The Compact Muon Solenoid Experiment. CMS Note. Mailing address: CMS CERN, CH-1211 GENEVA 23, Switzerland

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1 Available on CMS information server CMS NOTE 998/4 The Compact Muon Solenoid Experiment CMS Note Mailing address: CMS CERN, CH-2 GENEVA 23, Switzerland 29 July 998 Muon DTBX Chamber Trigger Simulation on H2 Test Beam Data Claudio Grandi University of Bologna & INFN, Bologna, Italy Abstract Muon data collected at the H2 test beam during summer 997 with the MB96 prototype of a DTBX chamber are analyzed using the level trigger simulation code. The trigger chain includes BTI, TRACO and Trigger Server, which generate the muon trigger primitives in the CMS barrel system. The performance of the algorithm is evaluated and it is found in good agreement with published numbers based on simulated tracks.

2 Introduction About 2 million events were collected at the H2 test beam from september to september 7, 997, using the MB96 prototype of the barrel muon chambers of the CMS detector. 2 GeV muons have been used. Test beam setup and general chamber performances are described in []. In this work a sub-sample of the data collected (about 7 events) has been used as input to the trigger simulation code, as can be extracted from CMSIM version 3. The full BTI + TRACO + Trigger Server chain is implemented. Trigger algorithms and hardware are described in [2], [3] and in the Muon TDR [4]. A simple reconstruction algorithm has been developed to find muon tracks in a way independent of the trigger algorithm. 2 Calibration The T for all the tubes are determined run by run by looking to the starting position of the time boxes. A tipical time distribution is shown in figure. The procedure is described in detail in []. The drift velocity is determined from the maximum drift time, i.e. the time corresponding to a 2 cm path from the I-beams to the wire. The maximum drift time T MAX is determined as the peak of the distribution of T sum=2 = 2 (T + T 2 + T 3 + T 4 ) for events with 4 aligned hits in the 4 layers of a super-layer. T i is the time of the hit in the i th layer. The T sum=2 distribution is shown in figure 2. The peak is at T sum=2 =342ns, but since in the trigger system the maximum drift time is parametrized in 2 ns steps (see the next sections), a nominal maximum drift time of 3 ns is used in this entire analysis: T MAX =3ns In all the analysis the chambers are considered to be in their nominal position, i.e. no correction is applied for layer or wire displacements. entries/ns 9 8 entries/2ns Time (ns) T(sum/2) Figure : Typical time distribution before T subtraction Figure 2: T sum=2 distribution (H2 run 369) 3 Track reconstruction A simple reconstruction algorithm has been developed to find muon tracks in the R- plane, in a way independent of the trigger algorithm. It is based on a least-squares fit to the 8 layers of super-layers and 3 (quadruplets and 2 in the CMSIM notation). Only the first hit in the range [; T MAX +]ns is considered. At least 4 fitted hits are required to form a track, or at least 3 hits out of 4 in a super-layer, in case no hits are found in the other one. 2

3 Figure 3: Fitted tracks in the R- plane: A) two tracks are fitted, one of which has only 3 hits in one superlayer and none in the other; B) a track is found with only 2 hits in each superlayer; C) a multi-track event. 3

4 SL V wire V strip V cathode Table : Voltage settings for the data used in this analysis A recursive method is used. At each iteration the combination of hits with the largest number of fitted points is kept, if the badness ) of the fit is less than.. If the number of fitted points is the same for many combinations, the one with lower badness is kept. When a track is built in this way, all the hits which form the track, and the corresponding symmetric points with respect to the wire, are marked as used. A new track is then looked for. If no tracks are found during an iteration, the maximum badness limit is relaxed by a factor of and the procedure is repeated on the unused hits. The procedure is terminated when either not enough unused hits are left, or when the maximum badness limit is more than.. In figure 3 a few examples of fitted tracks are shown. Black dots are fitted hits, white dots are unused hits with left-right ambiguity not resolved. The lines are the fitted tracks. In abscissa the x coordinate is shown. The position is defined to be in the leftmost corner of the first tube in layer. 4 Efficiency of tubes Data used for this analysis have been collected with voltage settings shown in table and in the center position. Not all the tubes were fully operational in the region of the chamber hit by the beam. Efficiency of the tubes of super-layers and 3 which are used in the trigger has been determined using a reconstructed track as evidence of the passage of a muon. In figures 4 and the efficiencies of the tubes as function of the x coordinate are shown. The boundaries of the tubes are also shown in the plots. In superlayer, TDC 3 was probably not working properly, and thus tubes up to 7 (x = 68 cm in odd layers and x =66cm in even layers) didn t have data. Other tubes show anomalous efficiencies. Efficiency issues are discussed in more detail in []. BTI simulation BTI s are described in [4]. In this work the BTI are numbered progressively from the leftmost cell in the first layer (cell number 4 in the BTI layout shown in figure 6). The configuration of BTI s used in this work is the same as the default in CMSIM. The drift velocity has been parametrized as maximum drift time corresponding to half the pitch of the cell (2 cm) in 2 ns steps. The value used is T MAX =4corresponding to a maximum drift time of 3 ns (7 m/ns). A track reconstructed using the algorithm described in section 3, defines the passage of a muon in the chamber. All efficiencies are calculated with respect to reconstructed tracks. A trigger at STEP = T MAX =4correctly identifies the bunch crossing (BX). Distribution of the STEP of BTI triggers is shown in figure 7 (open histogram). The hatched histogram is the distribution for HTRIGs i.e. triggers with hits in each of the 4 layers of the superlayer (the other accepted triggers are LTRIGs i.e. triggers with only 3 out of 4 layers hit). HTRIGs correctly identify the BX in most cases, while there s a big number of LTRIGs at wrong BX. This is a known feature of the mean-timer algorithm and requires low trigger suppression (LTS) in order to reduce the background. The track angle is given by the K parameter, which is related to the angle (see figure 6) by the relation: K =2H CELL tan( ) =2h T MAX 2cm tan( ) =8:2 tan( ) () where h =.3 cm is the height of a cell. Distribution of the K parameter for trigger which correctly identify the BX is shown in figure 8. Again, the hatched histogram is the distribution for HTRIGs. ) The badness of the fitisdefined as the residual sum of squares divided by (L - 2) where L is the number of fitted points, i.e. the content of the variable VAR given in output by the CERNLIB routine LFITW which is used for fitting. 4

5 .7. Super layer.7. Super layer x (cm), layer x (cm), layer Figure 4: Efficiency for the tubes in the four layers of super-layer as function of x. Data are from run 369 and 362. Figure : Efficiency for the tubes in the four layers of super-layer 3 as function of x. Data are from run 369 and 362. µ h A B 2 6 x C 4 8 D ψ Figure 6: Layout of a BTI. Layer s identification is inverted with respect to test-beam conventions: layer A is number 4 and layer D is number.

6 x x BTI step BTI K, correct step triggers Figure 7: Distribution of the BTI STEP for all triggers (open) and for HTRIGs (hatched). Figure 8: Distribution of the BTI K parameter for triggers at the correct BX, for all triggers (open) and for HTRIGs (hatched). Results for BTI s of the 3 superlayers are shown in the first three culumns of table 2, and compared with numbers reported by [2] in table and by [4] in table for 2 GeV muons (last two columns), which are based on simulated tracks. The environmental conditions of test beam are slightly different from those which were used in the simulation (whole CMS). In particular in the simulation some iron is placed in front of the muon chambers, thus generating electromagnetic showers which lower the BTI. These effect are anyway small. The most important difference between simulation and test beam environments is that in the test beam there are some inefficient cells. In order to get rid of tube inefficiencies, the BTI performances are also tested requiring at least 3, or 4, hits in the fitted track in the considered BTI (only for superlayers and 3 where a fitted track was available). Results are shown in columns 4 to 7 of table 2. Meaning of the rows is given below. Hr At least one HTRIG at correct step Hr+Hw HTRIG at correct step and at least one HTRIG at wrong step Hr+Lw HTRIG at correct step and at least one LTRIG at wrong step Lr At least one LTRIG at correct step Lr+Lw LTRIG at correct step and at least one LTRIG at wrong step Hw Only HTRIG at wrong step Lw Only LTRIG at wrong step Eff BX Bunch crossing identification HKr HTRIG at correct step with muon direction (within mrad) LKr LTRIG at correct step with muon direction (within mrad) Eff K Bunch crossing and muon angle identification Results for SL3 from column are comparable with those quoted in [2] and [4], the smaller fraction of HTRIGs is probably due to the partial in of tube 8 in layer 2. Low for SL is due to the already seen in of some cells. Triggers at wrong BX, when no other triggers at correct BX were seen, are rare. Demanding at least 3 fitted hits in the superlayer, also SL gives similar results. SL3 gives better results but still comparable with published numbers. Demanding 4 fitted hits in the superlayer gives much better results than in the simulations because events with inefficiencies (e.g. track too close to the wire or on the I-beams, distortions of the electric field, etc...) are eliminated. When 4 aligned hits are available to the BTI, the probability of not finding a trigger at the correct bunch crossing is below %. 6

7 All tracks 3 fitted hits 4 fitted hits Reference SL SL2 SL3 SL SL3 SL SL3 [2] [4] Hr 37.7% 63.% 68.7% 78.% 7.4% 88.6% 8.9% 76.4% 76.3% Hr+Hw.6%.4%.%.2%.%.4%.3%.9% Hr+Lw 37.3% 62.8% 68.% 77.% 7.8% 87.8% 8.% 7.% Lr 6.3% 6.% 2.7% 3.% 26.7%.8% 3.% 2.7% 8.4% Lr+Lw.% 3.9% 22.2%.4% 23.%.8% 3.3% 2.6% Hw.%.3%.2%.2%.2%.2%.3%.4% Lw 3.%.8%.4% 7.2%.%.3%.4%.9% Eff BX 43.9% 79.% 94.4% 9.% 98.% 99.4% 99.3% 98.% 94.7% HKr 37.7% 62.8% 68.7% 78.% 7.3% 88.% 8.7% 7.% LKr.2% 3.% 22.%.7% 23.% 8.% 9.8% 3.8% Eff K 42.8% 76.3% 9.7% 88.8% 94.3% 97.% 9.6% 9.3% Table 2: BTI performance for the 3 superlayers, for events with a track reconstructed. Column 4 and report results for superlayers and 3 requiring at least 3 hits in the fitted track in the superlayer, columns 6 and 7 requiring 4 hits, column 8 shows results from simulation reported in table of [2] for 2 GeV muons, and the last column shows results from simulation reported in table of [4], again for 2 GeV muons. Meaning of the content of the rows is given in the text. µ Out Out Out 2 Out 3 Out 4 Out Out 6 Out 7 Out 8 Out 9 Out Out Outer Layer D = 23.7 cm X cal K cal In In In 2 In3 Inner Layer Figure 9: Layout of a TRACO. 7

8 all 3 hits 4 hits from [4] HH 3.2% 63.6% 7.3% 4.8% HL+LH 9.2% 9.4% 7.3% 23.9% LL.9% 2.%.% 3.4% H+H 38.% 3.9% 7.3% 47.% L+L 9.8% 2.7%.9%.9% Eff TC 86.% 98.2% 99.4% 97.% Eff K TC 86.% 98.% 99.3% Table 3: BTI+TRACO performance for events with a track reconstructed. Column 2 reports results requiring at least 3 hits in the fitted track in superlayers and 3, column 3 requiring 4 hits, column 4 shows results from simulation reported in [4]. The sum of the fractions in the different channels sums up to more than because each TRACO can output up to 2 tracks. all 3 hits 4 hits from [2] and [4] all, n.g.s HH 3.2% 63.6% 7.3% 38.3% 3.2% HL+LH 9.2% 9.3% 7.2% 3.% 9.2% LL.9% 2.%.%.6%.9% H+H 37.% 2.3%.% 3.2% 6.9% L+L 9.%.%.% 6.% 23.6% Eff TS 86.% 98.3% 99.4% 97.2% 86.% Eff K TS 86.2% 98.2% 99.4% 93.7% 86.2% Fake 2 nd tracks.2%.3%.2%.% 43.% Table 4: BTI+TRACO+TS performance for events with a reconstructed track. Column 2 reports results requiring at least 3 hits in the fitted track in superlayers and 3, column 3 requiring 4 hits, column 4 shows results from simulation reported in [2] and [4]. The sum of the fractions in the different channels may sum up to more than because TS can output up to 2 tracks (the fraction of events with 2 tracks is shown in the last row). Column reports results without the ghost suppression algorithm used in the TS (see text). 6 TRACO simulation TRACO s are described in [4]. The TRACO layout is shown in figure 9. The configuration of TRACO used in this work is the same as the default in CMSIM. Comparison of TRACO s performance with published values (table 3) is more difficult because of the in of some of the tubes of the first layer. Again the results shown in table 3 are for all tracks, for events with at least 3 hits in each of the two superlayers and 3 and for events with at least 4 hits in each superlayer. Results from simulation, reported in table of [4] are in the last column. Efficiencies shown in column are obviously affected by superlayer inefficiencies. Requiring at least 3 hits per superlayer gives results comparable and even better that those quoted in [4]. 7 Trigger Server (TS) simulation Trigger Server (TS) is described in [3] and [4]. The configuration of TS used in this work is the same as the default in CMSIM. Results for the BTI+TRACO+TS chain are shown in table 4 together with the published values from simulation (tables 2 and of [2] and table of [4]). Results are much related to TRACO output. The lower number of events with 2 tracks reconstructed (last row of table 4) with respect to [4] is due to the mechanism of ghost suppression 2) in the TS: since a half of the cells in the inner superlayer (SL) is inefficient, a big number of uncorrelated outer tracks is present, which are suppressed. Without using ghost suppression, the 2) The TS ghost suppression mechanism consists in the rejection of uncorrelated outer tracks in the same and in the adjacent TRACO of a TRACO with the best track. 8

9 o o 2 o 3 o 4 o BTI results, 3 hits BTI Hr 73.7% 6.% 69.9% 9.6% 34.4% BTI Hr+Hw.%.2% 2.% 9.3% 7.6% BTI Hr+Lw 73.%.7% 69.9% 8.7% 33.4% BTI Lr 22.% 39.% 24.9% 36.% 9.8% BTI Lr+Lw 9.2% 33.4% 23.% 32.3% 7.% BTI Hw.2%.2%.%.4%.9% BTI Lw 3.4% 3.9% 4.4% 3.4% 3.7% BTI Eff BX 9.8% 9.2% 94.9% 96.% 94.2% (from []) 9.7% 93.% 8.9% BTI HKr 73.6%.9% 69.7% 8.3% 33.4% BTI LKr 8.9% 34.2% 2.% 33.%.% BTI Eff K 92.4% 9.% 9.2% 9.8% 83.3% TS results, 3 hits TS HH 63.6% 22.4%.9% 3.% 8.% TS HL+LH 9.3% 47.8% 28.9% 38.7% 2.% TS LL.9% 2.2%.4% 2.% 2.8% TS H+H 2.3% 2.% 9.%.4% 9.6% TS L+L.% 4.3% 4.% 4.% 23.% TS Eff BX 98.3% 96.% 97.2% 97.% 79.4% TS Eff K 98.2% 96.4% 97.% 97.4% 78.3% Table : First rows show BTI performance (average of SL and SL3, with at least 3 hits per fitted track in each superlayer) as function of beam incident angle. The bunch crossing identification efficiencies reported in table 3 of [] are also shown. Then TS performance for tracks with at least 3 fitted hits in each superlayer is shown. o o 2 o 3 o 4 o TS results, all tracks TS HH 3.2% 4.3% 43.7% 3.9% 7.3% TS HL+LH 9.2% 3.6% 24.3% 33.7% 9.% TS LL.9% 7.8% 4.%.%.6% TS H+H 37.% 3.8% 6.9%.% 7.9% TS L+L 9.% 7.%.% 6.3% 2.9% TS Eff BX 86.% 9.% 92.7% 92.8% 73.% TS Eff K 86.2% 89.8% 92.6% 92.7% 72.% Table 6: TS performance for events with one track reconstructed in the chamber, without requests on the number of fitted hits, as function of the beam incident angle. number of uncorrelated trigger increases without increasing the i.e. increases the number of fake second tracks. A small number of events with 2 tracks reconstructed is found. Results on the for 2 nd tracks are reported in the next paragraph. 8 Results from angle scan Data have been collected with different beam incident angles: o, o,2 o,3 o,4 o,6 o. Two runs at each angle have been analyzed, with o 4 o. Results for BTI s and TS are shown in tables and 6. In table results for BTI are given for tracks in which at least 3 hits were fitted in the desired superlayer. The for bunch crossing identification is quite stable w.r.t beam incident angle. The for K (i.e. angle) identification is decreasing when increasing the incident angle, as expected. The TS for bunch crossing identification and for K identification is stable up to 3 o, and it s lower for 4 o data, as expected. 9

10 .7. Super layer.7. Super layer x (cm), layer x (cm), layer Figure : Tube s efficienciy in the four layers of SL as function of x, for runs 368 and 369 ( o ). Figure : Tube s efficienciy in the four layers of SL3 as function of x, for runs 368 and 369 ( o )..7. Super layer.7. Super layer x (cm), layer x (cm), layer Figure 2: Tube s efficienciy in the four layers of SL as function of x, for runs 399 and 36 (2 o ). Figure 3: Tube s efficienciy in the four layers of SL3 as function of x, for runs 399 and 36 (2 o ).

11 .7. Super layer.7. Super layer x (cm), layer x (cm), layer Figure 4: Tube s efficienciy in the four layers of SL as function of x, for runs 394 and 39 (3 o ). Figure : Tube s efficienciy in the four layers of SL3 as function of x, for runs 394 and 39 (3 o ) Super layer x (cm), layer.7. Super layer x (cm), layer Figure 6: Tube s efficienciy in the four layers of SL as function of x, for runs 388 and 389 (4 o ). Figure 7: Tube s efficienciy in the four layers of SL3 as function of x, for runs 388 and 389 (4 o ).

12 o o 2 o 3 o 4 o from [4] fake 2 nd track.3% 2.2% 2.% 4.7%.% 3 hits.% fake 2 nd track.2%.4% 2.2% 4.% 4.6% all eff. for 2 nd track 2.% 4.2% 4.8% 2.8%.3% all Table 7: As function of beam incident angle, first 2 rows show the probability of generating a second track in the BTI+TRACO+TS trigger chain, for events with only one fitted track; the first row is for tracks with at least 3 fitted hits in each superlayer, the second for all tracks. The third row shows the probability of reconstructing a second track for events with two fitted tracks. The value published in [4] of the for 2 nd track (8%), is not directly comparable with the results of this analysis, since the average distance of two track is here of about 8-9 cm, while the simulaton was done with a flat distribution of the distance between tracks over a chamber. The results reported in table 6, i.e. without any requirement on the number of fitted hits in the track, are again very much correlated with the of the tubes. The plots for the tubes of SL and 3 for the different data samples are shown in figures 4, and to 7. The lower trigger efficiencies seen during the o and o runs can be explained by the lower efficiencies of the tubes hit by the beam. The probability of generating a fake second track in the BTI+TRACO+TS trigger chain is lowered by tube inefficiencies because of the ghost suppression mechanism in the TS, as said in the previous paragraph. For angles different from o and o the tubes are more efficient and the the probability of generating a fake second track is compatible with the published number ([4]), as shown in table 7. The determination of the for second tracks has been done using events with 2 tracks reconstructed at a distance grater than 6 cm. Again, the number of events with two triggered tracks is lowered by the TS ghost suppression mechanism in runs with big tube inefficiencies (see figure 8 A). The for second tracks reaches 2% for the runs at 3 o which are the ones with the best tube efficiencies. This number is not directly comparable with the published value of 8% reported in table of [4], since the average distance of two track is here of about 8-9 cm, while the simulaton was done with a flat distribution of the distance between tracks over a chamber. A smaller fraction of second tracks is lost due to the wrong correlation between segments in the TRACO, as shown in figures 8 B and C. 9 Conclusions Results of the analysis of muon data collected at the H2 test beam with the MB96 prototype, done using the level trigger simulation code, are in good agreement with published numbers based on simulated tracks and on the test of an FPGA prototype of a BTI. Some discrepancies are observed in regions of the chamber with inefficient tubes. Those cases have been studied and understood. In particular, for second tracks in events with two close muons is reduced by the presence of inefficient tubes in the inner superlayer. Nevertheless the results show that the trigger algorithm is robust and well behaved also in critical conditions. References [] S. Bethke et al. Performance and mechanical tolerances achieved with a full size prototype of a CMS Barrel muon Drift Tubes Chamber CMS TN/98-XXX (in preparation) [2] M. De Giorgi et al. Design and Simulations of the Trigger Electronics for the CMS Muon Barrel Chambers CMS TN/9- (2 January 99) [3] I. D Antone et al. Track-Segment Sorting in the Trigger-Server of a Barrel Muon-Station in CMS CMS TN/96-78 (3 May 996) [4] CMS Collaboration The Muon Project Technical Design Report CERN/LHC ( december 997) [] L. Castellani et al. Beam Test of a FPGA Prototype of a Front-end Trigger Device for Muon Barrel Chambers CMS TN/96-2 (3 January 996) 2

13 Figure 8: Trigger output (r- view): A) track lost due to ghost suppression in TS (Run 369, event 737); B) correlation has been done with the wrong segments (run 369, event 44); C) as in B, but in this case BTI 3 output is not passed by TRACO to TS (run 388 event 322). 3