Study of the RPC Level-1 trigger efficiency in the compact muon solenoid at LHC with cosmic ray data

Abstract We report a study of the Resistive Plate Chambers (RPC) Level-1 (L1) trigger system efficiency in the Barrel of the Compact Muon Solenoid (CMS) detector of LHC in the same region covered also by the DT trigger system. The method used to study the efficiency exploits the independency of the CMS Drift Tube (DT) and RPC trigger systems. Muon tracks in the event are triggered and reconstructed using the Drift Tube subsystem only, and for each of them we search for a compatible RPC L1 trigger object. We discuss in detail the method and the results of the performance obtained with cosmic ray data taken in 2008–2009.


Introduction
The Compact Muon Solenoid (CMS) Muon System [1] [2] has been designed to provide excellent muon identification, triggering and precise momentum reconstruction over the entire kinematic range foreseen at the Large Hadron Collider (LHC). The Muon System is divided in two regions: the Barrel, that covers the range of pseudorapidity |η| < 1.04, and the two Endcaps, covering the pseudorapidity range 0.8 < |η| < 2.1. The Barrel and Endcap regions thus overlap in the pseudorapidity range 0.8 < |η| < 1.04 A crucial feature of the Muon System is the redundancy provided by the combination of Drift Tube (DT) and Resistive Plate Chamber (RPC) independent sub-systems in the Barrel region , and Cathode Strip Chambers (CSC) and RPC sub-system in the Endcap region.
CMS has performed dedicated periods of data taking with the magnetic field on during october 2008 and july-august 2009 to collect cosmic ray data (Cosmic Runs at Four Tesla, CRaFT).
An optimized cosmics configuration for RPC L1 trigger was developed for the commissioning of L1 trigger during CRaFT.
We exploited the independence of the DT and RPC systems to develop a method for the measurement of the Barrel RPC L1 trigger efficiency.
We present results obtained on data collected during CRaFT.

The Barrel CMS Muon System
The Barrel Muon System[1][2] is composed of 5 Wheels along the direction of the LHC beam axis, referred to as z axis, named W-2, W-1, W0 , W+1, W+2 in the direction of positive z.
Defining φ as the polar angle with respect to the z axis, each wheel is divided into twelve sectors along φ.
Defining r as the radial distance from the z axis, For each sector there are 4 DT stations, from MB1 (the inner one along the direction of increasing r) to MB4 (the outer one). Corresponding to each DT station there is one RPC station, composed by one or two RPC layers, for a total of six concentric RPC layers in the Barrel Muon System.
Defining η as the pseudorapidity , an RPC layer is segmented into two or three η partitions, called rolls.

The L1 trigger system for Barrel RPCs
The RPC Level 1 trigger [3] is logically partitioned into sections. L1 trigger objects are searched for independently in each section. Sections in the η view will be referred as towers, and for each tower the partitions in the r-φ view will be referred as cones.
The definition of the η boundaries of towers (see Fig. 1) is based on a set of reference layers.
The RPC trigger logic has 33 towers. In 2009 the RPCs at highest eta were not installed yet, so the coverage of the trigger was |η| < 1.6 and the towers included in the trigger were 25. A total of 5+5+1 towers is entirely contained in the Barrel. On the reference layers, the strips are grouped in non-overlapping sets of 8 adjacent strips called segments. Each segment subtends a φ angle of 2.5 • , for a total of 144 segments (12 segments for each sector). Each cone must contain only one segment of a reference layer.

The L1 PACT logic
The PAttern Comparator Trigger (PACT) logic collects RPC hits from all stations and searches for spatial and time coincidences independently in each cone. The η and φ coordinates of the trigger objects are assigned on the reference station. By comparison with predefined patterns of hits, a P T value is also assigned to the candidate trigger object.
Trigger candidates are processed by a proper ghost identification and removal logic, and the remaining ones are sorted according to quality criteria.

Cosmic patterns in PACT
In order to increase the trigger efficiency for cosmic muons, which are not constrained to come from the interaction vertex, a looser pattern definition has been adopted with respect to collision runs. A cosmic pattern is defined as a time coincidence of hits on at least 3 different RPC stations in a cone (3/6 majority). No different patterns as a function of P T are defined, thus the system does not assign a P T value to the track in cosmics configuration.

The algorythm for efficiency measurement
The redundancy of the RPC and DT L1 trigger systems allows to study a statistically unbiased sample that has not been triggered exclusively by RPCs.
For a precise determination of the position where the cosmic particle hit the reference layer and of the momentum of the track, we use the tracks reconstructed with the Muon System, referred to as StandAlone tracks.
The tracks are matched to a DT trigger object. In this way we reject fakes and define a sample of tracks that have not been triggered exclusively by RPCs.
In order to prevent an eventual bias due to tracks that would not have been reconstructed without RPC hits, we re-run the reconstruction using DT only.
The track-trigger matching is performed in the φ coordinate only, which is the most accurate coordinate measured by both DT and RPC trigger systems.
The matching requirement is |∆φ t−DT | < 30 • , where ∆φ t−DT is the difference between the φ of the track at the reference layer and the φ of the DT trigger. If a match with a DT trigger is found, a RPC trigger that matches the track is looked for. Figure 2 shows the overall ∆φ S A−RPC as measured using both cosmic patterns and collision patterns (the latter one obtained by running the trigger emulator).
The second peak at ∆φ S A−RPC ≈ −0.06 for the residuals distribution of cosmics patterns is due to the fact that the cosmics pattern configuration cannot identify the P T of the track.
In case of two candidates with the same quality then the one with the smaller φ is selected. The plot shows that this feature is only relevant for cosmic ray patterns. Given the number of tracks matched to a DT Trigger object N DT match , under the assumption that RPC and DT triggers are uncorrelated the RPC trigger efficiency RPC L1 is given by the fraction of tracks in the sample that are matched also to an RPC trigger object: (1) We select tracks pointing to the p-p interaction region by requiring that the track passes through a cylinder centered in the interaction point, with the height parallel to the z axis h = 260 cm and a radius r = 90 cm (definition of TrackerPointing skim). In addition, the tracks are required to have: • Transverse momentum P T of the track evaluated at the track's innermost point > 5GeV/c • Number of hits in the DT chambers used to reconstruct the track N hits > 20; • χ 2 of the fit performed to evaluate the track parameters < 20.
The P T cut removes tracks which are bending in the transverse plane due to the magnetic field. The last two cuts ensure good quality of the DT reconstruction.  The efficiency of the trigger drops in the regions of separation between two adjacent sectors or wheels.

Efficiency on cosmic ray data
The gaps in the regions −200 < z < −220 cm, 45 < φ < 75 o and 180 < z < 200 cm, 75 < φ < 105 o are due to the presence of the cooling chimneys of the CMS magnet.
The cosmic particles distribution disfavours vertical sectors (sectors 1 and 7), which are less populated. Some regions of the plot are not populated because certain sectors of the detector were off during the particular data taking period.
However the loose trigger matching condition of 30 • when the RPC/DT trigger object is found in an adjacent sector can give a contribution in those regions.
We use the momentum of the reconstructed track in the Muon System to define the efficiency vs P T of the incoming cosmic particle.
We also introduce geometrical cuts in order to select only cosmic tracks in the central regions of the rolls and sectors. Indeed, in the border regions DT and RPC triggers are affected by common inefficiencies due to geometry, which introduces correlations between the two systems.
The fiducial cuts choice along φ is : |φ − φ center | < 5 o , where φ center is the value of φ at the center of each barrel sector. The fiducial cuts choice along z is : |z| < 100 or 200 < |z| < 300 or 450 < |z| < 550 cm.
The trigger efficiency vs. the P T of the tracks is shown in Fig. 4.  Table ??. The efficiency plateau is reached at around P T > 5GeV/c at a value 09 = 98.01 ± 0.08%.

Conclusions
A method to measure the L1 RPC trigger efficiency has been developed. It exploits as efficiency probes cosmic ray tracks matched to a DT trigger. It can be used to measure the trigger efficiency also for channels where there are not two back-to-back muons (W channels, top channels, etc.). The method has been applied to determine Barrel RPC trigger efficiencies with cosmics data from 2008 and 2009 and is ready to be applied on collision data.