Efficiency of finding muon track trigger primitives in CMS cathode strip chambers

Abstract In the Compact Muon Solenoid (CMS) experiment, muon detection in the forward direction is accomplished by cathode strip chambers (CSC). These detectors identify muons, provide a fast muon trigger, and give a precise measurement of the muon trajectory. There are 468 six-plane CSCs in the system. The efficiency of finding muon trigger primitives (muon track segments) was studied using 36 CMS CSCs and cosmic ray muons during the Magnet Test and Cosmic Challenge (MTCC) exercise conducted by the CMS experiment in 2006. In contrast to earlier studies that used muon beams to illuminate a very small chamber area ( 0.01 m 2 ), results presented in this paper were obtained by many installed CSCs operating in situ over an area of ≈ 23 m 2 as a part of the CMS experiment. The efficiency of finding two-dimensional trigger primitives within six-layer chambers was found to be 99.93 ± 0.03 % . These segments, found by the CSC electronics within 800 ns after the passing of a muon through the chambers, are the input information for the Level-1 muon trigger and, also, are a necessary condition for chambers to be read out by the Data Acquisition System.


Introduction
The Endcap Muon (EMU) system [1,2,3] of the Compact Muon Solenoid (CMS) experiment [4] is now being commissioned for the Large Hadron Collider (LHC) [5]. The technology chosen for the EMU system is cathode strip chambers (CSC) [6,7], the concept of which was first proposed by G. Charpak more than 30 years ago [8].
The CMS CSCs will detect muons in the pseudorapidity [9] range 0.9 < |η| < 2.4. At the time of the LHC start-up, the CMS Endcap Muon system will consist of 468 six-plane CSCs. The total sensitive area of all CSC planes is about 5 000 m 2 with about 2 000 000 wires.
The CMS cathode strip chambers are mounted on the steel disks enclosing the CMS magnet and are set perpendicular to the beam axis (Fig. 1). When viewed from inside of the LHC ring, the left and right Muon Endcaps of CMS are denoted by ME− and ME+, respectively. There are 4 stations of chambers on each side of the detector, ME±z n , where z n ranges from 1 (the closest stations to the interaction point) to 4 (the outermost stations). The muon stations have 1, 2, or 3 rings of chambers, each ring being labeled as ME±z n /r n ( Fig. 1 (left)). The rings themselves consist of either 18 or 36 trapezoidal chambers spanning 20 • or 10 • in azimuth φ. The chambers have labels ME±z n /r n /φ n . All CSCs, except for those forming the ME±1/3 rings, overlap to provide contiguous coverage in φ. A photo of the ME+2 disk is shown in Fig. 1   The CMS CSCs are comprised of 6 planes of anode wires interleaved between 7 trapezoidal cathode panels ( Fig. 2 (left)). Most of the CSCs have a gas gap of about 1 cm. An electron avalanche caused by a muon traversing a gas gap produces a signal on the anode wires ( Fig. 2 (right top)) which induces a distributed charge on the cathode strips ( Fig. 2 (right bottom)). By reading out signals from wires and strips, CMS CSCs measure 2 muon coordinates: the distance from the beam line r and the azimuthal angle φ in each of the 6 planes. As a muon goes through the CMS detector in the strong (4 T) magnetic field produced by the central solenoid, the change in its φ-coordinates allows its momentum to be measured. Hence, the requirements on the precision of measuring φ-coordinates are more stringent than those for r-coordinate measurements.
Wires run azimuthally and define the y coordinate of the muon track in the chamber's local coordinate system ( Fig. 2 (left)). For readout purposes, the wires are ganged in groups of about 1-5 cm width. Wire group signals are amplified and shaped to a standard pulse. The general idea of a pattern of wire group hits created by a muon is illustrated in Fig. 3 (left).

Local Charged Tracks
The CSC electronics is capable of very fast (800 ns) identification of patterns of hits in 6 chamber layers compatible with a high p T muon originating from the interaction point. The fast pattern recognition is performed by Field Programmable Gate Array (FPGA) chips. The found patterns, known as Local Charged Tracks (LCT), are primitives for the Level-1 muon trigger [11]. They are also a necessary condition for reading out CSC data, i.e., CSC data are present in the Data Acquisition System (DAQ) stream for High-Level trigger or offline analyses only when LCTs have been found in that chamber.
Anode Local Charged Track patterns (ALCT) are formed from wire group hits. At every bunch crossing (25 ns), the FPGA firmware checks if anode hits in 6 planes of a chamber form patterns consistent with muon tracks originating from the interaction point. The set of wire group hits among the 6 layers from which ALCTs can be created form a bow-tie-shaped envelope (Fig. 4). Desired ALCT patterns can be programmed individually within the boundary of this envelope. We used the default patterns fully spanning the envelope, which provides the widest acceptance. The third CSC layer is called the key-layer: for each wire group in the key-layer, the firmware seeks anode hits that lie within ALCT patterns keyed to that wire group. For a pattern to be valid, hits from at least 4 planes are required to be present in the pattern including the key-layer. Out of all ALCTs that may be present in a chamber, the electronics reports only the 2 best-quality ones per each bunch crossing, ALCT0 and ALCT1. This is adequate for the expected chamber track occupancy at the nominal LHC luminosity. The pattern quality depends on the number of planes present in a pattern and its y coordinate. The reported patterns have tags identifying the key wire groups they are associated with (marked as "×" in Fig. 4).
Similarly, Cathode Local Charged Track patterns (CLCT) are searched for among comparator half-strip hits. Unlike the case of ALCTs, there are 7 CLCT patterns. These patterns are shown in Fig. 5: the straight-through pattern corresponds to high p T muons, while more inclined patterns would detect softer muons. For a pattern to be valid, hits from at least 4 planes are required to be present in the pattern. In addition, 4 adjacent half-strip comparator bits are combined to form 1 di-strip bit. The electronics also checks for presence of patterns made of di-strips, which allows one to choose and trigger on highly inclined, i.e., low p T , muons. The CLCT-searching firmware reports the 2 best-quality CLCTs per bunch crossing, CLCT0 and CLCT1. The pattern quality depends on the number of planes present, whether the pattern is based on half-strips or di-strips, and the inclination of the pattern. The reported patterns have tags identifying the key half-strip number with which they are associated. In the future, the number of half-strip patterns will be increased to cover the full angular range, and di-strip-based patterns will no longer be used.
Further downstream, ALCTs and CLCTs are paired to form 2-dimensional LCTs. It is these 2d-LCTs that are used as input primitives for searching for and forming full muon tracks by the Level-1 muon trigger. The key half/di-strip is marked with a cross. The straight-through pattern (left) corresponds to high p T muons, while more inclined patterns would detect softer muons.

Magnet Test and Cosmic Challenge Setup
In the second half of 2006, during the Magnet Test and Cosmic Challenge (MTCC) [12] exercise, a substantial part of the CMS detector operated as one system. The Endcap Muon System was represented by a 60 • sector of the ME+ endcap. Figure 6 shows the layout of chambers that were present in the MTCC in the global CMS coordinate system. A total of 36 chambers were operational during these tests. The data used in this analysis were taken with the magnetic field turned off.
To perform an unbiased measurement of the CSC efficiency for finding muon trigger primitives, we ran the CMS detector Data Acquisition with a Level-1 trigger based on the ME+1 and ME+3 chambers. The ME+2 chambers were not used in the trigger, but were present in the readout whenever an LCT in these chambers was found in coincidence with the Level-1 trigger. It is these ME+2 chambers that we used to measure the efficiency.
The overall area available for studying the LCT-finding efficiency was of the order of 23 m 2 . This is an area far larger than what was available in the earlier beam tests studies [11,13], which, by necessity, were always limited to very small chamber areas, typically of the order of or less than 10 × 10 cm 2 .

Offline Event Selection
To eliminate ambiguities in predicting the muon track position in the middle ME+2 chamber, we required one and only one Track Segment (TS) among all ME+1 chambers and one and only one track segment among all ME+3 chambers. Track segments were identified using the simple algorithm described in Appendix B. It allowed us, using information only from the ME+1 and ME+3 chambers, to predict muon track positions in the ME+2 chambers with a few millimeter precision in both the x and y directions. The prediction accuracy was mostly driven by the multiple scattering of cosmic ray muons in the EMU steel disks (see Fig. 1). Since we used runs taken with the magnetic field turned off, the muon track was assumed to be a straight line going through the 2 space-points assigned to the ME+1 and ME+3 track segments.
The ALCT-and CLCT-finding electronics are designed to have high efficiency for muons originating from the Interaction Point (IP). We selected events where the predicted track direction would resemble "IP-like" muons. This was achieved by selecting events in which the local polar angle of the track θ µ (see Fig. 6) predicted from track segments in the ME+1 and ME+3 stations was within 0-1 rad. In addition, the φ n -number of the chambers with track segments in the ME+1 and ME+3 stations had to be the same (e.g., ME+1/3/27 and ME+3/2/27). Note that the quotes in "IP-like" are essential: we did not actually require selected muons to point back exactly to the IP; if we had, we would have had a very small event sample to work with.
Events in which the predicted tracks would miss the geometrical area of the ME+2 chambers (limited in the r-φ plane by upper and lower distances from the beam line as well as minimum and maximum azimuthal angles) were excluded from the analysis.
After these cuts, we ended up with 759 tracks going through ME+2/1 chambers and 14 100 tracks going through ME+2/2 chambers. There are fewer tracks through the ME+2/1 chambers because they are smaller in size and, more importantly, require more horizontal muons, which are sparse in cosmic rays. The predicted track positions in the key-layer of the ME+2/1 and ME+2/2 chambers are shown in Fig. 8.
The chamber wire planes are not contiguous from the narrow end to the wide end. There are 2 or 4 breaks of 25 mm width at approximately every 60 cm, which create 3 or 5 independent high voltage segments per plane. These break points are also used to introduce panel supports, without which the panels would bulge or cave in and stable chamber operation would not be possible. These break points, indicated by dashed lines in Fig. 8, result in dead zones. These dead zones line up horizontally and mostly effect tracks with smaller θ µ -angle.

Efficiency Measurement
For an event to be counted as efficient, we required at least one ALCT and at least one CLCT (i.e., at least one 2d-LCT) to be reported by the ME+2 chamber through which the predicted muon should have gone.
Although we do expect some loss of efficiency near chamber edges and between high voltage segments, we first obtained the chamber LCT-finding efficiencies without any fiducial cuts. The corresponding results (the number of events with predicted tracks going through ME+2 chambers, the number of events for which a 2d-LCT was not reported by the ME+2 chambers, and the corresponding efficiencies) are given in Table 1. The average efficiency, without any fiducial cuts, was around 97%-98%. The efficiency depends on the local polar angle θ µ of a muon's track as shown in Fig. 10 (left). One can see that the efficiency sags for smaller angle tracks. To lose an LCT, one needs to lose hits in 3 or more planes. A straightforward geometric analysis of how track with different θ µ -angles cross the dead areas between high voltage segments results in the curve also shown in the figure. Although the curve is somewhat simplistic as it includes neither the single plane detecting inefficiency nor errors in the θ µ -angle predictions, the data and the curve are clearly in good agreement. Angle of muon track (rad) Figure 10: Efficiency to report a muon LCT as a function of track angle θ µ without fiducial cuts (left) and after excluding "semi-dead" zones (right) in ME+2 chambers. The predicted efficiency curve based on geometric analysis is shown as the solid line.
To measure the true CSC efficiency, i.e., excluding geometrical dead zones, we applied fiducial cuts on the predicted tracks to eliminate those that would cross dead zones. The chamber areas with full acceptance are shown in Fig. 9 as dashed polygons. The borders for these areas were defined so that tracks with our selection of allowed directions would never miss 3 or more planes due to dead zones or chamber edges. These areas were reduced further by 1-1.5 cm to account for the finite precisions, σ dx and σ dy , with which we could predict muon track positions in the ME+2 chambers. These corrections corresponded to 3σ dx and 3σ dy (see Appendix B for details). After applying such fiducial acceptance cuts on the predicted tracks, only one 2d-LCTs in ME+2/1 and seven 2d-LCTs in ME+2/2 chambers were lost. In 1 of these 8 events, the 2d-LCT was actually in the neighboring chamber, 5 events had neither ALCTs nor CLCTs, and in 2 events an ALCT was reported with no matching CLCT. The CSC efficiency averaged over all chambers used in this study was found to be 99.93 ± 0.03%. Details are given in Table 2. The efficiency dependence of a track angle after applying the fiducial cuts is shown in Fig. 10 (right). It is greater than 99% for all angles.
To confirm that what we measured is the efficiency to find muon-associated 2d-LCTs (rather than just noise), we plotted the differences between the predicted muon track x and y positions and the actual 2d-LCT0s reported by the ME+2 chambers (Fig. 11). The positions of the 2d-LCT0s in the ME+2-chambers were defined by the centers of the ALCT0 key wire groups and CLCT0 key half-strips. The LCTs found in the ME+2 chambers are within ≈0.5-2 cm around the predicted positions, which is consistent with the expected multiple scattering of cosmic ray muons and the widths of the strips and wire groups. For further discussion, see Appendix B. Note that the ME+2/2 chambers are distinguished by a large σ dy ≈ 2.1 cm. This is because these chambers have very broad wire groups about 5 cm wide, which determines the spread of the residuals: (5 cm )/ √ 12 ≈ 2 cm.

Conclusions
The efficiency of the CMS cathode strip chambers to report muon trigger primitives was measured with cosmic ray muons over an area of ≈23 m 2 of installed chambers. The obtained efficiency was 99.93 ± 0.03%, which exceeds the design specification of 99%.

A Appendix A: CMS CSC Parameters
Parameters of chambers extensively used in this analysis are summarized in Table 3. ME1/1b refers to the larger part of the ME1/1 chambers covering |η| < 2.0.

B Appendix B: Track Segments Reconstructed Offline
To improve our ability to predict track coordinates in the ME+2 chambers based on measurements in ME+1 and ME+3 chambers, we used a very simple track segment reconstruction algorithm based on anode hits and cathode comparator bits. Using this algorithm, we could localize segments to within a few millimeters in both the x and y directions. As a result, the precision with which we could predict muon track coordinates in the ME+2 chambers was mostly driven by the multiple scattering of cosmic ray muons in the Endcap steel disks. Here we describe the algorithm and evaluate its performance using MTCC data.
Anode Segments (AS) were searched for among anode hits using the same pattern as shown in Fig. 4. Since muons with larger θ-angles are preferred 1) , the pattern was moved along a chamber starting from its wide side inward, one key wire group per step. If 6 layers with anode hits were present in the pattern at some step, then an anode segment was reported and all hits inside this pattern were deleted. Upon reaching the narrow end of the chamber, the procedure was repeated again with a requirement of 5 and, then, 4 layers with hits in the pattern. Anode segments were numbered sequentially, AS0, AS1, etc. The found anode segments were assigned (y AS , z AS )-coordinates by taking the center of gravity (COG) of hits associated with them. If there was more than 1 hit per plane in a pattern, the hit weights were reduced so that the total weight per plane was always 1. In addition, a linear fit was used to evaluate the segment slope dy/dz. For a wire group width w, the expected error (RMS) on the y AS coordinate would be w/ √ 12/ √ 6 ≈ 0.12 w, or 2-6 mm, depending on the chamber type.
Cathode Segments (CS) were similarly searched for using half-strip comparator bits and the 9 patterns shown in Fig. 12 (they were obtained from the most recent CLCT-finding firmware). Sequentially, all 9 patterns were moved across the strips from one side of a chamber to the other. In the first pass, we looked for 6 layers with hits present in a pattern; then, for 5 layers, and, finally, for 4 layers with hits in a pattern. Cathode segments were numbered sequentially, CS0, CS1, etc. Similarly to anode segments, (φ CS , z CS )-coordinates and track slopes dφ/dz were assigned to patterns. Using this technique, one would expect to achieve about 0.5-2 mm precision along the x coordinate, depending on the chamber type and muon hit location along the strips.
Anode and cathode segments were then combined to make a complete 2-dimensional Track Segment (TS). Whenever multiple ASs and/or CSs were found, we used all possible combinatorial pairings to make full 2d-TSs. If z CS and z AS were different, the track segment z coordinate z T S was taken as z T S = 0.5 × (z CS + z AS ) and (φ T S , y T S )-coordinates were recalculated for the new z T S -location using the dφ/dz and dy/dz slopes.
To evaluate the performance of the algorithm, we applied it to all the chambers in all 3 stations.
First, we found that the algorithm did find at least one track segment in all chambers with 2d-LCTs reported 1) In CMS, track segments at larger θ-angles are less likely to be due to backgrounds 1 Figure 12: Comparator bit patterns used for constructing cathode segments. The key half-strip is marked with a cross.
by hardware (total of 10 522 events). Therefore, the efficiency of finding track segments can be estimated to be > 99.97% at the 95% CL for chambers with hardware-found LCTs. Note that chambers in which hardware did not find an LCT would not be available for further analysis (High-Level trigger or offline).
Second, using track segments found in ME+1 and ME+3 (in the same way as described in the main body of the note), we predicted track positions in the ME+2 chambers and compared them to the track segments found by those chambers. The residuals are shown in Fig. 13 (ME+2/1 chambers) and Fig. 14 (ME+2/2 chambers). For these plots, if there were multiple TSs reconstructed in these chambers, we used the best track segment, TS0, even if it was not the closest to the predicted track position. One can see that the dx and dy distributions for ME+2/1 and the dx distribution for ME+2/2 have core widths σ ≈ 3.5 mm. The dy distribution for ME+2/2 has a core width σ ≈ 6 mm. Also, one can clearly see that residuals are not centered around zero; this is due to the Endcap disks' misalignment during the MTCC, which was confirmed by geodesic survey. To show that the obtained residuals are consistent with multiple scattering of muons, we performed the following calculations. A muon with an average inclination of 0.4 rad with respect to the horizon would lose approximately 9 GeV on its way through the whole CMS detector before hitting the Endcap Muon system (see orientation of the CSC chambers used in the MTCC, Fig. 6). A muon that hits the ME+1/1 chambers has to have an energy of at least 2 GeV to pass through 2 steel disks to reach the ME+3 station. The approximate cosmic ray muon spectrum dN/dE µ ∼ E −2.6 µ [15] is shown in Fig. 15 (left). The additional axis on this plot shows by how much the muon energy spectrum shifts after passing through CMS, just before hitting the ME+1 chambers. The filled area shows only the portion of the spectrum corresponding to muons that can reach the ME+3 chambers. Then, for a muon of a given energy, we calculated the expected, multiple scattering induced, dN/dx(E µ )-spread between the muon coordinate measured in the ME+2/2 chambers and the coordinate predicted from measurements in the first and third stations. After that, the 2 distributions, dN/dx(E µ ) and dN/dE µ , were convoluted. Finally, we added the expected spatial accuracy for TS as it was estimated above. The result for ME+2/1 is shown in Fig. 15 (right). It is clear that the observed residuals are consistent with our simple model. The same level of agreement was observed for other chambers and projections. From these plots, we can conclude that multiple scattering is the dominant contribution to the residuals of the cathode segment measurements. The anode segment measurement precision in ME+2/1 chambers is also dominated by multiple scattering. The large ME+2/2 chambers have wide wire groups, which limits the accuracy of coordinate measurements to 6 mm. Next, we looked at the number and quality of the found segments (the algorithm allows us to find as many segments as there are in a chamber). Distributions of the numbers of found anode, cathode, and combined 2-dimensional track segments (AS, CS, and TS) in ME+2 chambers are shown in Fig. 16.  Table 4 shows the numbers of events with different combinations of found segments. About 95% of the events were simple as they had only 1 AS and 1 CS (and, therefore, only 1 2d-TS). All events with multiple segments were visually scanned using an event display. Most of the events with 1 anode segment and 2 cathode segments (and vise versa) looked like they had 2 close-by tracks and the anode (or cathode) segment searching algorithm was not able to separate them. Events with 2 anode segments and 2 cathode segments were either clean 2-track events or more complex broad showers. The final ≈1% of events with 3 or more segments in 1 or both projections were all due to broad showers with many hits spread over the chamber. It is worthwhile pointing out that, in cases when there were 2 or more track segments found in the ME+2 chambers, the reconstructed segment closest to the predicted muon track position typically (> 80%) had a better quality than all other segments. Fig. 17 shows the distribution of the pattern qualities for the closest and all other segments. Finally, we benchmarked the CPU performance of the algorithm using MTCC data. The average time required to reconstruct all segments in a chamber with at least 1 track was approximately 0.3 ms (Intel Pentium M 1.6 GHz processor). At this speed, the algorithm is well suited for the High-Level trigger.