DRAFT CMS Paper. The content of this note is intended for CMS internal use and distribution only

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1 DRAFT CMS Paper CMS PAPER MUO-- The content of this note is intended for CMS internal use and distribution only 2/3/29 Head Id: 4764 Archive Id: 4789M Archive Date: 2/3/26 Archive Tag: trunk Performance of the CMS muon detector with 7 TeV pp collisions at the LHC The CMS Collaboration Abstract The performance of all subsystems of the CMS muon detector is studied by using 7 TeV pp collision data from the LHC in 2. This box is only visible in draft mode. Please make sure the values below make sense. PDFAuthor: PDFTitle: PDFSubject: PDFKeywords: CMS Muon Detector group Performance of the CMS muon detector with 7 TeV pp collisions at LHC CMS muon detector CMS, detector performance, muon system, DT, CSC, RPC, DQM, software, calibration, resolution, efficiency, trigger, timing, synchronization, simulation, alignment, backgrounds Please also verify that the abstract does not use any user defined symbols

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3 Figure : An r-z cross-section of one quadrant of the CMS detector with the axis parallel to the beam (z) running horizontally and radius (r) increasing upward. The interaction region is at the lower left. Shown are the locations of the various muon stations and the steel disks Introduction Muon detection is a powerful tool for recognizing signatures of interesting processes over the very high background rate expected at the LHC. This is particularly true as the luminosity increases. The CMS muon system has 3 functions: muon identification, momentum measurement, and triggering. Good muon momentum resolution and triggering are provided by the high-field solenoidal magnet and the flux-return yoke. This flux-return yoke also serves as a hadron absorber, which enables the identification of the muons. The CMS muon system (Fig. ) is designed to reconstruct the momentum and charge of the muons over the entire kinematic range of the LHC. CMS uses 3 types of gaseous particle detectors for muon identification. Because of the central solenoidal magnet, it is natural to have a cylindrical, barrel region and 2 planar endcaps. Because of the large area to be covered and the inaccessibility of the detector, it is important that the muon detectors be inexpensive, reliable, and robust. In the barrel region where the muon rate is low, the neutron background is relatively small, and the magnetic field is mostly uniform, drift chambers with standard rectangular cells are employed. The barrel drift tube (DT) chambers cover the pseudorapidity region η <.2. They are organized into 4 stations at different radii and interspersed between the yoke return plates.

4 2 Introduction In the 2 endcap regions of CMS, where the muon rates and background levels are high and the magnetic field is high and non-uniform, CMS uses cathode strip chambers (CSC). These chambers have a fast response time, fine segmentation, and relative immunity to the non-uniform field. The CSCs cover the region from η values of.9 to 2.4. Each endcap has 4 stations of chambers mounted on the faces of the endcap disks, and roughly perpendicular to the beam. The cathode strips run radially outward and provide a precision measurement in the r-φ bending plane. These muon detector elements cover the full pseudorapidity interval η < 2.4 with no acceptance gaps ensuring good muon identification over a range corresponding to < θ < 7. Offline reconstruction efficiency for the muons is typically 96% 99% except in gaps between the DT station elements ( η =.25 and.8) and the transition region between the DTs and the CSCs. Owing to the amount of material before the first muon station, the punchthrough is negligible. A crucial characteristic of the DT and CSC systems is that they can each trigger on the p T of muons with good efficiency and high background rejection independent of the remainder of the detector. In addition to these muon detectors, CMS has added a complementary, dedicated triggering detector with good time resolution to measure the correct beam-crossing time at the highest LHC luminosities. The resistive plate chambers (RPC) are located in both the barrel and endcap regions, and they provide a fast, independent trigger with a sharp p T threshold over a large portion of the rapidity range ( η <.6). The RPCs are double-gap chambers, operated in avalanche mode to ensure good operation at high rates. The CMS muon system functions primarily as a tag to identify the muon tracks. Because of the large amount of steel in the return yoke, the muon resolution within the muon system is degraded both by multiple scattering and the complicated magnetic fields in this return yoke. Except for the highest momentum muons, the resolution comes from the Tracker which has high resolution and measures the muon before any significant multiple scattering. However, the muon trigger comes from the muon system, which must get a good enough resolution to identify high p T tracks. Thus, in CMS the triggering scheme for the muons relies on 2 independent and complementary triggering technologies: cathode strip chambers (CSC) in the endcaps, drift tubes (DT) in the barrel, and resistive plate chambers (RPC) in both endcaps and barrel. The CSC and DT systems provide good resolution and reasonable timing, while the RPC system provides excellent timing with somewhat lower resolution. The CMS muon detector system was designed between 992 and 995 and was approved after the submission of the Muon Technical Design Report [] in 997. During 2, proton proton collision data were successfully collected at instantaneous luminosities up to L = 32 cm 2 s with a total integrated luminosity of 36 pb. Four layers of gaseous detectors hermetically cover a pseudorapidity region up to η= 2.4. The first and fourth layers cover the inner and outer faces, respectively, of the huge yoke of magnetized steel that surrounds the big and powerful (3.8 T) central solenoid. The other two layers are embedded within the steel yoke. Four detecting stations and the presence of the magnetic field allow a second muon momentum measurement independent of that obtained from the central Tracker. The yoke was designed to convey as much as possible of the magnetic flux FIXME: FG: how much? generated by the central solenoid and is highly symmetrical to ensure excellent homo-

5 geneity of the field inside the coil and to prevent uncompensated stresses on it. The magnetic field is very low in the volume housing the barrel chambers, FIXME: need to define barrel and endcap but is high and non-homogeneous in most of the volume of the endcaps. The intensity of the magnetic field in the steel is non-uniform and decreases with increasing radius in the barrel and in the z direction FIXME: z should be shown in a figure in the endcaps. This was one factor that led to the choice of multi-wire proportional counters with segmented cathode read out (cathode strip chambers (CSC)) in the endcap and of drift chambers (drift tubes (DT)) in the barrel region. Both of these detector types have good spatial resolution, but intrinsically poor time resolution owing to the unavoidable uncertainty of the time taken by the ionization electrons to drift from the track position to the amplifying wires. Typical values for the maximum drift time are 5 6 ns for a CSC and few hundred nanoseconds for a DT. The muon transverse momentum resolution dp T /p T is limited up to very high momentum ( 2 GeV/cFIXME: FG: check this value) by a constant term owing to multiple Coulomb scattering (MCS) in the thick plates of steel between the chamber stations. It starts to increase at higher momenta due to the chamber resolution and to the available knowledge of their relative positions in space, i.e., by the alignment precision. Taking into account the sizes of the detectors, the precision of the chamber location does not exceed to 3 µm going from the inner to the outer detectors, and this fixes the figure of about µm requested as the ultimate useful space resolution in the location of the tracks inside the detectors. FIXME: the boldface text needs clarification The negligible contribution of the chambers themselves to the MCS as compared to the effect of the thick steel plates separating them motivated a design characterized by several layers of wires per chamber and by a relatively heavy but robust structure. Assuming the µm space resolution mentioned above, the multiple layer structure sets a comfortable limit on the single layer resolution that is easily achievable by the chosen detector types. It should be noted that while below about 2 GeV/c the most precise momentum measurement is provided by the central tracker, above this value the central tracker resolution is limited by its radius (about half of the solenoid radius), which does not allow exploitation of the full available bending power. The full B dl is recovered at higher momenta by a common fit of the information from the tracker and the muon detectors. This also implies that the most important muon chambers for the momentum measurement are those of the inner stations. And of the local magnetic field in the steel. FIXME: the previous boldface text needs to be clarified The modest spatial precision requirement for a single detecting layer allowed a large freedom in the chamber design, which was exploited in an effort to obtain the challenging level of time resolution that is required for triggering purposes. In fact, the basic layout of the muon system, that is, the choice of suitable detector types for various regions of the yoke and the number and geometry of the layers inside the chambers, was influenced by the requirement of generating a fast and accurate muon trigger. Proton bunches in the LHC cross inside CMS at frequency of 4 MHz (every 25 ns). An interesting crossing is identified if different parts of the detector, the electromagnetic and hadronic calorimeters and the muon system, identify at the same time a suitable topology of released energy and particle momenta. The muon detector must identify a muon as a very penetrating particle, and produce a prompt and rough measurement of its position and momentum that are combined with the data of other parts of CMS to trigger the data acquisition of the full detector. This implies that every subpart of CMS involved in the trigger, including each chamber in the case of the muon detector, must be able to associate its space and momentum information with the bunch crossing that generated the event with a time dispersion much smaller than the 25 ns

6 4 2 Timing and Synchronization that separate two successive bunch crossings. A coincidence is generated by sending to each trigger-generating part of the detector the LHC clock delayed by an amount such that each part will record the same time, i.e., the time of crossing of the proton bunches at the center of CMS. This goal is achieved by the combination of an appropriate chamber geometry and fast and innovative front-end electronics, which allows the parallel processing of the signals of a suitable number of strips and wires to detect and measure, in each chamber, the position and direction of a track with a fixed delay and a time uncertainty of a couple of nanoseconds FIXME: FG had a? here to check this. This performance can be compared to the typical time figures of the adopted detectors. For example, the drift times in a single layer is 6 ns for a CSC and 35 ns for a DT, the single layer time resolution is 5 6 ns for a DT and reaches 25 ns FIXME: check for the cathode signal processing in a CSC, and the typical time propagation along the DT wires is 2 ns. The overall performance of the muon detector depends critically on the accuracy of the time and space alignment of each individual chamber. A precise reference for both aspects that allowed the final fine tuning of the alignment is supplied by the resistive plate chambers (RPC) associated with each tracking detector system, and by a hardware alignment system capable of locating each tracking chamber in space... FIXME: Is there more to be written here? An RPC is characterized by loose position resolution and subnanosecond time precision related to the absence of drift of the ionization electrons. Local amplification in the gas makes RPCs insensitive to the effect of the magnetic field on the drift velocity and their timing insensitive to the presence of delta rays or electromagnetic showers generated by the passing muons. This feature allows the fine time tuning needed to keep the fraction of mistimed bunch crossings at the trigger level to below 3. The RPC system also provides an important and independent check of the overall trigger efficiency. The hardware alignment system plays an important role in providing precise chamber positions in the central CMS reference frame that are independent of the track reconstruction, which suffers from uncertainties on the intensity of the inhomogeneous magnetic field present inside the steel and from uncertainties on the relative positions of the central tracker and the different parts of the muon system. These strict limits are crucial for achieving a further and non-ambiguous refinement of the positions using tracks from selected events coming from proton proton interactions. The above considerations show that the final trigger and reconstruction performance of the detector depends on a careful calibration and tuning of all its components. The following chapters describe the methods used to tune and calibrate the most important parameters of the detector and how well they etc etc..fixme: needs to be completed Timing and Synchronization The timing parameters of the LHC are such that proton bunches potentially cross inside CMS every 25 ns. The purpose of the trigger system is to find event candidates fulfilling a predefined set of criteria and to assign them to an appropriate Bunch Crossing (BX) number. At the LHC many interesting physics signatures contain muons, and the muon subdetectors are therefore included in the Level (L) trigger system. It is the L Accept signal (LA) broadcast to all subdetectors which initiates readout of the event. Trigger synchronization is of great importance for two reasons. As hits in multiple chambers are required for an L trigger, out-of-time chambers can reduce overall trigger efficiency. If the L muon trigger fires early or late relative

7 2. Common Synchronization Procedure to the collision time, it forces readout of the entire detector in the wrong BX. For these reasons the online synchronization of the muon chambers was an essential priority for early in the 2 run period. Trigger synchronization of a subsystem must be achieved at three levels: intrachamber synchronization, chamber-to-chamber relative synchronization, and subsystem-to-subsystem synchronization. Although each muon subsystem faced unique challenges due to differences in chamber design, trigger electronics design, and physical position on the detector, the general synchronization procedures were similar. The general procedure is discussed in Sec. 2.. The details and results of the separate DT, RPC, and CSC trigger synchronization methods are found in Secs. 2.2, 2.3, and 2.4, respectively. The overall L Global Muon Trigger results are discussed in Sec For physics analyses, the time assigned offline to the muon hits once the event has been collected and fully reconstructed is also important. For a muon produced in a pp collision in the center of CMS in an event with the correct BX assignment, the offline time of any hit it leaves in the muon chambers should be reported with time t=. Any deviations from may be caused by backgrounds such as cosmic rays, beam backgrounds, chamber noise, or out-of-time pileup, or it may be an indication of new physics such as a slow moving, heavy charged particle. In Sec. 2.6 the offline time alignment procedure and results are shown. FIXME: maybe update this paragraph to announce resolution results too The performance shown in this section are the results of iterative improvements achieved over the course of 2 running. Further refinements for each subsystem are planned for early Common Synchronization Procedure When a muon crosses a chamber, the BX of the resulting trigger primitive (a track segment) depends on the muon time of flight from the interaction point to the chamber; individual chamber properties and/or their geometrical position; latency of trigger logic electronics; length of cables and fibers connecting the chamber electronics to the peripheral crates. The last three items are properties specific to each chamber and were already studied during cosmic data-taking, before pp collisions were recorded at CMS. The tool used by CMS sub-detectors for the synchronization of trigger and data acquisition chains is the Trigger and Timing Control system device (TTC)[25]. The aim of the TTC is to provide machine clock distribution to the various parts of the detector and broadcast the LA strobe trigger signal. Prior to collisions, each muon subsystem adjusted its TTC delays to roughly synchronize chamberto-chamber using cosmic-ray data and/or early single-beam data. Additional adjustments were introduced based on calculated time-of-flight paths to each chamber. Once collisions started, each subsystem used high p T muon data to refine internal delay settings so the onchamber clocks would be in the optimal phase with respect to the LHC machine clock. This procedure was iterative. Each subsystem s trigger primitive is different in nature, so the subsystemspecific figures of merit for synchronization are presented in the next sections.

8 6 2 Timing and Synchronization DT Trigger Synchronization To time the detector for collision data, two independent steps, called coarse and fine synchronization, were carried out. The former is related to (chamber-to-chamber) adjustment of the overall DT Local Trigger (DTLT) latency, in terms of multiples of BXs, performed to provide equalized input to the DT Regional Trigger. The latter refers to the tuning of the sampling phase of the DTLT with the precision of a few ( 2) ns in order to optimize the system response to muons coming at a fixed latency with respect to bunched beam crossings. Every DT is equipped with a Trigger and Timing Control Receiver (TTCrx) device that, among other things, provides a parameter to adjust the clock phase between on-board electronics and the CMS master clock (TTCrx delay parameter). The latter is used to perform the fine synchronization of the DTLT and is configurable in steps of. ns. As it is possible to tune TTCrx delay parameters only chamber-by-chamber, delays due to signal propagation between the boards equipping a single DT chamber have to be taken into account because they can set a limit on the accuracy of the chamber internal synchronization. To cope with this effect, the DTLT internal timing was equalized using cables of adequate length. The maximum skew of the clock distribution after equalization has been measured to be around ns, allowing to consider every chamber as an intrinsically synchronous device within this precision. Such level of accuracy compares well with the design performances, thus online DT software has been designed to allow timing adjustments only with a precision of ns. As it is relevant later on in this article (see Sec. 7..), it is worth mentioning that DT chamber on-board electronics are designed in such a way that TTCrx delay parameter tuning affects both readout and DTLT boards. Therefore every adjustment related to trigger timing optimization has to be be followed by an update of the DT calibration pedestals used for local segment reconstruction. A detailed procedure to synchronize the DTLT with collision data is extensively described in [26]. The method exploits the possibility to extend the straight-line fit used to determine position of the DT track segment during local reconstruction. By adding an additional parameter it is in fact possible to measure the particle s arrival time with respect to the BX crossing phase. During commissioning of the detector with cosmic ray muons, the DT Local Trigger response as a function of this parameter was studied in order to identify the timing working phases where the system has optimal performance. A chamber-by-chamber map of these observables, to be used as a reference to time in the detector during bunched beams operation, was thus computed. As soon as sufficient bunched beam data were available, the timing distribution of reconstructed segments matched to global muons coming from the interaction vertex was computed, relying on the aforementioned method. The latter was then compared to the map of phases parameters measured from cosmic data to estimate timing corrections which optimize DTLT performance in term of BX identification efficiency. The procedure was iterated 4 times to reach the final configuration. Figure 2a shows the BX distribution of the local trigger primitives of highest quality found in the DTLT readout window of triggering stations crossed by offline reconstructed muons from LHC collisions. Data from all DT chambers are summed together.

9 2.3 RPC Trigger Synchronization Out-of-time primitives populate symmetrically the bins to the right and to the left of the correct BX. The pre- and post-firing rates of the highest quality DTLT primitive are both on the order of 2%. These are mainly due to the presence of DTLT out-of-time ghosts that can occasionally be generated together with in-time trigger primitives. As outlined in Sec. 3 this effect has been carefully investigated, and in the present timing conditions, the efficiency to deliver a trigger primitive at the correct BX and rate of out-of-time triggers are at a manageable level at present LHC luminosities and in good agreement with with TDR expectations and simulation studies. The last set of DTLT timing corrections was applied by the end of August 2. Data collected during the rest of the 2 LHC operation period were analyzed to compute a further set of adjustment parameters, which will be tested at the beginning of the 2 LHC run. 2.3 RPC Trigger Synchronization The RPCs possess very good intrinsic timing resolution (below 2 ns) [27], therefore they are very well suited for the task of muon triggering and BX assignment. However, hit signals originating at the chamber level are discriminated, which may introduce different offsets for individual chambers. The signal path may be summarized as follows: amplification and discrimination at the Front End Boards located on the chambers; transmission through cables to Link Boards situated on the balconies in the experimental cavern; zero-suppression and transmission through optical fibers to the trigger electronics outside of the experimental cavern; reception at electronics room and distribution of signals to the individual processing elements of the Pattern Comparator (PAC) trigger system. Signals coming from a single chamber may be shifted in time in steps of order. ns to achieve synchronization. By using the information on cable lengths and muon time of flight it was possible to produce a first approximation of synchronization constants set. These were further refined during studies of beam halo and beam splash events. Beam splash refers to events from intentional beam dumps about hundred meters from the CMS detector hall and resulting in many simultaneous hits in the chambers. After start of normal LHC operation the recorded collision data were used in order to further improve the synchronization. The experimental procedure consisted of selecting global muons with tracks that would cross the RPC system. Furthermore, only the first hit from any chamber was selected, since it is known, that sometimes a particle crossing a RPC may provide afterpulses. The distribution of the hit BX relative to the true event BX was studied for all chambers. In cases where the distribution was asymmetric or shifted, the synchronization parameters were changed to obtain a symmetric distribution centered at zero. This procedure was repeated 3 times and final results obtained in this way are presented in Fig. 2b. The data used here correspond roughly to million muon tracks. One can see, that hits outside the central BX value contribute significantly less than one per mil. It may be noticed also, that a 5% decrease of number of hits outside of central bin has been obtained between steps.

10 8 2 Timing and Synchronization dn/d(bx) dn/d(bx) DT chamber BX (a) DT RPC chamber BX (b) RPC dn/d(bx) dn/d(bx) CSC chamber BX (c) CSC L Muon Trigger BX (d) L Muon Figure 2: BX distributions for the trigger primitives of the (a) DT, (b) RPC, and (c) CSC subsystems relative to the true event BX. In each distribution, data from all chambers are summed together to show the overall subsystem synchronization. (d) shows the combined L.

11 2.4 CSC Trigger Synchronization CSC Trigger Synchronization A CSC triggers when there is a coincidence of an Anode Local Charge Track (ALCT) and a Cathode LCT (CLCT), which are formed when anode and cathode hits match the patterns expected from collision muons. As the slewing time of the anode discriminator is, by design, significantly faster than the cathode signal development, the BX assignment of the combined LCT is determined by the ALCT BX. The pattern matching algorithms and trigger path are described in detail in [29], but the anode signal development is briefly outlined below. As a collision muon passes through a CSC, charge collected on the anode wire is input into a constant fraction discriminator in the Anode Front End Board (AFEB). If the charge is above the detection threshold, a 35 ns pulse (digitized every 25 ns) is output to the chamber s ALCTboard. The ALCT is formed and assigned a BX when there are anode hits in at least 4 layers that match an ALCT pattern. The anode hit time is defined as either the single BX or the average of the two BXs of the hit. When the chamber anode hit times are averaged over several events, it yields a characteristic chamber anode time. Though the anode hit time is quantized in 2.5 ns steps, a chamber anode time may be any value and is sensitive to changes in the TTCrx delay to the ALCT boards (coarseness of 2 ns). A sample of high-quality collision muons was used in order to correlate the average chamber anode time with the fraction of early (- BX), on-time (BX=), and late (+ BX) ALCTs. After identifying a target anode time for optimal performance, the clock delays for individual ALCT boards were adjusted to effect the desired shift. The post-shift distribution of the ALCT BX relative to the true event BX is shown in Fig. 2c and is intentionally asymmetric. When two ALCTs have different BXs, the L trigger logic chooses the later BX, so the optimal performance point is set slightly earlier than perfectly centered. 2.5 L Muon Trigger Synchronization Results The L muon triggers are formed from trigger primitives (DT, CSC) or hits (RPC) forwarded from multiple chambers and possibly from different muon subsystems. The final L BX is assigned by regional triggers [33] according to a logic that depends on the muon subsytems involved and that combines primitive or hit information reducing the contribution of early/late signals from individual chambers. An event collected when the L trigger fires at a wrong BX might be rejected by the High Level Trigger (HLT). Therefore biases introduced by the HLT selection mechanism have to be taken into account if one wants to measure the rate of out of time L triggers using HLT-recorded data samples. To avoid to cope with these kind of effects, a dedicated DAQ stream was developed to collect at high rate a fraction of the CMS RAW data content consisting only of L trigger information, before any HLT processing. By comparing the BX of the L muon trigger to the BX where collisions are expected according to the LHC filling scheme, one can measure the L synchronization. Results obtained this way for L muon triggers with no minimum p T requirement are shown in Fig. 2d. As a consequence of the reduced data content available, no reconstruction based cuts for rejecting cosmic background or beam halo background were available. Instead the L trigger rate attributable to cosmic rays was computed from regions of the LHC orbit that were not populated in a given machine filling scheme. Likewise, the beam background was estimated from the L muon trigger rate during the region of the orbit when a single bunch was present in CMS. After contamination from cosmic-ray muons and beam halo was subtracted, the fraction of pre- and post-fired events was on the order of.2% and.% respectively. These results exceeded the TDR expectations of 99% in time triggering [28]. Small improvements are expected from 2 synchronization refinements.

12 3 The DT and CSC Local Triggers Offline Timing Alignment For physics analyses the time assigned offline to the muon hits once the event has been collected and fully reconstructed is also important. For a muon produced in a pp collision in the center of CMS in an event triggered in the correct BX, the offline time of any hit it leaves in the muon chambers should be reported with time t=. Any deviations from zero may be caused by backgrounds such as cosmic rays, beam backgrounds, chamber noise, or out-of-time pileup, or it may be an indication of new physics such as a slow moving, heavy charged particle. Short paragraph describing the DT offline timing. Plots currently residing in resolution section. The CSC hit time is based on the cathode signal, which is amplified, shaped, and then sampled every 5 ns. Eight 5 ns samples are saved with the first two bins serving as dynamic pedestals [3]. The peak time of the pulse is found in a five pole fit. The measured single hit resolution is 5 ns [32]. Using calibrations and muons from collisions, offsets were derived to shift the average hit time for each chamber to zero. These offsets are applied during reconstruction. To define a CSC segment time, the cathode hit times are combined with the anode hit times defined in Sec The resulting segment time distribution is shown in Fig. 3b. Mean.4972 Mean.4972 RMS 3. RMS CSC Segment Time [ns] (a) DT (placeholder for now, repeating CSC plots) CSC Segment Time [ns] (b) CSC Figure 3: Segment time distributions for muons with p T 2 GeV The DT and CSC Local Triggers In each barrel and end-caps chamber the local trigger provides the trigger segments that are used by the Track Finder to build the muon trigger candidates. In the barrel this task is performed by the DT local trigger (DTLT) and in the end caps by the CSC local trigger (CSCLT). The RPC trigger is not based on local trigger devices, as muon trigger candidates are reconstructed from the spatial and temporal coincidence of hits in the RPC muon stations. The DTLT system and its performance are described in detail in Refs. [33], [34], [35], [36]. Only the main functionalities and characteristics are summarized here. The trigger segments are found separately in the transverse plane x-y (called φ view) and in the plane that contains the z direction (called θ view). The maximum drift time in the DT system is almost 4 ns, which is much longer than the 25 ns interval that separates two consecutive collisions. Therefore the

13 DTLT system must first associate each trigger segment to the correct bunch crossing (BX). For each BX the system provides up to two trigger segments per chamber in the φ view, and one in the θ view. In the φ view, each trigger segment is associated with the following quantities: the BX at which the corresponding muon candidate was produced; the position and direction in the local coordinate system of the chamber; a quality word describing how many aligned DT hits were found; and a bit flagging the segment as a first or second candidate, ordered according to their assigned quality, for that BX. One set of such quantities is called DT trigger primitive. The trigger primitives are provided separately in each station. A muon DT trigger candidate is then reconstructed by the DT Track Finder if a proper spatial and angular matching between at least two trigger primitives in two different DT stations is found [33]. A ghost-suppression mechanism is performed by the DTLT electronics to discard additional trigger candidates attributable to false signals ( ghosts ). False copies can arise from the presence of additional non-aligned hits around the muon track, or from the fact that adjacent electronics units devoted to deliver the trigger primitives share a common group of DT cells, and a hit alignment can be found twice. The segment selection and ghost-suppression algorithms are flexible and can be configured to match various experimental conditions, such as the presence of groups of noisy or disconnected DT cells in a chamber. To measure the DTLT performance, two data samples containing reconstructed muons are used for this study: a minimum bias sample and a sample of W/Z events decaying to muons. Muon candidates in minimum bias events are characterized by low transverse momenta, p T > 3 GeV/c, whereas W/Z decays produce muon tracks in the range p T > 2 GeV/c. A simulated sample of approximately 7 minimum bias events containing at least one reconstructed muon track is also used. The CSCLT system is described in detail in [33]. Signals are sent by the front-end cathode and anode electronic boards connected to the chambers. Segments of muon tracks are found separately in the the nearly orthogonal cathode and anode planes, where the 6-layer redundancy of the system is used to measure the muon-segment BX, its pseudorapidity η and the azimuthal angle φ. Up to two cathode and two anode local tracks can be found in each chamber at any BX, then combined into three-dimensional tracks by a timing coincidence in the trigger electronics device. The CSCs are readout in zero-suppressed mode, requiring a pretrigger which depends on specific patterns of cathode and anode local tracks. Hence, the CSC readout is highly correlated to the presence of CSCLT segments. This feature is taken into account when measuring the trigger efficiency. DTLT Efficiency (%) Station DATA MC Station MB 92.9 ± ±.9 Station MB ± ±.9 Station MB3 93. ± ±.9 Station MB4 93. ± ±. Table : Average DTLT efficiency for the different station types, for data and simulation The CSCLT measurements are performed on a minimum bias event sample corresponding to a total luminosity of approximately 2 pb, and on a sample of events containing J/ψ decays, corresponding to 29 pb. A simulated sample of 2.5 million minimum bias events containing at least one muon at the generator level is also used for comparison, as well as samples of

14 2 3 The DT and CSC Local Triggers simulated events containing a J/ψ and Z decaying to two muons. Muon candidates from J/ψ decays are characterized by a transverse momentum p T < 2 GeV/c, whereas muon tracks from Z decay have p T > 2 GeV/c. 3. Measurement of the DT Local Trigger Efficiency To measure the DTLT efficiency, selected events must be triggered by the RPC system, without any requirement on the presence of the DT trigger, which could bias the measurement. The presence of a reconstructed muon track in the event is then required. To remove contamination from cosmic rays, muon candidates must have an impact parameter in the transverse and longitudinal plane respectively d xy <.2 cm and d z < 24 cm. Their pseudorapidity must be in the range η <.2 to be within the acceptance of the inner stations of the muon barrel. The number of DT hits associated to the track, N DT, must be N DT > 3. This requirement does not introduce any bias in the performance of the DTLT, as at least four aligned hits are necessary to deliver a trigger primitive. Bad reconstructed muon tracks are removed requiring the normalized χ 2 of the track fit to be χ 2 <. Efficiency. Efficiency CMS 2 Preliminary MB MB2 MB3 MB4.7.6 CMS 2 Preliminary MB MB2 MB3 MB P t (GeV/c) η Efficiency CMS 2 Preliminary MB MB2 MB3 MB φ (rad) Figure 4: The DTLT efficiency as a function of the muon transverse momentum p T, the pseudorapidity η and the azimuthal angle φ. Results for the four different station types are superimosed To measure the DTLT efficiency in a chamber, the presence of one track segment reconstructed in the φ view of the same chamber is required. The segment must have at least 4 out of 8 TDC hits in its φ view. Defining ψ the local-track segment angle with respect to the direction to the interaction point, it must be ψ < 4, to be fully contained in the angular acceptance of the DTLT units. If more than one track segment is found in the chamber, the track segment is

15 3. Measurement of the DT Local Trigger Efficiency not used for the efficiency calculation. The efficiency of the DTLT in the chamber is defined as the fraction of the selected track segments that have an associated trigger primitive in that chamber, with the correct BX assignment. This definition of efficiency allows the measurement of the effective net trigger capability, excluding the geometrical acceptance and the DT cell efficiency. About 3% of the DT chambers have known hardware failures that affect their DTLT efficiency. Neglecting these units, the average DTLT efficiency is 93. %, which is % better than the value predicted in [33]. The average efficiency measured in simulated events is 95.6 %. The average DTLT efficiency is shown in table, for data and simulation. The uncertainties are dominated by systematic effect: small variations of the DTLT efficiency from station to station are due to small variations in the time-synchronization of the local trigger electronics, and to differences in the average angular incidence of the muon tracks. The overall systematic uncertainty is estimated from the observed spread of the measured DTLT efficiencies over the various stations, once the stations with known hardware problems are removed. The DTLT efficiency as a function of the muon transverse momentum p T, the pseudorapidity η and the azimuthal angle φ is shown in fig. 4, for the four different station types. All the DT chambers are used for this measurement, and the inefficiency observed in the region 2.5 < Œ <.5 is due to a known hardware failure in a station of type MB2. Two methods were developed to measure the CSCLT efficiency: the single track matching and the tag and probe methods. Both methods use tracks reconstructed using tracker tracks, with no usage of the muon system information, to perform an unbiased measurement of the CSC trigger primitive efficiency. The selected events contain at least one primary vertex (PV) associated to at least four tracks. To reject cosmic-ray muons traversing the detector near the interaction point, the PV must have r < 2 cm, and z < 24 cm, being r and z the distance of the PV from the nominal interaction point respectively in the transverse and longitudinal plane. In the single track matching method, a good tracker track crossing a CSC station (tag station) is selected, and the CSCLT efficiency is measured in another station (probe station) placed in front of the tag station. The track in the tag station is selected in such a way that the probe station must have been crossed by the same track. If the tag station is of type ME2 (ME3) the probe station is ME (ME2). Therefore this methid can measure the CSCLT efficiency only for station types ME and ME2. Selected events must contain tracker tracks with pseudorapidity within CSC geometrical coverage,.9 < η <.24. Each track must fulfill d xy <.2 cm and d z < 24 cm. The track momentum is required to be p > GeV/c, and the track must have at least hits in the silicon tracker. To select well measured tracks in the tracker detector, each candidate must have the normalized χ 2 of the track fit χ 2 < 4, the pseudorapidity η and the transverse momentum p T measured respectively with an uncertainty η/η <.5 and p T /p T <.5. The track is also required to cross the CSC chamber at least 5 cm from its edge, to be fully contained in the sensitive area of the detector. If more than two tracks hit the same chamber, they are not used in the measurement. The quantity D trk seg = (X trk proj X seg ) 2 + (Y trk proj Y seg ) 2 provides the distance of the track projection to the nearest CSC segment, in the tag station. A good tag candidate is identified if D trk seg < cm. The quantity D trk LT = (X trk proj X LT ) 2 + (Y trk proj Y LT ) 2 provides the distance of the projection of the track to the position of the nearest local trigger (LT) primitive in the probe station. The CSCLT is considered efficient if D trk LT < 4 cm. If

16 4 3 The DT and CSC Local Triggers the station is affected by some known major hardware failure, it is not used to compute the efficiency. The CSCLT efficiency is measured in data and simulation. The average efficiency for station of type ME and ME2 is reported in Tab. 2. The uncertainties are dominated by systematic effects, related to the selection criteria applied to the tracks and the trigger segments. CSCLT Efficiency (%) Single Track Matching Method Tag and Probe Method Station DATA MC DATA MC ME 97.9 ± ± ± ± 2. ME ± ± ± ± 2. ME3 NA NA 94.9 ± ± 3.4 ME4 NA NA 93.5 ± ± 2.4 Table 2: Average CSCLT efficiency for the different station types, for data and simulation In the tag and probe method, muon candidates from J/ψ and Z decay are used. Among the two muon candidates from the resonance decay, one is used as a tagging track and the second acts as a probe. Selected events are triggered by the single muon HLT or by the J/ψ dedicated trigger. The tag track must fulfill the following tracker track selection criteria: d xy <.2 cm and d z < 24 cm; p t > 5 GeV/c; at least hits in the silicon tracker; the normalized χ 2 of the track fit χ 2 < 4. It can point anywhere in the CMS detector, and it is required to match the muon HLT object that triggered the event within the angular distance R = (η trk η HLT ) 2 + (φ trk φ HLT ) 2 <.4, where η trk, φ trk, η HLT and φ HLT are respectively the η and φ values of the track and the HLT candidate. The tag track is also required to match at least two track segments in two different stations. The probe track must be a tracker fulfilling the track selection criteria described for probe tracks in the single track matching method. The invariant mass of the tag and probe tracks is fitted to extract the J/ψ and Z signal yields for both the denominator and the numerator of the efficiency ratio. The latter is done after requiring that the probe matches a CSCLT segment. Contrary to the single track matching method, the tag and probe method can be applied to any CSC station type. The average CSCLT efficiency for the tag and probe method is reported in Tab. 2 both for data and simulation. The CSCLT efficiency measured using the single track matching and the tag and probe methods is shown in Fig. 5 for station of type ME and ME2 as a function of η, φ and p T. 3.2 DT False Triggers False copies of the DT trigger primitive can survive the ghost-suppression algorithm. The false copies that occur at the correct BX are called in-time ghosts. They can produce spurious dimuon trigger signals if at least two of them are matched together by the DTTF. The probability for the DTLT algorithm to generate such false trigger signals in a given station is defined as the number of events with two trigger primitives in that station, both delivered at the correct BX, divided by the number of events in which at least one trigger primitive is delivered. The intime ghost probability is shown in Fig. 6 (left) as a function of the muon transverse momentum, for the four different station types. The result is in very good agreement with the Trigger TDR predictions [33], that range from 2 to 4 % as a function of the muon p T. False copies of the trigger primitive delivered at a wrong BX, in addition to the one that cor-

17 3.2 DT False Triggers Efficiency.9.8 Single Track Matching Efficiency.9.8 Single Track atching.7 Tag And Probe.7 Tag And Probe η η.. Efficiency.9.8 Single Track Matching Efficiency.9.8 Single Track Matching.7 Tag And Probe.7 Tag And Probe φ (rad) φ (rad).2 Single Track Matching.2 Single Track Matching. TagAndProbe. TagAndProbe Efficiency.9.8 Efficiency P 2 t (GeV/c).6 P 2 t (GeV/c) Figure 5: Comparison between the CSCLT efficiency measured using single track matching (red) and the tag and probe method (blue), as a function of the muon pseudorapidity η (top), the azimuthal angle φ (middle) and the transverse momentum p T (bottom) for station of type ME (left) and ME2 (right).

18 6 3 The DT and CSC Local Triggers In-time Ghosts Fraction MB MB2 MB3 MB4 Out-Of-Time Ghosts Fraction MB MB2 MB3 MB P t (GeV/c) P t (GeV/c) Figure 6: Left: fraction of the DTLT in-time ghosts as a function of the muon transverse momentum. Right: fraction of the DTLT out-of-time ghosts as a function of the muon transverse momentum. Results for the four different station types are superimposed rectly identifies the BX, are called out-of-time ghosts. If at lest two such false triggers are matched by the DTTF, a muon trigger candidate would be delivered at the wrong BX. The probability of out-of-time ghosts in a station is defined as the number of events with two trigger primitives, one at the correct and one at the wrong BX in that station, divided by the number of events in which at least one trigger primitive at the correct BX is delivered. The out-of-time ghost probability is shown in Fig. 6 (right) as a function of the muon transverse momentum, for the four different station types. The results are at least a factor 3 better than the Trigger TDR predictions. Nevertheless a direct comparison is not possible in this case, as in this latter case the study was performed over a wider BX range than for data [33]. Fraction of Triggers R.M.S. =.98 cm Position difference (cm) Fraction of Triggers R.M.S. = 4.8 mrad Incidence angle difference (mrad) Figure 7: Left: distribution of the difference between the position of the local track segment and the DTLT segment. Right: distribution of the difference between the angle of the local track segment and the DTLT segment. Results are shown for a station of type MB DT Trigger Primitive Position and Angular Resolution The track segments obtained by fitting the TDC information in each DT chamber are used for offline muon reconstruction and they provide an accurate determination of the position and the incidence angle of the muon in the chamber, independently of the DTLT output. The position and angle of the reconstructed track segments are compared with the corresponding information assigned by the DTLT to the trigger segments to determine the position and angular resolution of the DTLT primitives. Figure 7 (left) shows the distribution of the difference between

19 the position computed by the reconstructed track segment and the DTLT segment for a station of type MB, taken as an example. The RMS of the distribution is mm. The position resolution of the trigger segment is the same for every station type. This measurement is in agreement with previous test beam results and cosmic rays measurements [34], [36]. The uncertainty related to the track position measurement is neglected. Figure 7 (right) shows the distribution of the difference between the incidence angle of the reconstructed track and the DTLT segment. The RMS of the distribution is 4.8 mrad. The result is again in agreement with previous measurements [34], [36], and it guarantees that the expected performance in terms of position and transverse momentum resolution at the output of the Level- trigger is achieved [33] Spatial Resolution In this section, measurements of the spatial resolution of the DT, CSC, and RPC systems based on data recorded during the first year of LHC collisions are discussed. Hit resolution is determined from the distribution of hit residuals with respect to the muon trajectory. This is possible in DTs and CSCs with no need of an external reference by using the track stubs ( segments ) reconstructed with a straight line fit of the hits in the different measurement layers. Therefore, the relative alignment of chambers does not affect the result. No attempt was made to remove layer-by-layer misalignments, which are small compared to the resolution (cf. Section 6). The residual of hits with respect to the reconstructed segment is a biased estimator of the resolution, because of the contribution of the hit under study to the segment fit if all available hits are included in the segment; or because of the uncertainty in segment extrapolation or interpolation if the fit is performed removing the hit under study. In both cases, the bias can be corrected for using the statistical relationship between the width of the residual distribution for layer i (σ Ri ) and the actual resolution (σ i ), which can be obtained from Gaussian error propagation of the explicit expression of the residual with respect to the straight line obtained with a least-square linear fit [3, 45]: σ i = c i σ Ri, () where c i is a factor that depends on the distance of the layer from the middle of the measurement planes, and is smaller than one in case the hit under study is removed from the segment, and larger otherwise. Monte Carlo studies have shown that in both cases these corrections allows the true resolution to be obtained with good accuracy. Residuals in RPC chambers, which provide a single measurement of the trajectory, are defined extrapolating the segment of the closest DT and CSC chamber. The following sections describe the details and results for each subdetector. The measurements are performed using a pure sample of high-momentum muons, obtained selecting candidate W and Z muon decays [4]. Muons are selected in the acceptance of the corresponding subdetector and with p T > 2 GeV. 4. DT Resolution In DT chambers, segments are reconstructed independently in the eight layers of both Rφ superlayers and, where present, in the four layers of the RZ superlayer [5]. All available hits are included in the fit, using Eq. to obtain the resolution from residuals with the coefficients reported in Table 3.

20 8 4 Spatial Resolution Table 3: Correction factors c i of Eq. derived for the DT geometry and for the case of a segment fit including all available hits. Layer SL (Rφ) SL2 (RZ) SL3 (Rφ) For each layer, σ Ri is obtained with a Gaussian fit of the core of the segment residual distribution. The result is averaged separately for all Rφ and RZ layers of a chamber Only segments with at least seven hits in the Rφ SLs and, in the innermost three stations, with four hits in RZ SL are used. In addition, segments are required to point towards the beam line, with a cut on the incidence angle on the chamber in the transverse plane φ < 25. The single-hit resolutions obtained with this method are reported in Table 4 and shown in Fig. 8, separately for Rφ and RZ layers and averaged over all sectors in each wheel and station. The spatial resolution of the segment fitted in the whole chamber is reported in Table 5. Resolution [µm] W W- W-2 CMS 2 Preliminary s = 7 TeV W+2 W+ W-2 W-W W+2 W+ W W- W-2 W+2 W+ W W- W-2 W+2 W+ φ superlayers θ superlayers MB MB2 MB3 MB4 Figure 8: Single-hit DT resolution for Rφ and RZ layers, averaged over all sectors in each barrel wheel and station Several features can be noted: for both Rφ and RZ layers, the resolution of W+ (W+2) is approximately the same as that of W- (W-2), given the geometric symmetry of the system; in Wheel the resolution is the same for Rφ and RZ layers; The resolution varies moving towards external wheels due to the effect of the larger longitudinal incidence angle (θ) of muons on these chambers. For RZ superlayers, θ is the angle in the measurement plane; therefore the resolution is significantly degraded in external wheels, due to the increasing deviation from linearity of the space-time relationship with larger angles of incidence of the particles. For Rφ layers, θ is the angle in the plane orthogonal to the measurement plane; the larger angle

21 4.2 CSC Resolution 9 Table 4: Single-hit DT resolution for Rφ and RZ layers expressed in µm, averaged over all sectors in each barrel wheel and station. SL Type Station W-2 W- W W W2 MB Rφ MB MB MB MB RZ MB MB Table 5: DT chamber resolution in the Rφ and RZ projections, expressed in µm, averaged over all sectors in each barrel wheel and station. SL Type Station W-2 W- W W W2 MB Rφ MB MB MB MB RZ MB MB in external wheels results in longer paths inside the cells that increase the primary ionization statistics, causing a a slight improvement in the Rφ resolution; the worse resolution of Rφ layers in MB4 compared to MB-3 is due to the fact that in this station, where a measurement of the orthogonal coordinate is missing, it is not possible to correct for the actual muon time of flight and signal propagation time along the wire. In particular, the signal propagation time along the wires is up to about 9.8 ns, which corresponds to differences in reconstructed position of up to about 54 µm. This correction can be applied at a later stage, during the fit of a muon track using all stations. For comparison, the single-hit resolution obtained in a test-beam is of about 9 µm for normal incidence on the chamber, with a deterioration to about 45 µm for an incidence angle of 3 degrees in the cell measurement plane and improving to about 5 µm for an incidence angle of 3 degrees in the orthogonal (non-measurement) plane [4]. 4.2 CSC Resolution A detailed description of the CSC chambers is given elsewhere [7]. The CSC spatial resolution is determined by the design parameters of the chambers, as well as certain characteristics of each muon track, the physics of multi-wire proportional chambers and the reconstruction. For the purposes of this study, the coordinate of interest is the coordinate measured by the strips. In global coordinates, this would be Rφ, but most of the results presented here are expressed in strip coordinates. The strip coordinate, s, is the Rφ coordinate relative to the centre of the strip, divided by the strip width at the position of the hit. Apart from resolution To accommodate the End Cap CMS geometry the CSC chambers have a trapezoidal shape, with strips running

22 2 4 Spatial Resolution effects, one has.5 < s <.5. In order to obtain a resolution in physical units, the residual is then multiplied by the mean width of a strip in the given chamber. The mean strip widths, < w >, are shown in Table 6. Table 6: Selected physical specifications of the cathode strip chambers. The range of strip width is given, as well as the the average width. For more information, see Ref. [7] Ring Chambers per ring Strips per chamber Strip width, w (mm) < w > (mm) Pitch (mrad) ME/a ME/b ME/ ME/ ME2/ ME2/ ME3/ ME3/ ME4/ The spatial resolution depends on the track position within the strip; it is worse for a track passing at the center of a strip. This effect is seen more strongly in wider strips. To compensate for this, the CSC layers (except ME/, having more narrow strips) [7 9] were staggered by half a strip width to have every time 3 layers out of 6 in the area of the best spatial resolution. Two different expressions are thus used to characterize the chambers resolution, one for the staggered chambers and one for the non-staggered ME/. For both chamber types, a single Gaussian fit to the residuals distribution limited to the core region of the residuals distribution is used. For the staggered chambers, this fit is performed for hits in the centre half of the strip (σ c ) and outside of the centre half of the strip (σ e ). These two measurements are combined according to: ( 3 σ seg = + 3 ) /2 σc 2 (2) For the non-staggered ME/, the following expression is used: σ seg = ( σ 2 e 6 σ 2 layer ) /2, (3) where σ c, σ e and σ layer are the layer resolutions calculated by Eq.. The 5 hit fit is used to estimate the width of the residual distributions. The correction factors c i for different CSC types are listed in Table 7. In order to reduce backgrounds, cleaning cuts were applied to the hits and segments that were used to measure the resolution. These are: 6 hits on segment 592 χ 2 seg < 2/8 and χ 2 seg strip fit only < 5/4 593 exclude segments with largely displaced hits (leading to residuals of >.2 strip 594 widths) along radial lines. The solution of radial strips has the consequence that the strip width increases with R as shown in tab.6. As a result the resolution of the same chamber depends on R. This makes natural to quote the resolution in function of fraction of strip width.

23 4.3 Results 2 Table 7: Correction factors c i for 5 hit fit. Layer ME/ chambers ME/2 edge ME/2 centre All others edge All others centre Table 8: Average chamber resolutions in µm. Chamber group Run type/period /b /2 /3 2/ 2/2 3/ 3/2 4/ Cosmics Cosmics Collisions pp MC 2 (37) segment points roughly towards the interaction point: dx/dz <.5; dy/dz <.5 (in local coordinates, where y is measured along and x perpendicular to the strips) reconstructed hit charge C is in reasonable range: 5< C <2 ADC counts, see fig. 9. Hits with high charge are often distorted by delta electrons. for pp collision data, require a well reconstructed muon (reconstructed using muon chamber and central tracker information) within η <.7 of the segment These cuts are similar to those used in previous studies [] Entries 4582 χ 2 / ndf 34.2 / 25 Landau Const 78.4 ± 5.3 Landau par.8563 ±.72 Landau Max ± Charge 3x3 in ADC counts Resolution ( strip units ) Charge(3x3) in ADC counts Figure 9: Left: Charge distribution, Q3x3. Right: Variation of the layer resolution as a function of Q3x Results The residuals distributions for each chamber type are shown in fig.. The distributions are found to agree reasonably well with a single Gaussian distribution in the central region. The fits shown are used to extract the value of the resolution, which is then scaled by the average strip width per chamber. The measured chamber resolutions obtained using equation 2 and 3 are summarized in table 8. The resolutions obtained from cosmic muons are found to be slightly worse than those measured on collision data. This is expected behavior due to several reasons, which include the fact that cosmics arrive uniformly distributed in time which worsens the hit resolution, have a

24 22 4 Spatial Resolution 2 6 ME/ σ =.23 5 ME/2 =.23 σ e 8 4 =.33 σ c Strip width units Strip width units ME/3 =.6 σ e =.29 σ c Strip width units ME2/ =.22 σ e =.43 σ c Strip width units ME2/2 =.2 σ e =.4 σ c 4 3 ME3/ =.2 σ e =.42 σ c Strip width units Strip width units ME3/2 =.22 σ e =.42 σ c Strip width units ME4/ σ e =.2 =.42 σ c Strip width units Figure : Residuals distributions for different CSC chamber types, corrected per layer according to Eq.. The distributions are shown in units of strip width. The Gaussian fits to the central region (within σ of ±2.5) are shown as well. For chambers with staggered layers, both the residuals distribution for the center (σ c ) and for the edge (σ e ) of the strip are shown.

25 4.4 RPC Resolution larger variance of angles of incidence, and that there are backgrounds that can be removed in the collision events by requiring the presence of well reconstructed muons with p T > 2 GeV which cannot be removed in cosmic muon data. Reasonable agreement with simulated events is found for pp collision data. There are known differences for the ME/b chambers (in parenthesis in table 8): while the HV in the data was lowered by 4%, the MC still uses the design HV setting 2, which leads to the observed better resolution in the MC. Further smaller differences seen between data and MC are understood to be due to differences in simulating the deposited charge and all will be addressed for future releases of the MC. All measured resolutions are close to and mostly even exceed the requirements noted in the CMS muon TDR [], which required 75 µm for the ME/ and ME/2 chambers and 5 µm for the remaining chambers. 4.4 RPC Resolution In the CMS muon system RPCs are used as trigger detectors, nevertheless hits are provided for reconstruction and muon identification. In order to measure the resolution of the RPC system, DT and CSC segment extrapolation was performed using the very same technique explained in efficiency section (ref to be done), where the extrapolated point is compared with the reconstructed RPC hit (the average position of the strips fired when a muon passes through a given RPC chamber). The RPC hit resolution depends on the strip-pitch (summarized in table 9), the cluster size (summarized in table ), and the alignment of the RPC chambers. Since no alignment constants are applied during muon reconstruction, the rms is shown with and without alignment in table. The residuals distribution with its gaussian fit is shown in Fig. 2 for the barrel and in Fig. for the endcap. Finally the gaussian fit results for all the different RPC pitches in CMS is summarized in table 2, this table would be considered as the final resolution measurement for the RPC system. Table 9: Strip Pitch for the RPC Chambers Ref.(to be done) Barrel End Caps Layer Pitch (cm) Ring Average Ring Average Pitch (cm) Ring Pitch (cm) RBin 2.28 RE/2/A 2.38 RE(2,3)/2/A 2.55 RBout 2.45 RE/2/B 2.9 RE(2,3)/2/B 2.23 RB2in 2.75 RE/2/C.74 RE(2,3)/2/C.95 RB2out 2.95 RE(,2,3)/3/A 3.63 RB RE(,2,3)/3/B 3.3 RB4 4. RE(,2,3)/3/C Time resolution In addition to a measurement of the track position and direction, DTs and CSCs provide a measurement of the arrival time of the track in the chamber. The resolution of these measurements is discussed in the following sections. 2 The HV for the ME/ chambers is currently set to lower than design values as the design resolution can be obtained already at this setting which increases also the lifetime of the chambers. If necessary the HV can be increased and the spatial resolution improved further.

26 24 4 Spatial Resolution Table : Average Cluster Size for different pitches Barrel End Caps Layer CLS Ring CLS Ring CLS RBin 2.2 RE/2/A 2.8 RE(2,3)/2/A.88 RBout 2.2 RE/2/B 2.29 RE(2,3)/2/B 2. RB2in.96 RE/2/C 2.27 RE(2,3)/2/C 2.46 RB2out.93 RE(,2,3)/3/A.64 RB3.8 RE(,2,3)/3/B.57 RB4.63 RE(,2,3)/3/C.8 Table : RMS Residual Distribution, with and without alignment for different pitches RMS Barrel RMS End Caps Layer Ali(cm) no-ali(cm) Ring Ali(cm) no-ali(cm) Ring Ali(cm) no-ali(cm) RBin RE/2/A.8.7 RE(2,3)/2/A RBout RE/2/B..99 RE(2,3)/2/B RB2in RE/2/C..9 RE(2,3)/2/C.4. RB2out RE(,2,3)/3/A.77.7 RB3.6.6 RE(,2,3)/3/B RB RE(,2,3)/3/C Table 2: σ resolution distribution with alignment Barrel End Caps Layer σ (cm) Ring σ (cm) Ring σ (cm) RBin.8 RE/2/A.94 RE(2,3)/2/A.7 RBout.9 RE/2/B.88 RE(2,3)/2/B.96 RB2in.3 RE/2/C.5 RE(2,3)/2/C.86 RB2out.99 RE(,2,3)/3/A. RB3.6 RE(,2,3)/3/B.28 RB4.32 RE(,2,3)/3/C. Figure : Residuals with gaussian fit for different strips pitches in the EndCap

27 4.5 Time resolution 25 Figure 2: Residuals with gaussian fit for different strips pitches in the Barrel Time measurement in the DTs [FIXME: not yet clear in which section this part would have to go.] The arrival time of a track in each DT Chamber is reconstructed leaving a common displacement of the hits from the wire position as a free parameter in the segment fit [2]. Assuming a constant drift velocity, this common displacement corresponds to a shift in the time of the track with respect to the mean value of the times of the sample of prompt high-p T muon tracks used during the calibration process (cf. Section 7.2). The distribution of the times, as measured in the Rφ projection in a sample of a high-p T prompt muon tracks (p T > GeV/c) is shown in Fig. 3; the overall resolution is better than 2.4 ns. Systematic biases in the different chambers and φ regions are within.2 ns. The tail at low values is due inclusion of delta-ray hits in the fit, which mask the real track hit in the same cell. dn / [.5 ns] time ( all segments) CMS 2 Preliminary, sqrt(s) = 7 Tev 8 time ( segments after quality cut ) Mean.399 [ ns ] Mean RMS [ ns ] local time [ ns ] Figure 3: Distribution of the local times, as measured in in the Rφ projection of DT chambers in a sample of a high-p T prompt muon tracks. [FIXME: PLOT TO BE UPDATED]

28 26 5 Local reconstruction efficiency Time measurement in the CSCs [FIXME: CSC timing part is currently elsewhere in the note ] Local reconstruction efficiency The global reconstruction of muons relies on the local reconstruction of objects inside the individual muon chambers. The 3 muon detector sytems (DT, CSC, and RPC) use different techniques to register and reconstruct signals originating from charged particles penetrating them. Still, in all cases the basic objects are reconstructed hits (i.e., 2- or 3-dimensional spatial points with assigned uncertainties) and segments, obtained by fitting the reconstructed hits. Local track reconstruction in the barrel DT chambers proceeds in 2 steps: first, a hit reconstruction consisting of deriving spatial points from the TDC time measurements; second, a linear fit of these points in the 2 projections of a chamber (8 Φ layers and 4 Θ layers), in order to perform a local pattern recognition and obtain reconstructed segments. The first step starts with the calibration of the TDC output in order to get the real drift times of the ionized charge within the tube. Since a DT cell is 42 mm wide and has a central wire, the maximum drift distance is 2 mm. Then, multiplying the drift times for a known drift velocity, a pair of space points (rechits) are obtained, left and right, at equal distance from the wire. These are the input to the linear fit that attempts to associate the majority of rechits to a segment. Hits that are inconsistent with the fit, yielding high segment χ 2 values, are discarded. In the endcap CSCs, the rechit reconstruction is based on information from the strips (local x or φ coordinates) and wires (local y coordinate). The strip width varies between.35 and.6 cm for different chamber sizes and locations, and a typical muon signal is contained in 3 to 6 strips. The charge distribution of the strip signals is well described by a Gatti function ([3], [? ]), which is the basis of the the local x coordinate reconstruction. The wire signals are grouped in wire groups with widths between 2 and 5 cm and typically only wire group is fired. The uncertainties on the position measurements are data driven and extracted from studies performed from measurements using both cosmic and collision data. The proper error correlation matrix is assigned to a rechit (strips and wires are not perpendicular). Segments are built from the available rechits in the 6 layers of the chambers and at least 3 hit layers are required to build a segment. Rechits that are rejected by the fit have positions typically distorted by the presence of delta electrons. The RPC local reconstruction has as input the strips that were fired on a given event. The strips that are next to each other are grouped in what is called a strip cluster, and the average position of the strips that conform the cluster is what constitutes the reconstructed hit of a given RPC detector. The uncertainty on the measurement follows the standard deviation of a uniform distribution (i.e., simply the size of the cluster along each direction divided by 2). A crucial aspect of the efficiency measurements is the definition of the probe used to measure the efficiency of an object. There are few basic alternatives which can be explored. One can use the muons from the decay of neutral particles (J/ψ, Υ, Z ) and consider one of the muons as the tag to probe the efficiency using the other muon (so-called Tag-and-Probe technique). This technique does not necessarily rely on any information from the probed muon chambers, which makes it suitable for such studies. On the other hand, data can be limited both because of the number of resonance events available in the collected data sets and because of the applied selection criteria. An alternative method can be used in addition for the efficiency

29 5. Segment reconstruction efficiency in DT and CSC based on Tag-and-Probe methods calculation: a measurement based on inclusive single (or multiple) muons from any process. This method provides a large sample of probes, especially in the forward region and at low p T, though it requires much more stringent selection criteria to reject background. Both of the methods above require propagation of tracks from the inner tracker region to the muon system, which makes them unsuitable for very precise investigations. To investigate the efficiency response inside the chambers, the reconstructed segments are used as probes to measure the efficiency for hit reconstruction in individual layers. Similarly, for the specific case of the RPC system, where the chambers are firmly attached to the DT and CSC chambers, segments reconstructed in the DT or CSC are directly used as RPC probes. They are extrapolated to the RPC chamber layers to measure the hit reconstruction efficiency. Hereafter, we present results from the measurement of efficiencies for reconstructing local objects in the 3 muon detectors of CMS: rechits and segments. 5. Segment reconstruction efficiency in DT and CSC based on Tag-and-Probe methods The segment reconstruction efficiency measurement was performed using the Tag-and-Probe method applied to well-identified muons from J/ψ and Z decays selected from 2 collision data at s=7 TeV. Corresponding samples of simulated events were used to compare the observed efficiency distributions with the expected one. For the DTa, the passing probes are those that were matched by the global track reconstruction to a segment reconstructed within the chamber. For the CSCs, the passing probes are required to match a local CSC segment within a distance of 4 cm, which is a loose requirement but further reduces the small background from cosmic muons or other muons and jets present in the event. The selected probe-tracks were propagated to the muon stations, starting from their point of closest approach to the interaction point. The propagation procedure allows the position of the track to be determined at any crossed surface. Uncertainties on the extrapolated position, due to multiple scattering, match the MC expectations. The presence of reconstructed segments was checked for each individual chamber crossed by the probe-tracks. To reduce the apparent loss of efficiency owing to propagation errors, the intersections between probe-track and chamber were required to be away from the chamber edges, reduced by the error on the position of the intersection itself. The residual effects of propagation errors are included in the measured efficiency. The segment reconstruction efficiency is defined as ɛ = N pp N p, (4) where N p and N pp are the number of probes and passing probes, respectively, obtained after fitting the tag and probe pair to the J/ψ and Z invariant mass spectra. The uncertainty on the efficiency is given by

30 28 5 Local reconstruction efficiency Figure 4: Segment reconstruction efficiency in DT chambers by sector. ɛ = ɛ ( ɛ) N p. (5) The efficiency was evaluated as a function of the intersection position in the chamber and of the p T, η, and φ of the traversing probe-track. Compared to the J/ψ, the Z dimuon sample allows higher p T ranges to be explored. Overall, efficiency results are consistent between both the J/ψ and Z samples. Owing to energy losses in the traversed material there is a minimum momentum (or p T at a given η) threshold for muons to reach the muon detector. The p T threshold is GeV for the forward region and increases to 4 GeV in the central region. To reduce the effect of multiple scattering on the efficiency measurement and to assure the muon has the energy to further penetrate all the muon stations a requirement on the minimal p T (p) of the track probes is imposed. In the following, a common selection of p T > GeV was applied (except for the p T dependent measurement). The overall performance of the barrel DT system is summarized in Fig. 4, which shows the segment efficiency in each sector to be typically well above 9%. Figure 5 shows the segment efficiency computed for all barrel sectors and wheels of the MB2 DT stations as a function of the local x and z coordinates, respectively (where x is along the

31 5. Segment reconstruction efficiency in DT and CSC based on Tag-and-Probe methods 29 Figure 5: Segment reconstruction efficiency in the MB2 DT station. LEFT: as a function of local x, RIGHT: as a function of local z. Figure 6: Efficiency as a function of transverse momentum in the 4 barrel DT stations. The vertical line separates the ranges covered by probes originating from J/ψ (left) and Z (right) decays layer, normal to the beams, and z is along the beams). The observed efficiency matches very well the Monte Carlo expectations all the way to the edges of the chamber. Similar distributions have been obtained for all other barrel DT stations. Figure 6 shows the segment efficiency as a function of p T of the probe-track, for the 4 barrel DT stations. Figure 7 shows the segment efficiency as a function of p T, η, and φ of the probe-track, for 2 endcap CSC stations and the comparisons with MC results. The overall segment reconstruction efficiencies measured in the endcap (CSC) and barrel (DT) muon systems are summarized in Table 3. Here the systematic uncertainties are obtained by estimating the impact of the multiple-scatting effects on the probes: varying the distance between the position of the projected track onto the probe station and the position of the CSC segment by ± cm. varying the distance between the position of the projected track onto the probe station and the chamber edge by 3 to +5 cm.

32 3 5 Local reconstruction efficiency CSC Local Reconstruction Efficiency Pt (GeV/c) Data: Station 2 MC: Station 2 2 CSC Local Reconstruction Efficiency Data: Station 2 MC: Station η CSC Local Reconstruction Efficiency Data: Station 2 MC: Station φ Figure 7: Comparison between real data (red) and MC (blue) of the local reconstruction efficiency versus p T, η, and φ for endcap CSC station 2. The vertical line on the p T distribution separates the ranges covered by probes originating from J/ψ (left) and Z (right) decays The average expected deviation of the track (due to multiple scattering effects) is less than or on the order of the variations applied. In summary, the reconstructed segment efficiency determined using the tag and probe method with real data is at the level of 92 98% in all muon system stations with a systematic uncertainty of less than 2%. We see an overall good agreement between data and Monte Carlo simulation within the uncertainties. Table 3: Local segment reconstruction efficiency for stations, 2, 3, and 4 of the barrel (DT) and endcap (CSC) muon systems. DT Efficiency (%) CSC Efficiency (%) DATA(DT) MC(DT) DATA(CSC) MC(CSC) Station 9.9 ± ± ±.4 ± ±.2 ±.6 Station ± ± ±.4 ± ±.2 ±.8 Station ± ± ±.4 ± ±.2 ± 2.9 Station ± ± ±.8 ± ±.4 ± Efficiency measurements from inclusive single muons To avoid trigger biases in the muon sample, reconstruction efficiencies were measured by using single prompt muons reconstructed from a jet-enriched data sample. To avoid background biases from non-prompt (decay) muons and hadron punchthrough, a stringent muon selection is imposed, which is summarized in Table 4. The tracker part of the selected muon is propagated through the magnetic field and the detector materials to the muon chambers. This defines the probe used to measure the reconstruction efficiencies. If a reconstructed object (rechit or segment) is found near the track propagation point (an area defined by a cone of R <. aperture around the track) in a given station the probe is considered efficient. In the CSC system, the reconstructed signals are by construction a function of the incidence angle since the system is designed to be highly efficient for high p T tracks coming from the interaction region. Low p T tracks could have significantly different impact angles (after magnetic field and multiple-scattering effects) on a chamber. Increasing the selection cut on the p T of the probe track decreases the systematic uncertainty on the efficiency measurements but increases its statistical uncertainty. A compromise is in place. The selection applied is useful for getting a complete overall picture of the chamber performance, but it suffers from edge effects, which are never completely avoidable. To improve the

33 5.2 Efficiency measurements from inclusive single muons 3 Table 4: Criteria applied to select a muon probe for efficiency measurements in the muon endcap. Muons reconstructed in both the inner tracker and the muon system 2 p T > 6 GeV and 5 GeV < p < GeV (to minimize multiple scatterings and mis-reconstructions) 3 Muon consistent with coming from the interaction point (decays in flight, mis-reconstruction) 4 The presence of a minimum number of hits in the tracker part of the muon (quality of the momentum estimation) 5 The presence of hit(s) in the muon system for the muon fit (decays in flight, mis-reconstruction) 6 Good quality of the fits in the tracker and the overall tracker and muon systems 7 At least 2 stations penetrated by the muon (punch-through by pions and kaons, jets) 8 Only muon per (z) hemisphere 9 The investigated chamber should not be at the end point of the muon reconstruction, i.e., use interpolation only (except for the outermost station 4) quality of the probes, another tight requirement is applied on the point at which the probe trajectory penetrates the investigated chamber. The requirement is that it should be at least cm away from a chamber dead region (edges and high voltage boundaries). Although this effectively excludes from the measurements strips and wires close to these regions, it makes it nevertheless possible to measure the intrinsic chamber efficiencies. Figure 8 shows the rechit and segment efficiencies in these active regions for the CSC endcap stations and chambers. The segment efficiency is naturally defined per chamber as segments are built from the information of all (6) chamber layers. On the other hand, the rechit efficiency is defined per single chamber layer. Assuming that no correlation exists between layers (this assumption depends on the mechanism by which rechits are lost; for example, an inactive HV region could affect a single layer whereas an inactive cathode readout board could affect all 6 CSC layers) one can define the CSC chamber rechit efficiency as with an estimated uncertainty of ɛ = i ɛ i L ɛ = = i n i N L (6) ɛ ( ɛ) L N, (7) where L = 6 is the number of CSC layers, ɛ i is the efficiency in layer i (i =,.., 6), n i is the number of efficient probes for layer i, and N is the number of all probes traversing the chamber. With this method, the reconstruction efficiency is 96.4 ±.% and 97. ±.% for rechits and segments, respectively, averaged over all endcap CSCs (considering their active region; up to.5% systematic effect could be expected because of the excluded inactive regions, i.e., around edges and high voltage segments). These results include non-operating chambers and chamber regions which have been switched off as a result of hardware failures. Providing better precision, the results are in agreement with the Tag & Probe results.

34 32 5 Local reconstruction efficiency Figure 8: Reconstruction efficiency in active chamber regions (per chamber). LEFT: Segments, RIGHT: Rechits Rechit efficiency based on segment propagation 5.3. DT and CSC The hit reconstruction efficiency is measured using reconstructed local segments. In the absence of major hardware failures (HV faults, gas or readout problems), that may cause serious malfunctioning or signal losses in single cells or groups of cells, the signal production in different layers of the same chamber can be considered as a set of statistically independent processes. However, to reduce possible biases, a very loose selection quality was applied to the reconstructed segments in order to discard poor quality segments originating from fakes and background particles. In a barrel DT Φ (Θ) chamber layer, reconstructed segments were required to have at least 5 (3) hits, located in at least 4 out of 8 (3 out of 4) chamber layers, and a local inclination angle of φ < 4. In the endcap CSCs, segments were required to be close ( R < ) to a probe muon track as described in Table 4, and have at least 4 out of 6 layers. Using the set of hits associated with a reconstructed segment, the segment was fitted again, once per layer, each time discarding the hit present in that layer (if any). Therefore, the position of the segment in the layer under study is determined in an unbiased way. Two kinds of efficiencies were considered: the efficiency to find a reconstructed hit within a cell/chamber of the segment position, and the efficiency to actually associate a hit to the segment. The latter efficiency is by definition lower, as it includes the effects of the calibration and fitting procedures. Figure 9, left, shows both hit reconstruction and hit association efficiency as functions of the position in a DT cell. Apart from the known inefficiency induced by the cathode I-beams at the edges of the cell [4], the hit reconstruction efficiency is everywhere 99%. The hit association efficiency is, as expected, % 2% lower, as it depends on the details of the calibration and contributions from δ-rays. Indeed, because of the ns electronics dead time, δ-rays may cause an early hit that hides the good one. Finally, the hit association efficiency is higher in the central region of the cell, where the presence of strip electrodes make the drift field more linear []. Figure 9, right, shows the hit reconstruction and the hit association efficiencies as functions of position in the layer for a subset of DT MB chambers. The efficiency is constant along the layer and the cell structure is clearly visible. Overall, the hit reconstruction efficiency in the barrel DT system is on average 98%, whereas the association efficiency is 96%. Figure 2 shows the rechit efficiency in the endcap CSCs of station 2, ring 2, for all layers (but could be per layer) as a function of the local y coordinate (left) and the strip φ angle (right).

35 5.3 Rechit efficiency based on segment propagation 33 Figure 9: LEFT: Hit reconstruction (black) and hit association (red) efficiency as a function of the track position in the cell. RIGHT: Hit reconstruction (black) and hit association (red) efficiency as a function of the track position in a layer. Figure 2: CSC rechit reconstruction efficiency based on the segment propagation. LEFT: As a function of the local y (wire groups) coordinates, RIGHT: As a function of the strip φ coordinates The dead chamber regions located between the high voltage segments are clearly visible on the left plot. A slight inefficiency is observed at the boundaries between consecutive cathode readout boards (CFEB) in the φ efficiency plot (right). The rechit efficiency in the active CSC regions is well above 99.5%. The association efficiency is 97. ±.% for the 4 central (out of 6) layers and there is a small bias (< %) in the 2 outer layers related to the procedure of removing bad hits inside a segment RPC The barrel and endcap RPC systems are mainly used as trigger detectors; however they do contribute to the muon reconstruction by providing additional track space and time information to that provided by the DT and CSC systems in the barrel and endcap regions. Every RPC is located close ( behind ) to a DT or CSC and therefore the extrapolation of a segment reconstructed by the latter should point to a specific RPC strip and to a particular location within the strip. In a sense, an RPC can be considered as an additional DT or CSC layer. This allows the use of reconstructed DT and CSC segments as probes for determining the RPC efficiency and, more generally, study the hit cluster size, survey the chamber geometry, perform electronics connectivity tests, and address system alignment issues. Figure 2 provides a visualization of the technique explored. To validate this method, several

36 34 5 Local reconstruction efficiency Figure 2: Sketch of the segment extrapolation technique Monte Carlo simulations were performed, setting the RPC efficiency to different values and later measuring it with simulated data. The RPC hit reconstruction efficiency is defined as the probability of getting an RPC reconstructed hit when a muon is passing through the RPC under study. The efficiency is computed as the ratio between the expected number of hits, estimated from segment extrapolation, and the number of observed rechits. A match between the extrapolated DT or CSC segment and the RPC rechit is performed when the distance between the border of the RPC cluster that contains the rechit and the extrapolated point is less than 4 strips. This parameter was tuned to minimize subtle effects from strip masking (needed for some channels) inside clusters without introducing significant bias from noise. Only probes which are more than 8 cm away from the chamber edges are considered in order to completely avoid edge effects (e.g., Fig. 25). The efficiency and its error are defined by eqs. 4 and 5, but the probes here are the (DT, CSC) segments and the passing probes are segments matched to RPC hits. The expected rechit efficiency of the RPC system is 95%. The measured efficiency is shown in Fig. 22, separately for the barrel (left) and endcap (right) RPCs. In the course of the 2 datataking period, the tuning of the HV of the endcap RPC system led to significant improvement of the chamber efficiency as shown in Fig. 22, right. Figures 23 and 24 show the hit reconstruction efficiency for individual RPCs in the 5 barrel wheels and the 2 forward/backward endcaps, respectively. With the exception of a few nonoperating and unstable (low efficiency) chambers, the system has been performing according to expectations. Figure 25 shows a high resolution efficiency map for all the RB3 backward chambers in the barrel. Finally, Table 5 summarizes the average hit reconstruction efficiency measured in the RPC barrel and endcap stations. 5.4 Conclusions The CMS muon system has proved to have performed with remarkable stability during the 2 collision runs, with figures of merit matching the performance design. The efficiency for reconstructing local segments and hits is on average about 95% per station. Monte Carlo

37 35 Figure 22: Efficiency distribution per roll. LEFT: Barrel and RIGHT: Endcap. Rolls with known problems are excluded from the plot. Table 5: RPC local reconstruction, average efficiency per RPC chamber, the value in parenthesis is the RMS of the efficiency distribution. Efficiency (%) barrel endcap (5.37) (6.46) simulations confirm the observed behavior down to the fine details of the individual detector geometries and responses. The overall excellent local performance of the muon tracking systems represents the ideal starting point towards achieving the highest efficiency in reconstructing and identifying muons from decays of standard particles or from decays of the Higgs boson or other exotic candidates Alignment Precise measurement of muons up to the TeV momentum range requires the DT and CSC muon chambers to be aligned with respect to each other, and to the central tracking system, with an accuracy of a few hundred microns, comparable to their intrinsic spatial resolution. The RPC chambers are already aligned to the limit of their spatial resolution, which is about cm. The muon transverse momentum is measured from the curvature of tracks in the rφ plane. The precision on displacements in the rφ direction and rotations of chambers around their local axis parallel to z is therefore directly related to the momentum resolution. In these two degrees of freedom, the alignment system is designed to acheive a resolution of 4 µrad and 5 µm for MB and ME chambers, which have the largest weight on the muon momentum measure-

38 36 6 Alignment Figure 23: Efficiency of the barrel RPCs. Chambers are identified by sector and wheel. Figure 24: Efficiency of the endcap RPCs. Chambers are identified by station and ring. LEFT: negative endcap; RIGHT: positive endcap ment. Alignment in other degrees of freedom affects the momentum measurement as higherorder corrections. This section describes the current muon alignment and its performance. In order to determine the positions and orientations of the muon chambers, the CMS alignment strategy combines precise survey and photogrammetry information, measurements from an optical-based hardware alignment system, and the results of alignment procedures based on muon tracks. The muon hardware alignment consists of a Barrel and an Endcap system linked together and to the central tracker by a Link system. Details about the track-based and hardware-based alignment methods are given in references [5] and [6]. 6. Muon Barrel Alignment The DTs in the barrel have been aligned independently by the hardware alignment system and by the use of muon tracks. The current CMS reconstruction uses the results of the hardware alignment, which is based on rigid, radial carbon fibre structures (MABs) supported on the faces of the five wheels of the CMS iron yoke. A dedicated reconstruction program called CMS

39 6. Muon Barrel Alignment 37 Figure 25: Local efficiency map during LHC run 2 for all RB3 backward rolls barrel. The low efficiency points correspond to the location of the spacers in the gas gaps Object-oriented Code for Optical Alignment (COCOA) [7] is used to transform the various optical measurements into a reconstructed DT aligned geometry. The current implementation of the hardware barrel alignment performs a complete alignment of all DTs in stations, 2 and 3 in one single computation. Station 4 DTs are added in a second step to the resulting aligned structure from the previous calculation. The motivation for this factorization is two-fold: the computational problem becomes significantly simpler, allowing the reconstruction program to run much faster, and the knowledge of camera positions mounted on the MABs is less precise near the zone of the outer station, and therefore the internal barrel structure is essentially not affected by excluding station 4. Once all DTs and MABs are aligned relative to each other, the resulting barrel structure is treated as a floating rigid body which must be positioned and oriented in space with respect to the inner tracker. The 2 external barrel MABs (6 on each end of the barrel) are reconstructed independently by the barrel alignment system (in an arbitrary reference frame) and by the link system. An initial tracker barrel cross-alignment is therefore achieved by fitting the external MABs of the aligned, rigid barrel to the MAB positions determined by the link system. This cross-alignment is further refined by a track-based alignment method which uses internally aligned tracker and muon barrel systems and obtains their relative position and orientation using only a few tens of thousands of global muon tracks. 6.. Validation Alignment results must be validated before they can be used for track reconstruction and data reprocessing. The barrel alignment is validated by three independent cross-checks: comparison of photogrammetry measurements with alignment results obtained from measurements in the absence of magnetic field ( T), residuals of standalone muon segments extrapolated to a neighboring station, and comparison with an independent track-based alignment of chambers.

40 38 6 Alignment An estimate of the accuracy of the barrel alignment can be obtained by comparing the results from geometry reconstruction at T with photogrammetry measurements, in which all MABs and DTs in the same wheel are measured simultaneously. Care must be taken when comparing photogrammetry measurements, which are taken with an open detector, to alignment measurements after detector closing. Since wheels can move and tilt upon closing of neighboring structures, and since the same MABs are used to measure DTs sitting on different wheels, only the relative positions of DTs within each wheel can be expected to agree. For this reason, all comparisons are made independently for each wheel. Large disagreements between photogrammetry and alignment are expected to show clear trends which evidence an overall wheel movement between the two sets of measurements, as illustrated in Figure 26 (top) for YB+2. After correcting for this movement, the internal wheel structure can be compared, as shown in Fig. 26 (bottom). Table 6 shows the RMS of the differences in rφ and z for all DTs of Chambers on YB2 Fit of X' local of Chambers on YB2 Fit of Y' local [mm] X' local MB MB2 MB3 MB4 [mm] Y' local 5 5 MB MB2 MB3 MB Sector after the fit on YB2 Residuals of X' local Sector after the fit on YB2 Residuals of Y' local X' local -Fit [mm] RMS = 476 µm Y' local -Fit [mm] RMS = 826 µm Sector Sector Figure 26: Differences in rφ (left) and z (right) between photogrammetry measurements and barrel alignment at T for DTs in YB+2 before (top) and after (bottom) correcting for the relative overall wheel movement in each wheel between photogrammetry and alignment at T after factorizing out collective wheel movements. Table 6: The RMS of the differences in rφ and z for all DTs in each wheel between photogrammetry and barrel alignment at B = T after correcting for overall wheel movements. Barrel Wheel rφ RMS [µm] z [µm] RMS YB YB YB 7 99 YB YB Another way to test the barrel alignment is to make use of stand-alone muon tracks for which the momentum and trajectory are fitted using the aligned chamber positions. Track segments

41 6.2 Muon Endcap Alignment inside a given DT are extrapolated into the DT of the next station in the same wheel and sector, and the residuals between the extrapolated segments and the actual track segments are studied. Figure 27 shows the residual distributions for all such DT pairs for the four coordinates measured by DTs before and after alignment. In the absence of systematic effects, the means of these residuals are expected to be close to zero, while the RMS of the distributions get a contribution from the alignment precision (both for the overall chamber position and for the internal DT alignment) and from other tracking effects. The improvement of the residual distributions after alignment is clear. Figure 27: The difference before and after alignment between the measured and extrapolated stand-alone muon track segments going from one DT station to the next in the same wheel and sector for all such DT pairs in the four coordinates measured by DTs: local x, y, dx/dz and dy/dz Finally, the hardware and track-based alignment results are compared. Both alignments successfully reproduce the overall, large corrections needed with respect to the design geometry, in which all chambers are placed at their design position. These corrections are mostly due to vertical and axial compression of the wheels due to the huge gravitational and magnetic forces acting on them. Both alignments agree in rφ to the level of mm. 6.2 Muon Endcap Alignment The muon endcap was aligned using information from four different sources: photogrammetry, the Muon Endcap Alignment System, tracks from beam-halo muons, and tracks from collisions muons. Some of these sources measure the same alignment parameters in different ways, providing cross-checks between the different systems, while others do not. To combine information, alignment corrections were applied in a well-defined sequence, such that each step benefits from the previous. Potentially interdependent corrections were iterated to obtain a mutually consistent solution Measurement of disk bending with the Muon Endcap Alignment System The muon endcaps suffer a significant deformation when the solenoid is energized to its operating field intensity of 3.8 T. Some CSC chambers can move towards the center of the detector by as much as 4 mm, and they can rotate around their local x axis by as much as 3.5 mrad.

42 4 6 Alignment Figure 28: Schematic CSC chamber, indicating the local coordinate system The hardware endcap alignment system measures these movements using laser straight lines running nearly radially across each disk as described in detail in [6] Internal-ring alignment using beam-halo tracks CSC chambers overlap slightly along their edges, and muons passing through these narrow regions provide information about the relative displacement of the neighboring chambers. To produce a complete geometry from the pairwise chamber information, the following objective function is minimized: χ 2 = ( constraints (m ij A i + A j )2 + λ m ij σ 2 ij N chambers chambers i A i ) 2 (8) where A i are the chamber coordinates to optimize, m ij ± σ ij are the pairwise chamber measurements, and λ is a Lagrange multiplier to constrain the floating coordinate system. Two types of constraints are used: beam-halo tracks and photogrammetry measurements, with the latter applied only to pairs of chambers that were missing track data due to inefficient read-out electronics (4 out of 396 pairs of neighboring chambers). The alignment proceeds in alternating passes, first aligning rφ positions (A i are interpreted as positions and m ij are residuals), then φ z angles (A i are chamber angles and m ij are residuals-times-lever arm). The alignment fully converged after one rφ pass and one φ z pass. Although photogrammetry information was used to constrain a fraction of the chambers, much larger weights were given to the beam-halo data, in inverse proportion to the square of the measurement uncertainties in the two methods. As seen in Fig. 29, the level of agreement between the track-based technique and photogrammetry is.3.6 mm. This is much smaller than the typical scale of chamber corrections from design geometry (2 3 mm) Whole-ring placement using collisions muons To complete the endcap alignment, the internally aligned rings must be aligned relative to one another and the tracker. Tracks from the tracker were propagated to the muon chambers and whole-ring corrections were derived from the pattern of rφ residuals as a function of global φ. A constant offset in the residuals is interpreted as a rotation of the ring in φ z, while terms proportional to cos φ and sin φ are interpreted as displacements in global x and y, respectively. Figure 3 provides an example of an alignment fit for one ring (ME 2/). The alignment was performed in one pass, with a second iteration to verify self-consistency.

43 6.2 Muon Endcap Alignment 4 2 RMS.2577 RMS RMS ME/2 rφ aligned - rφ PG [mm] ME2/, 3/, 4/ rφ aligned - rφ PG [mm] ME2/2, 3/2 rφ aligned - rφ PG [mm] Figure 29: Chamber positions after internal-ring alignment compared with photogrammetry, split by ring. (ME/ chambers were not measured by the photogrammetry.) Figure 3: Residuals plot used to align a ring: the color scale is the residuals distribution versus φ, black points are a profile derived from truncated-gaussian peak fits in each φ bin, and red points are the average of peak-fits to muons and antimuons separately. The fitted curve is interpreted as three alignment degrees of freedom. Vertical dashed lines indicate the boundaries between chambers.

44 42 6 Alignment rφ residual [mm] ME+3/ to ME+4/ φ [rad] rφ residual [mm] ME+3/ to ME+4/ φ [rad] Figure 3: Residuals from beam-halo tracks used to cross-check the alignment performed with collisions. The symbols in these plots have the same meaning as Fig. 3, though residuals were calculated differently (see text). Left: before alignment. Right: after alignment using collisions (not beam-halo) To cross-check the alignment using a qualitatively different method, beam-halo tracks crossing an entire endcap (three or four stations, depending on distance from the beamline) were used to calculate residuals by extrapolating segmemts from one station to another. Figure 3 shows an example, in which ME+3/ segments were propagated linearly (no corrections for material or magnetic field) to ME+4/. These plots were not used to perform the alignment, so the fact that the strong φ trend observed before alignment is eliminated in the aligned geometry adds confidence to the result. 6.3 Alignment Impact of Physics Performance The most important test for any calibration or alignment is to study the effect it has on reconstructed quantities. In the case of muon alignment, higher-level objects related to muon tracks must be studied. It is important to keep in mind is that, by design, the momentum resolution is dominated by the central tracker for muons with transverse momentum below 2 GeV/c. A well-aligned muon system is therefore expected to induce minor beneficial changes at reconstruction level for low momentum global muons, and to improve global muon measurements for very energetic muons. Figure 32 shows distributions of muon-related quantities for low momentum muon tracks from pp collisions collected during 2. The solid red and dotted black distributions correspond to the aligned and design (no alignment corrections) muon chamber geometries respectively. From the top-left figure one can see that the alignment corrections induce an improvement in normalized χ 2 for global tracks. The top-right plot shows the difference in track curvature, q/p T, measured for the same muon when it is reconstructed as a global muon (including tracker information and therefore dominated by it) and as a standalone muon, which includes only muon chamber hits. This difference is indicative of the curvature resolution of the muon spectrometer (assuming the tracker resolution to be much better for low momentum muons). The bottom plots show an improvement in the dimuon mass resolution in the Z region. At least one standalone muon is required in order to see an improvement, since the invariant mass for pairs of global muons at these muon energies is completely tracker-dominated. In order to see the effect of the alignment on highly energetic muons, cosmic ray muons must be used, because there are currently very few muon tracks above 2 GeV/c from pp collisions. Cosmic muons collected in 2 traversing CMS from top to bottom are split into a top and

45 43 Figure 32: Muon track quantities reconstructed with design (black) and aligned (red) muon chamber positions. Top-left: normalized χ 2 for global muon tracks. Top-right: difference in q/p T between muons reconstructed as global and as stand-alone. Bottom: dimuon invariant mass for global-standalone muon pairs (left) and standalone-standalone muon pairs a bottom leg, and the momentum resolution is inferred from the difference in momentum measured for each leg separately. Figure 33 shows the q/p T resolution as a function of muon p T for muons reconstructed using the tracker plus the design and aligned muon geometries. Muons reconstructed using only the tracker are also shown for comparison. It can be seen that the aligned muon geometry improves the momentum measurement at energies above 2 GeV/c, where global muons begin to have a better resolution than tracker-only muons Calibration This section describes the procedures used in the extraction of the main calibration parameters that affect the performance of the CSC, DT and RPC sub-detector systems. Calibration constants are stored as conditions data. They are produced both online, directly from the detectors front-end electronics and by dedicated calibration algorithms run offline. The CMS conditions database [8] relies on three databases for storing non-event data: the OMDS (Online Master Database System) is in the online network at the detector site and stores the data needed for the configuration and proper settings of the detector and the conditions data produced directly from the front-end electronics; the ORCON (Offline Reconstruction Condition DB Online subset), also located at the detector site, stores all condition data that are needed at the HLT, as well as for detector performance studies; finally, the ORCOFF (Offline Reconstruction Condition DB Offline subset) is located at the CERN computing center (Tier-) and contains a copy of the information in ORCON. It is the database used for all offline processing and analysis. In order to provide a fast reaction to changing operation conditions, the calibration offline workflows profit from dedicated data streams, with reduced information, necessary to perform the calibration procedures [8]. They are available with very low latency and can be analyzed

46 44 7 Calibration rel. residual T Width of q/p. Tracker-only Global, design constants.8 Global, aligned constants p (GeV/c) T Figure 33: Gaussian width of the difference in q/p T between top and bottom reconstructed cosmics using design and aligned muon chamber positions compared to tracker-only reconstruction at the CERN Analysis Facility (CAF) for a prompt determination of new constants. 7. Cathode Strip Chamber system calibration Each CSC is trapezoidal in shape and has six gas gaps, each having a plane of radial cathode strips which are perpendicular to a plane of anode wires. All CSC s overlap in φ to avoid gaps in muon acceptance, except those in the third ring of the first endcap (ME/3). A charged particle traversing each plane of a chamber produces charge on the anode wire and an image charge on a group of cathode strips. The fast wire signal is used in the L Trigger, and the precision of the otherwise coarse position measurement is increased by determining the center of gravity of the charge distribution induced on the cathode strips. Spatial resolution for each chamber is about 2 µm, with angular resolution in φ of mrad. Calibration tests are performed on the CSC s themselves, as well as on the anode and cathode front-end electronics boards. These tests monitor the system stability, measure configuration constants which are to be downloaded to electronics modules, and provide calibration information required in the HLT and Offline reconstruction. The configuration constants include Anode Front-End Board (AFEB) discriminator thresholds and delays, Cathode Front-End Board (CFEB) trigger primitive thresholds and mode bits, as well as numerous timing constants for the peripheral crate electronics. The main monitoring parameters are the chamber noise, counting rates and channel connectivity. The calibration constants required for reconstruction relate to strip-to-strip crosstalk, strip channel noise and strip pulse-height gains. 7.. Calibration run modes and constants used in local reconstruction Two internal capacitors are incorporated on the 6-Channel Amplifier-Shaper ASIC (the BUCK- EYE chip) for each cathode amplifier channel, and one precision external capacitor is mounted on the CFEB board servicing a single BUCKEYE chip. Each capacitor can be used to generate a test pulse, and pulses are activated in parallel (broadcasted) so that pulses for calibration runs can be completed during beam injection. The amplifier linearity and offset, as well as tests to the amplifier saturation are determined by varying the test pulse amplitude incrementally, for every channel. The effect of cross-talk is estimated by injecting a fixed-sized pulse to each amplifier channel, and measuring the output on neighboring channels.

47 7.2 Drift Tube system calibration There are four crosstalk constants associated with a strip, which are labeled as the left crosstalk slope X SL, the left crosstalk intercept X IL, the right crosstalk slope X SR, and the right crosstalk intercept X IR. They describe the crosstalk via the expressions: X L (T) = X SL [5(T ) + T] + X IL + X o f f set X R (T) = X SR [5(T ) + T] + X IR + X o f f set X C (T) = X L (T) X R (T), (9) where T =, 2, 3 are the three time bins centred on the peak time bin, X o f f set is.3 ns, and T = 5t max t peak, with t max being the time bin containing the maximum ADC counts in the central strip and t peak the time found for the pulse in the central strip using a fit in time. The three values X L, X C, and X R are used to form a 3 3 matrix: X j C X j L X T = X j R X j C X j+ L X j R X j+ C 87 which describes the crosstalk coupling between a strip j and its neighbors j and j +. The observed charges, Q (Q L, Q C, Q R ), in a given time bin are then corrected as Q = XT 88 Q. 89 Each of the crosstalk-unfolded charges is summed over three time bins, and the resulting 9 charges are then used as input to the position calculation. 9 In order to measure the pedestals on each chamber strip, the amplifier output is sampled con- 92 tinuously at 2 MHz. For each strip and time sample, the average and RMS are calculated. For five charges Q i the covariance matrix elements C ij = Q i Q j Qi 93 Q j are determined 94 from which the mean and variance are extracted The pedestal-subtracted ADC values for all strips and all time bins, are corrected using the gains. Each ADC value is divided by a weight factor defined by W s = G s /G, where G s is the individual strip gain, and G is the average gain over all strips in the CSC system. The successive local maxima in the gain-corrected pulse height distribution of the strips in a chamber layer are used to build clusters of three strips each which are input to the local position reconstruction. 7.2 Drift Tube system calibration The basic element of the DT system is the drift cell, shown in Fig. 34. The cell has a transverse size of 42 3 mm 2 with a 5 µm diameter stainless steel anode wire at the center. The gas mixture (85%/5% of Ar/CO2) provides good quenching properties and a saturated drift velocity of about 54 µm/ns. The maximum drift time is 39 ns. Four staggered layers of parallel cells form a super-layer. A chamber consists of two super-layers measuring the r φ coordinates, with the wires parallel to the beam line, and an orthogonal super-layer measuring the r z coordinates. A schematic view of a chamber is shown in Fig. 34. Charged particles crossing a drift cell ionize the gas in its volume. The drift time of the ionization electrons is obtained by the time measured using a high performance Time to Digital Converter (TDC) [9], subtracted by a time pedestal. The time pedestal contains contributions from the latency of the trigger and the propagation time of the signal, within the detector and the data acquisition chain. The hit position, i.e. the distance of the muon track with respect to the anode wire is reconstructed as: x hit = t drift v drift ( t TDC t ped ) vdrift, ()

48 3 MB4 4 5 MB3 MB2 3 MB y x Calibration 9 4 Figure 2.3: Numbering of stations and sectors Figure 2.4: Section of a drift tube cell. Figure 34: Left: Schematic view of a DT chamber. Right: Section of a drift tube cell showing the drift lines and isochrones. the boundary of the cells and serve as cathodes. I-beams are insulated from the planes by a.5 mm thick plastic profile. The anode is a 5 µm stainless steel wire placed in the centre of the cell. The distance of the track from the wire is measured by the drift time of electrons produced by ionisation. To improve the distance-time linearity, additional field shaping is obtained with two positivelybiased insulated strips, glued on the the planes in correspondence to the wire. Typical voltages are +36 V, +8 V and -2 V for the wires, the strips and the cathodes, respectively. The gas is a 85%/5% mixture of Ar/CO 2, which provides good quenching properties and a saturated drift velocity, of about 5.4 cm/µs. The maximum drift time is therefore 39 ns, i.e. 5 bunch crossings. A single cell has an efficiency of about 99.8% and a resolution of 8 µm. Four staggered layers of parallel cells form a superlayer, which provides the where t TDC is the measured time, t ped the time pedestal and v drift the drift velocity, considered constant in the cell volume. The drift velocity depends on parameters such as the gas purity and the electrostatic configuration of the cell, the presence of a magnetic field within the chamber volume, and the inclination of the track. The working conditions of the chambers are monitored continuously []. The high voltage supplies have a built-in monitor for each channel; the gas is at room temperature and its temperature is measured on each preamplifier board inside the chamber; the gas pressure is regulated and measured at the gas distribution rack on each wheel, and is monitored by four further sensors placed at the inlet and outlet of each chamber. The adequacy of the flow sharing from a single gas distribution rack to 5 chambers is monitored at the inlet and outlet line of each individual chamber. A possible leakage in the gas line can be detected via the flow and the pressure measurements. Small gas chambers, called Velocity Drift Chambers (VDC) [2, 2] are located in the accessible gas room adjacent to the cavern, outside of the CMS magnetic field. They are used to measure the drift velocity in a volume of very homogeneous electric field. Each of these chambers is able to selectively measure the gas being sent to, and returned from, each individual chamber of the wheel thus providing rapid feedback on any changes due to the gas mixture or contamination. The average noise rate in the full DT system amounts to 8 Hz and corresponds to around. % of all DT channels. In general, no noticeable variation of the parameters described above is expected among different regions of the spectrometer. The magnetic field however varies substantially from chamber to chamber, as they occupy different positions in the return yoke, and affect the overall system behavior. 7.3 Time pedestal offline calibration The drift time is obtained from the TDC measurement after the subtraction of a time pedestal. In an ideal cell, the time distribution from the TDC (t TDC ) would have a box shape starting at zero, for muon tracks passing near the anode, up to about 39 ns, for those passing close to the cathode. In practice, different time delays, related to the trigger latency and the cable lengths to the read-out electronics contribute to the time measured by the TDC: t TDC = t drift + t wire + t L + t TOF + t prop, () 43 where the different contributions to the time pedestal can be classified as:

49 7.3 Time pedestal offline calibration t wire, the channel-by-channel signal propagation time to the read-out electronics, relative to the average value in a chamber; it is referred to as inter-channel synchronization, since it is used to equalize the response of all the channels within a chamber; t L, the latency of the Level- trigger; t TOF, the time-of-flight (TOF) of the muon produced in a collision event, from the interaction point to the cell; t prop, the propagation time of the signal along the anode wire. The inter-channel synchronization (t wire ) is determined by test-pulse calibration runs. It is a fixed offset, since it only depends on the cable/fiber lengths. The design of the data acquisition system allows test-pulse runs to be taken during normal physics data taking, by exploiting the collision-free interval of the LHC bunch structure, or abort gap. A test pulse is simultaneously injected in four channels of a front-end board, each from a different layer in a super-layer, simulating a muon crossing the detector. The same test pulse signal is also distributed to other four-channel groups, 6 channels apart, such that the entire DT system is scanned in as many cycles. The remaining contribution to the time pedestal is extracted for each super-layer from the data. It is computed as the turn-on point of the TDC time distribution (see [22, 23]), previously corrected for the inter-channel synchronization; channels identified as noisy are not considered. It is referred to as t Trig, since it is dominated by the Level- trigger latency, and includes the contributions from the average time-of-flight, roughly corresponding to muons reaching the center of the super-layer, as well as the average signal propagation time along the anode wire, taken from the center of the wire to the front-end board. The correction for the propagation time along the wire, and the muon time-of-flight to the cell, is done at the reconstruction level, after the 3D position of the track segment is known [5]. The segment is built in a multi-step procedure. First the reconstruction is performed in the r φ and r z projections independently. Once the two projections are paired, the segment position inside the chamber can be estimated and the drift time is further corrected for the propagation time along the anode wire and for the time-of-flight from the center of the super-layer; the 3D segment is then updated. An additional correction to the t Trig pedestal is calculated using the hit position residuals. The residuals are computed as the distance between the hit position and the intersection of the 3D segment with the layer plane, reconstructed as described above. This procedure aims at removing the bias introduced in the definition of the turn-on point of the TDC time distributions. The offset in the mean of the residual distribution, for each super-layer, is used as an estimate (divided by the drift velocity) of the correction which is added to the time pedestal (subtracted from the drift time reconstruction); this procedure is repeated iteratively until the bias is fully removed. The t Trig values derived from a representative subset of the 2 collision data are shown in the left panel of Fig. 35, for the first r φ super-layer (SL) in each chamber of the DT system. Similar values are obtained for all super-layers Drift velocity calibration The drift velocity depends on many parameters: the gas purity and the electrostatic configuration of the cell, the presence of a magnetic field within the chamber volume, and the inclination of the track. The value used in the hit reconstruction (see Eq. ) is an average computed for each super-layer in the DT system. Two methods have been used to estimate the drift velocity: the first is based on the mean-time

50 48 7 Calibration (ns) t Trig MB MB2 MB3 MB4 (µm/ns) v drift MB MB2 MB3 MB Wheel Wheel Wheel 2 Wheel - Wheel -2 MB Wheel Wheel Wheel 2 Wheel - Wheel -2 MB2 Wheel Wheel Wheel 2 Wheel - Wheel -2 MB3 Wheel -2 MB4 Wheel 2 Wheel Wheel Wheel - 53 Wheel Wheel Wheel 2 Wheel - Wheel -2 MB Wheel Wheel Wheel 2 Wheel - Wheel -2 MB2 Wheel Wheel Wheel 2 Wheel - Wheel -2 MB3 Wheel -2 MB4 Wheel 2 Wheel Wheel Wheel - Figure 35: Left: Time pedestal computed for all chambers in the DT system. Only values corresponding to the first r φ super-layer (SL) in each chamber are shown. Right: Drift velocity for all chambers in the DT system. Chambers belonging to the same station and wheel were merged in the drift velocity computation technique (see e.g. [22]) while the second relies on the track fit in the local muon reconstruction in a chamber [5]. In the mean-time method [22], the maximum drift time in a cell, T max, is calculated from the drift time at nearby cells in three adjacent layers. In general, T max depends on the track inclination and on the pattern of cells crossed by the track. A linear approximation is used to determine the drift velocity, v eff drift = L semi-cell <T max >, where L semi-cell = 2. cm is half the width of a drift cell. The drift velocity obtained with the mean-time method depends directly on the measured drift time and hence on the time pedestal. Conversely, the time pedestal (see Sect. 7.3), corrected from the mean of the hit residual distributions, is itself dependent on the drift velocity value used in the hit position computation (Eq. ) and the two parameters cannot be fully disentangled. An alternative method for computing the drift velocity relies on the full reconstruction of the trajectory within the muon system (see [23]). A track is reconstructed under the assumption of the nominal drift velocity (v drift = 54.3 µm/ns) and in a second step is refit treating as free parameters the drift velocity and the time of passage of the muon through the chamber. The drift velocity is taken as the mean value of the track-by-track drift-velocity distribution. The method is applied to the r φ view of the track segment in a chamber [5], where up to eight hits can be assigned to the track. The r z super-layers, where only four points are available, cannot, however, profit from this method. The right panel of Fig. 35 shows the drift velocity values obtained for each chamber in the DT system (corresponding to r φ super-layers), from a subset of the 2 collision data. Since the drift velocity is not expected to vary substantially among different sectors, the distributions corresponding to all chambers in each station were merged thus yielding a constant value per station. A clear shift is observed in the external wheels of the innermost station (MB), where the magnetic field is stronger. 7.4 Validation & monitoring of calibration constants A detailed validation is performed in order to assess the quality and monitor the stability of the calibration constants. For each new calibration set, a comparison to previous constants is carried out and the impact on the reconstruction performance is analyzed. The CMS Data Quality Monitoring (DQM) framework [24] is used throughout the validation procedure.

51 7.4 Validation & monitoring of calibration constants The impact of the calibration in the local muon reconstruction is studied by analyzing the hit position residuals. The hit position resolution in the CSC system is shown in Fig. 36, for each Muon Endcap. The effect of changing calibration constants calculated before and after extended run periods on the hit position distributions in each ME has been shown to be very small; testing and validation of new constants is performed regularly and possible changes due to the effect of calibration are closely monitored. The local hit reconstruction in the DT system is directly dependent to variations in the time pedestal, as well as the drift velocity calibration; while they remain mostly stable, small changes in the system are accounted for with new calibration constants, thus providing an improved chamber performance. Figure 37 shows the mean and width as extracted from a Gaussian fit to the core of the hit residual distributions from a subset of the 2 collision data, for the first r φ super-layer (SL), in each DT chamber. The mean values are well centered around zero, after the correction to the time pedestal outlined in Sect. 7.3; similar values are obtained in the entire system. The estimated resolution is within 3 µm for r φ super-layers and slightly worse at the outermost station (MB4), as well as for r z super-layers, where the drift velocity has not been optimized. Average Position (cm) /2 -/3 -/4-2/ -2/2-3/ -3/2-4/ +/ +/2 +/3 +/4 +2/ +2/2 +3/ +3/2 +4/ +4/2 CSC Muon Endcap Figure 36: Mean value of hit positions with error bars corresponding to resolutions in each of Muon Endcaps. Mean of residuals (cm) MB MB2 MB3 MB4 Sigma of residuals (cm) MB MB2 MB3 MB Wheel Wheel Wheel - Wheel -2 MB Wheel Wheel 2-2 MB2 Wheel Wheel Wheel - Wheel Wheel 2-2 MB3 Wheel Wheel Wheel - Wheel Wheel 2-2 MB4 Wheel 2 Wheel Wheel Wheel - Wheel Wheel Wheel - Wheel -2 MB Wheel Wheel 2-2 MB2 Wheel Wheel Wheel - Wheel Wheel 2-2 MB3 Wheel Wheel Wheel - Wheel Wheel 2-2 MB4 Wheel 2 Wheel Wheel Wheel - Figure 37: Mean values of hit position residuals and resolution for all chambers in the DT system. Only values corresponding to the first r φ super-layer (SL) in each chamber are shown.

52 5 8 Data Quality Monitoring Data Quality Monitoring The primary goal of CMS data quality monitoring (DQM) [37] is to maximize the amount of high quality data by detecting problems as early as possible. DQM for the muon detectors focuses on monitoring the efficiency of the detectors, primarily determined by rates of readout errors, and the distribution of hits across the detectors. Additional monitoring plots are available to investigate issues more deeply. DQM checks are made online and offline. The online checks provide fast response to obvious problems unpowered regions, problems with data acquisition, or improper calibrations and a first evaluation of the suitability of the data. The offline checks use the information available from full event reconstruction with calibration, and different trigger paths to provide a more detailed evaluation of the data. Offline DQM is used to certify the quality of reconstructed data and validate calibration results, software releases, and simulated data. The DQM infrastructure provides tools for creation, filling, storage, and visualization of histograms and scalar elements. D-, 2D-, and 3D-histograms, D- and 2D-profiles, integers, floats, and string messages can be booked, filled, and updated anywhere in the analysis code. The infrastructure also offers functionalities to perform statistical tests and automated certification. 8. Operational Procedures In 2, CMS went to central shift crew operation of the detector. The shift crew is responsible for ramping the muon chamber high voltage (HV) after beam injection, bringing down the HV when beams are dumped, and similarly ramping up and down during cosmic ray data taking. Procedures were established for the conditions under which HV can be ramped up and down, and steps to follow when a problem is encountered. 8.2 Online Monitoring Online monitoring of data quality is part of the central shift crew duties. A special stream of events is used to perform DQM operations online [38]. The stream contains detector and trigger raw data, level-one and high level trigger (HLT) summary results, in addition to HLT by-products essential for monitoring trigger algorithms. Events are delivered to data quality applications at about Hz. Delivery speed strongly depends on the rate with which subsystem application process event data. There is no event sorting or handling, and no guarantee parallel applications receive the same events. We check for readout errors in the raw data stream, occupancy of detector channels, and the rates of muon trigger primitives. Catching readout errors is a vital and unique part of the online monitoring. For example, format errors in the data stream can indicate that the detector readout is out of synchronization with the level-one trigger accepts, or that a rapid sequence of trigger accepts has overflowed the readout buffers. These and a multitude of other possible errors are monitored during running. The readout system can tolerate and recover from periodic errors, but persistent errors indicate a problem that needs expert attention. There are differences in specifics between the three subdetector types of the muon system, but the basics are the same. At this stage, data are declared good if a large fraction of the detector channels register hits. A small number of readout errors is tolerated. If there are problems, the shifter can consult more detailed information to diagnose the problem. Detector experts are called to resolve potential problems as soon as possible.

53 8.2 Online Monitoring 5 Figure 38: DQM workflows for online (a) and offline (b).

54 52 8 Data Quality Monitoring Histograms aggregating information from the detectors and procedures for using them to evaluate muon system operational integrity have been developed for the shift crew. Examples of the aggregated status summary for the DT and CSC systems are shown in Fig. 39. The components of the system are shown in a condensed form with a simple color coding: green for good, red for bad, white for off, and grey for not installed The overall status flag in the upper right of the CSC summary is generated automatically based on criteria determined by the subsystem. Figure 39: Top level histogram of the DT (left) and CSC (right) online DQM. The subsystems demonstrates GOOD performance status, with a majority of the subdetectors registering hits. Wheel or disk identifiers appear on the left, and the sector numbers (DT) appear along the bottom, or chamber numbers (CSC) within the boxes. Green chambers are good, red indicates a problem, white are disabled, and gray chambers are foreseen as an upgrade An example of the RPC system aggregated status summary is displayed in Fig. 4. The color coding indicates the fraction of each sector that is reporting data correctly, with color coding indicated by the bar on the right. The summary on the left reports the percentages numerically, and the top line shows the aggregate for the system, 96.7% in this case, sufficiently high for these data to be considered good. Figure 4: The automated certification results for RPCs as displayed by the DQM GUI. The barrel (wheel) and endcap (disk) stations are labeled along the bottom.

55 8.3 Offline Monitoring 53 Table 7: Summary of the system operational performance during 2. DT CSC RPC fraction of luminosity sections passing DQM 99% 99.7% 99% fraction of system operational 99.6% 98% 98% fraction of runs with stable beams passing DQM 99% 99.8% 97% Offline Monitoring Offline DQM, schematically represented in Fig. 38(b), runs as part of the reconstruction process at Tier-, of the re-reconstruction at the Tier-s, and of the validation of software releases, simulated data, and alignment and calibration results. Here we focus specifically on the DQM performed on newly acquired data. Offline DQM of reconstructed data is carried out first by offline DQM shifters, then by members of the subdetector groups, normally with a latency from a few days to a week. Standard data certification checks the readout errors and detector occupancies again, as done in the online checks, but in greater detail. We can now look at reconstructed data from the minimum bias stream, single-muon trigger stream, or dimuon trigger stream. Except at the very low luminosities of early LHC operation, the minimum bias event rate is small, often yielding poor statistics for judging detector performance. But the higher rate muon trigger events exhibit patterns in detector occupancy related to the interaction of the muon trigger system and the detector. Investigation of these effects leads to a deeper understanding of the detector performance. Additional sources of information are available to aid the experts in the final pronouncement on data quality. These include logbooks for the subsystems, the insights of field managers and hardware experts, and information from full event reconstruction. In addition, the DT and CSC systems monitor segment related information. Monitored quantities include: the distribution across the detector of the rate of reconstructed segments the distribution of residuals between hits and reconstructed segments (mean and sigma) the efficiency of matching hits to segments and/or matching segments to standalone tracks timing of hits and segments gas gain and noise in the chambers As an example, the overview in Fig. 4 shows the DT frame with plots to be checked by the off line shifter for data taken the end of October Muon Performance in 2 The muon system performed extremely well during the 2 campaign. Generally, greater than 9% of the channels were operational, and the systems produced high quality data for nearly all collision runs. These results are summarized in Table 7. The problems that affected data quality varied; the most common related to integrating the muon system into CMS detector operation. The muon system contributed negligibly to CMS downtime in 2, much less than %.

56 54 8 Data Quality Monitoring Figure 4: DQM GUI screen shot of DT frame with the DQM plots chosen to discriminate the quality of the data taken by DT, for a reference run with high statistics taken during the last period of data taking in 2. The plots show: the summary of segment occupancy by wheel and sector (upper left); the means (upper right) and sigmas (lower left) of the segment-hit residuals distributions for each chamber; and the segment efficiency summary (lower right).