken

into account by making the threshold depend onthe bend angle of the source track segment. Thechoice of the thresholds is a trade-o! between track"nding e$ciency and purity: Choosing a largethreshold yields a high e$ciency, but makes wrongassociations of track segments more likely, because

the probability that there is an additional tracksegment (from another muon or background) in theextrapolation window increases. The initial settingswill be based on simulation results. After startup ofthe detector, the values can be adapted to the realbackground conditions.

The matching criterion can be written as

/ii,%91104

"/i104

#D%95

(/i"%/$

) (1)

DD/ii,%91104

!/ii104

DD4D5)3

(/i"%/$

) (2)

where /i104

is the measured azimuthal position ofthe source track segment, /i

"%/$the measured bend

angle of the source track segment, D%95

(/i"%/$

) theexpected change of azimuthal position between thesource and target station as a function of the bendangle, /ii,%91

104the expected azimuthal position in the

target station, /ii104

the measured azimuthal posi-tion of the target track segment, /ii,%91

104!/ii

104the

extrapolation deviation that is the di!erence be-tween the expected and measured position andD5)3

(/i"%/$

) the extrapolation threshold that is themaximum allowed extrapolation deviation fora match.

Fig. 6 shows station pairings for which unam-biguous extrapolation is possible. The abscissa inthese plots displays the bend angle of the sourcetrack segment. The ordinate shows the di!erencebetween the azimuthal positions of the target andthe source track segment. Due to the zero crossingof the bend angle near station 3, extrapolation fromstation 3 to any other station is ambiguous, asshown in Fig. 7. This is not a problem because onecan extrapolate from any other station to station 3.

Since tracks can change /-sector and z-wheel asthey traverse the muon system, in general, eachextrapolated track segment has to be compared totrack segments in six chambers of the target station:the same and the two adjacent /-sectors, and thesame and the next outer z-wheel. Since there are upto two track segments per chamber, each tracksegment has to be compared to up to 12 tracksegments for a given station pairing.

3.2. Assignment of transverse momentum p5

Once a track candidate has been identi"ed bythe track "nding stage, the p

5-assignment unit


Fig. 6. Unambiguous extrapolations. Knowing the track's bend angle and position in the source station, one can unambiguously inferthe track's position in the target station for the station pairings shown here.

determines the track's transverse momentum p5.

This value is used by later trigger stages for ap-plying a p

5-cut.

Measurement of transverse momentum is based onthe momentum-dependence of the track's de#ectionin the magnetic "eld of the detector. In the barrelregion bending takes place mainly in the projectionperpendicular to the beam axis (bending plane).

At low momenta, resolution is limited by mul-tiple scattering and energy loss #uctuations in theabsorber material. At high momenta, the resolution

is limited by the position resolution of the triggerprimitive generation.

Using data from the muon system alone, thereare two basic ways of measuring the transversemomentum. First, one can use the track's bendangle (/

"%/$), that is the angle between the tangent

to the track and the radius vector in the bendingplane, as de"ned in Fig. 4. This method implicitlyuses a vertex constraint.

Secondly, the track's sagitta can be used asa measure of p

5.


Fig. 7. Ambiguous extrapolation. The bend angle has a zero-crossing near station 3, so from the bend angle in station 3 (MS3), thestrongly curved low-p

5track and the straight track cannot be distinguished. Therefore, no unambiguous extrapolation from station 3 to

any other station is possible.

Each station measures bend angle and azimuthalposition of the track. The bend angle can thus betaken directly as the measured bend angle froma single station (Fig. 8), or it can be determinedfrom the di!erence of measured positions in twostations. The "gure also shows that there is anambiguity in station 2, where two di!erent p

5-

values can correspond to the same bend angle, thisbend angle is therefore used only for tracks whichreach station 4 and hence have p

5above 5 GeV/c.

The drawback of the sagitta method is its highercomplexity of the hardware implementation: Todetermine a sagitta either two measured bendangles or three measured positions can be used. For

that reason, the p5-measurement is based on the

bend angle-method. Which bend angle is used, andwhether the measurement is based on a single sta-tion or on the di!erence of positions in two sta-tions, depends on which stations contribute tracksegments to the track under consideration andwhat their track segment qualities are (Section 4.2).

4. Hardware implementation

Fig. 9 shows the top-level block diagram of thehardware. Trigger primitive data from the chambertrigger logic enter the system from the left. The


Fig. 8. Bend angle /"%/$

as a function of transverse momentum p5in all four barrel muon stations.

track "nder links the track segments to tracks andoutputs the addresses of track segments that werecombined to tracks. Based on these addresses thetrack segment data are extracted from the pipeline,where they have been stored during the track "n-der's processing, by the track router. The trackrouter passes the track segment data for each foundtrack on to the assignment units, which computethe track parameters from the track segment data.

The hardware shown covers one detector seg-ment, corresponding to a sector of about 303 inazimuth / and a z-wheel of 2.5 m length. The seg-

mentation of the trigger hardware closely matchesthe segmentation of the detector. Each of thesedetector segment processors can output up to twotracks. Tracks from the twelve /-sectors of onez-wheel are sent to the ring sorter [14], whichselects the four highest-momentum tracks. Eachring sorter passes the data of all found tracks on tothe detector sorter, which in turn selects the fourhighest-momentum tracks in the muon system andpasses them on to the global muon trigger [7]. Inthe following sections, the detector segment proces-sor is described in detail.


Fig. 9. Block diagram of the muon trigger track "nder for onewheel in the barrel. TS"Track Segment; AU"Assign-ment Unit.

Fig. 10. The track "nding chain: EU"ExtrapolationUnit, ERS"Extrapolation Result Selector, TSL"TrackSegment Linker, STS"Single-Track Selector, TSel"TrackSelector.

Fig. 11. The Extrapolation Unit (EU).

4.1. Track xnding stage

Fig. 10 shows the track "nding chain.

4.1.1. Extrapolation Unit (EU) and ExtrapolationResult Selector (ERS)

The Extrapolation Unit (EU) (Fig. 11) performsthe matching by extrapolation and assigns an ex-trapolation quality to each matched track-segmentpair. There is one EU per source track segment andstation pairing, giving a total of 2]6"12 EUsin each detector segment. Each EU comparesits source track segment to 12 target track seg-ments. Of the 12 possible matches, at most two arepassed on by the Extrapolation Result Selector(ERS).

Extrapolation itself is carried out by RAM-basedlook-up tables. Since they are RAM-based, theirvalues can be updated easily if experimental condi-tions such as magnetic "eld or amount of materialchange. The same holds for the implementation ofextrapolation thresholds. The threshold values canbe stored in the same look-up tables. The ERS usesa priority encoder to select at most 2 out of up to 12possible matches, passing on the address of thematching track segment relative to the source tracksegment, encoded in a 4-bit word.

4.1.2. Track Segment Linker (TSL)The Track Segment Linker (TSL) joins track

segment pairs formed by the extrapolation stage totrack segment triples and quadruples. There is oneTSL per possible starting track segment and trackclass. The principle will be illustrated for a trackconsisting of track segments in stations MS1, MS2and MS3 (track class 123).

Since there are up to two track segments in MS2that can match the starting track segment in MS1,each of which in turn can match up to two tracksegments in station 3, up to four tracks can beoutput by this TSL. In general, each TSL canoutput up to 2n~1 tracks, where n is the number ofstations in the track class of the TSL. These pos-sible tracks are branching o! from the startingtrack segment, like the ones shown in Fig. 13; allbut one of these branches will be removed by theSingle Track Selector (STS), described in subsec-tion 4.1.3.

The inputs to the TSL for track class 123 havethe following sources (represented by rounded rec-tangles in Fig. 12):

f 1 ERS for extrapolation from MS1 to MS2 pro-vides the addresses of up to two track segmentsin MS2 that match the starting track segment inMS1 (top right of Fig. 12).

f 12 ERSs for extrapolation from MS2 to MS3;each of the 12 belongs to one of the track seg-ments in MS2 that may match the starting tracksegment in MS1, and each of them provides theaddresses of up to two track segments in MS3that match that track segment in MS2. This gives


Fig. 12. The Track Segment Linker (TSL). In this "gure, &TS' is always to be understood as the relative address of the track segment.

a total of up to 24 addresses of track segments inMS3, which might be linked to the starting tracksegment in MS1 via a matching track segment inMS2 (left of Fig. 12).

Out of the 24 addresses of track segments inMS3, the TSL should pass on only those thatmatch a track segment in MS2 which in turnmatches the starting track segment in MS1.

Fig. 12 shows how the track segment addressesoutput by the ERS are used as multiplexer selectinputs to pass on only the addresses of those tracksegments that form a string of three matching tracksegments. Each of the rounded boxes represents theaddress of a matched track segment, where theaddress is relative to the source track segment ofthe extrapolation. Since each track segment is com-pared to 12 track segments, this address consists of4 bits. A special address code denotes the lack ofa match. Each of the 4 Multiplexers (MUX) passeson the address of the track segment in MS3, if any,that matches the track segment in MS2 whose

address is sent to the select input (sel) of theMultiplexer.

4.1.3. Single Track Selector (STS) and Track Selector(TSel)

There is one Single Track Selector (STS) perTSL. Its task is to reduce the number of outputtracks from up to 2n~1 (Section 4.1.2, Fig. 13) to atmost 1. The selection criteria are the track segmentpair qualities, which are routed through the TSLalong with the track segment addresses.

Starting from the outermost station, it success-ively removes those branches with lower quality.The hardware implementation employs multi-plexers: The qualities of the track segments in thetwo competing branches are compared, the com-parison result controls the select input of the multi-plexer to pass the address of the winning tracksegment.

The Track Selector (TSel) [9] selects up to twotracks out of all those found in a detector segment.Its selection is based on the track class.


Fig. 13. Branching tracks as they may be output by the TSL.

4.2. Assignment of p5

Hardware implementation of the p5-assignment

algorithm can be divided into two tasks. The pri-mary task is the p

5-assignment itself. The second

task is to decide which p5-assignment method is to

be used for a given track. For a track with tracksegments in only stations 1 and 2, for example,there are two possibilities: use the bend angle fromstation 1 only, or the di!erence of the azimuthalpositions. In this example, using the di!erence ofazimuthal positions yields the best resolution and isthe method of choice.

The hardware implementation of the p5-assign-

ment method is straightforward: The mapping frombend angle to p

5is accomplished by a look-up table.

If the bend angle is computed from the di!erence oftwo azimuthal positions, the positions are "rstrouted to a subtractor, and the di!erence is thensent to the look-up table.

The optimal p5-assignment method is chosen by

converting the quadruple of track segment qualitiesof the track to a code that determines whichmethod is to be used. That conversion can be im-plemented with a look-up table. The reason forusing the full quality information and not only the1-bit information (station present/not present in thetrack) is that it provides the possibility to take intoaccount the resolution with which the track seg-ment quantities have been measured. The tracksegment's bend angle is measured with much "nerresolution, if drift cells in both superlayers of thechamber contribute to the track segment. The codeoutput by that look-up table is used as select inputto a multiplexer, which routes the result from the

selected p5-assignment method to the output. In

this implementation all p5-assignment methods run

in parallel and o!er their outputs, but only one ofthem is chosen.

5. Simulated performance and assessment

Section 2.4 has de"ned the requirements on thetrigger processor. The current section will verifywhether the presented design meets those require-ments.

f Performance. See below.f Deadtime. The algorithm is implemented in

a pipelined design, which is inherently dead-time-free.

f Flexibility. All parameters of the algorithm arestored in RAM-based look-up tables, renderingmodi"cations in situ trouble-free. The initial setof parameters will be based on simulation resultsand can be updated using real data once theexperiment starts taking data.

Several handles are built into the algorithm tocope with higher than expected backgrounds.Input track segments can be rejected if theirquality is below a set threshold (by default, alltrack segments, even those based on only threelayers out of the 2]4 layers of a chamber, areaccepted). The size of the extrapolation windowfor track segment matching can be scaled bya p

5-dependent scaling factor. That allows to

keep the full acceptance for the more interestinghigh-p

5tracks while reducing the acceptance for

low-p5tracks. The number of track classes accep-

ted can be decreased. By default, even a trackproducing track segments in stations 3 and4 only is accepted.

f Hardware feasibility and latency. A prototype ofthe trigger has been built using FPGAs [10,11],demonstrating that the algorithm can be imple-mented in hardware. Today's FPGAs, however,cannot cope with the high I/O rate, and theprototype operates at a 20 MHz clock rate ratherthan the required 40 MHz. Therefore, a studyemploying ASICs has been conducted to provethe feasibility of an implementation of theprocessor with today's technology, ful"lling all


Fig. 14. p5-resolution in the barrel zone.

Fig. 15. E$ciency curves in the central z-wheel of the barrelzone for p

5-thresholds of 3.5, 20, 40 and 50 GeV/c.

requirements [10,11]. For this implementationstudy, the already outdated gate array techno-logy Motorola H4C 0.7 lm [12] was used. Thestudy proved that the processor can be imple-mented even with this technology, consuming 14bunch crossings latency only.

Fig. 14 shows the p5-resolution as a function of

the track's p5. The resolution varies with the

method chosen on the basis of the track segmentqualities as described in Section 4.2. A track thathas track segments in stations 1 and 2 can beassigned a p

5with very "ne resolution. A track with

track segments in stations 3 and 4 only will have itsp5measured with a much poorer resolution.Fig. 15 shows the e$ciency curves for the barrel

region for p5-thresholds of 3.5, 20, 40 and 50 GeV/c

respectively. These curves have been obtained bygenerating on average 20 minimum-bias events perbunch crossing on top of a muon track and simula-ting the response of detector and trigger logic. Inthe detector simulation all particle interactionswith the material of the detector are included, thustaking the major sources of background into ac-count [13].

One source of ghost tracks in the output is due toghosts created by the chamber trigger logic: Theprobability for a single muon passing througha chamber to give a second track segment in thesame chamber is about 45% [13]. The contamina-tion of the output tracks by ghost tracks due to thise!ect is about 5%. E!orts to reduce the ghost rateon the trigger primitive level will improve this num-ber. A residual source of ghosts, that is entirely dueto the track "nding algorithm and not to back-grounds or trigger primitive ghosts, is the follow-ing: If a track gives track segments in all fourstations, and if pairwise matching between e.g. sta-tions 1 and 2 on the one hand and stations 3 and4 on the other it is successful, but there is no matchbetween track segments in stations 2 and 3, thetrack "nding algorithm will output two tracks, oneconsisting of stations 1 and 2 and the other consist-ing of stations 3 and 4. The rate of this type of ghostis (1% of the total number of tracks [13]. Thetotal ghost rate is about 5.5% of the total trackrate, but this number is expected to be reduced to(1% by an improvement of the trigger primitivegeneration.


6. Summary and conclusions

We have designed a regional muon trigger basedon drift tubes for the barrel region of the CMSmuon detector. This device receives input from 240muon chambers, performs track "nding andmeasures the transverse momentum and directionof tracks with a processing time of 350 ns. Theperformance of the algorithm has been determinedusing simulation by software.

References

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[7] N. Neumeister et al., CMS Internal Note CMS IN-1997/023.

[8] A. Kluge, W. Smith, CMS Technical Note CMS TN/97-091.

[9] A. Kluge, T. Wildschek, in: Proceedings of the SecondWorkshop on Electronics for LHC Experiments,CERN/LHCC/96-36, 1996, p. 319.

[10] A. Kluge, T. Wildschek, CMS Note 1997/093.[11] A. Kluge, Ph.D. Thesis, Technische UniversitaK t Wien, 1997

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Feasibility study of the CMS first-level muon trigger track finder

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