Performance of the ATLAS muon trigger in pp collisions at √ s = 8 TeV

The performance of the ATLAS muon trigger system is evaluated with proton–proton collision data collected in 2012 at the Large Hadron Collider at a centre-of-mass energy of 8TeV. It is primarily evaluated using events containing a pair of muons from the decay of Z bosons. The efﬁciency of the single-muon trigger is measured for muons with transverse momentum 25 < p T < 100GeV, with a statistical uncertainty of less than 0.01% and a systematic uncertainty of 0.6%. The p T range for efﬁciency determination is extended by using muons from decays of J /ψ mesons, W bosons, and top quarks. The muon trigger shows highly uniform and stable performance. The performance is compared to the prediction of a detailed simulation.


Introduction
Muons in the final state are a distinctive signatures of many physics studies performed using collisions of high energy protons at the LHC.These studies include the discovery and measurements of the Higgs boson, searches for new phenomena, as well as measurements of Standard Model (SM) processes, for instance of the electro-weak bosons, top quarks, heavy flavour resonances.Therefore, a high-performance muon trigger is essential.The ATLAS muon trigger system is designed to select muons in a wide momentum range with high efficiency.The selection is performed in three steps [1].Signals from the fast-response muon trigger detectors are processed by custom-built hardware to generate a Level 1 (L1) trigger.The next step is performed in the High Level Trigger (HLT), which is software-based and is subdivided into the Level 2 (L2) trigger and the Event Filter (EF).The L2 trigger performs a fast reconstruction of muons with simple algorithms.Then the EF makes use of the offline muon reconstruction algorithms to refine the trigger decision by utilising full detector information.
The ATLAS experiment collected proton-proton collision data in 2012 at a centre-of-mass energy of 8 TeV with a maximum instantaneous luminosity of 7.7 • 10 33 cm −2 s −1 .The number of interactions occurring in the same bunch crossing (called pile-up interactions) was about 25 on average.In order to address a wide variety of physics topics in this challenging environment, a suite of muon triggers were deployed.The single-muon trigger with the transverse momentum (p T ) threshold of 24 GeV is used in many physics analyses.In addition, muon triggers in combination with electrons, jets and missing transverse momentum, as well as moderatep T multi-muon triggers, increase sensitivity for various physics topics which benefit from a lower p T threshold.For the B-physics program, various low-p T multi-muon triggers are used with a special configuration that allows a high efficiency also for non-prompt muons.
In this paper the performance of the ATLAS muon trigger is evaluated, primarily using samples containing muon pairs from Z boson decays.The performance of the low-p T muon trigger is evaluated with samples containing a pair of muons from the decay of J/ψ mesons.The performance for high-p T muons is evaluated using events containing top quarks 1 or W bosons, where a W boson decays into a muon and neutrino.

ATLAS detector
The ATLAS detector is a multi-purpose particle physics apparatus with a forward-backward symmetric cylindrical geometry and near 4π coverage in solid angle. 2  The detector consists of four major sub-systems: the inner detector (ID), electromagnetic calorimeter (ECal), hadronic calorimeter (HCal) and muon spectrometer (MS).A detailed description of the ATLAS detector can be found in Ref. [2].The ID measures tracks up to |η| = 2.5 in an axial magnetic field of 2 T using three types of sub-detectors: a silicon pixel detector closest to the interaction point, a semiconductor tracker (SCT) surrounding the pixel detector, and a transition radiation straw tube tracker (TRT) covering |η| < 2.0 as the outermost part of the ID.The calorimeter system covers the pseudorapidity range |η| < 4.9 and encloses the ID.The high-granularity liquid-argon electromagnetic sampling calorimeter is divided into one barrel (|η| < 1.475) and two endcap components (1.375 < |η| < 3.2).The hadronic calorimeter is placed directly outside the ECal.An iron scintillator/scintillator-tile calorimeter provides hadronic coverage in the range |η| < 1.7.The endcap and forward regions, spanning 1.5 < |η| < 4.9, are instrumented with liquid-argon calorimeters.The calorimeters are then surrounded by the MS.

Muon spectrometer
The MS is based on three large air-core superconducting toroidal magnet systems (two endcaps and one barrel) providing an average magnetic field of approximately 0.5 T. Fig. 1 shows a quarter-section of the muon system in a plane containing the beam axis.The deflection of the muon trajectory in the magnetic field is detected using hits in three layers of precision drift tube (MDT) chambers for |η| < 2. For η in the region 2.0 < |η| < 2.7, two layers of MDT chambers in combination with one layer of cathode strip chambers (CSCs) are used.Muons are independently measured in the ID and in the MS.Three layers (called stations) of resistive plate chambers (RPCs) in the barrel region (|η| < 1.05), and three layers (called stations) of thin gap chambers 2 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the z-axis along the beam pipe.The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upward.Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the beam pipe.The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2).(TGCs) in the endcap regions (1.05 < |η| < 2.4) provide the L1 muon trigger.

Level-1 muon trigger
Muons are identified at L1 by the spatial and temporal coincidence of hits either in the RPC or TGC trigger chambers pointing to the beam interaction region [1,2].The degree of deviation from the hit pattern expected for a muon with infinite momentum is used to estimate the p T of the muon with six possible thresholds.The number of muon candidates passing each threshold is used in the conditions for the global L1 trigger.Following a global trigger, the p T thresholds and the corresponding detector regions (called Region of Interest (RoI) information) are then sent to the HLT for further consideration [1,2].The typical dimensions of the RoIs are 0.1 × 0.1 (0.03 × 0.03) in ∆η × ∆φ in the RPCs (TGCs) [2].The geometric coverage of the L1 trigger is about 99 % in the endcap regions and about 80 % in the barrel region.The limited geometric coverage in the barrel region is due to gaps at around η = 0 (to provide space for services in the ID and calorimeters), the feet and rib support structures of the ATLAS detector and two small elevator shafts in the bottom part of the spectrometer.

Level-2 muon trigger
The RoI information given by L1 enables the L2 algorithms to select the region of the detector in which the interesting features reside, therefore reducing the amount of data to be transferred and processed [1].The L2 muon standalone algorithm constructs a track (called L2 SA muon) by using the data from the MDT chambers [3].To achieve the needed resolution in sufficiently short time, the p T of the L2 SA muon is reconstructed with simple parameterised functions.An algorithm called L2 CB [3] then combines the L2 SA muon with a track found in the ID.This algorithm selects the closest ID track in the η and φ planes as the best matching track, and refines the p T value by taking the weighted average between those of the L2 SA muon and the ID track (called the L2 CB muon).

Event Filter muon trigger
Muons in the EF are found by two different procedures.
The first focuses on regions of interest defined by the L1 and L2 steps described above and is referred to as the RoI-based method.The second procedure searches the full detector without using the information from the previous levels and is referred to as the full-scan method.
The RoI-based method is implemented with two independent algorithms.Muon candidates are first formed by using only the muon trigger and precision chambers (called EF SA muons), and are subsequently combined with ID tracks (called EF CB muons).This is called the outside-in algorithm.The other algorithm, called the inside-out algorithm, extrapolates ID tracks to the muon detectors to search for corresponding track segments, and forms EF CB muons.These two algorithms were used such that the outside-in algorithm is run first and, if it fails, it is subsequently complemented by the inside-out algorithm.In this way, the highest efficiency is obtained with the least processing time.Additionally, the degree of isolation for the EF CB muon is quantified by summing the p T of ID tracks with p T > 1 GeV found in a cone of ∆R = (∆φ) 2 + (∆η) 2 < ∆R cut , centred around the muon candidate after subtracting the p T of the muon itself (Σ ∆R<∆Rcut p trk T ).The full-scan procedure is used in the EF to find additional muons that are not found by the RoI-based method.In the full-scan muon finding, EF SA muon candidates are first sought in the whole of the muon detectors, and then ID tracks are reconstructed in the whole of the ID detectors.Combined pairs of these ID and MS tracks form muon candidates (called EF FS muons).

Trigger logic
The trigger system is configured to use a large set of selection criteria for each event.Each criterion is referred to as a chain because it consists of sequential selections at L1, L2 and EF.The set of all the chains that an event can satisfy to be selected is called a menu.
In the data recorded in 2012 (called 2012 runs), the six programmable p T thresholds of the L1 trigger were set as MU4, MU6, MU10, MU11, MU15 and MU20, where the number after MU denotes the p T threshold in GeV.The thresholds are optimised to give an efficiency at the designated threshold that is typically 95 % of the maximum efficiency achieved well above the threshold.The L1 triggers generated by hits in the RPCs require a coincidence of hits in the three layers (three-station coincidence) for the MU11 and higher thresholds, and a coincidence of hits in two of the three layers (twostation coincidence) for the rest of thresholds.The L1 triggers generated by hits in the TGCs require a threestation coincidence for the MU6 and higher thresholds. 3able 1 shows the single muon trigger chains which were used without a prescale 4 for the all 2012 runs.The chain mu24i is designed to collect isolated muons with p T > 25 GeV with a loose isolation criterion of Σ ∆R<0.2 p trk T /p T < 0.12.The chain mu36 is designed to collect muons with large p T without making an isolation requirement.The chain mu40 SA barrel is designed to recover possible inefficiency due to MS and ID combination at large p T , and the decision is based only on MS reconstruction.It was active only in the barrel region due to its high rate in the endcaps.
Table 2 shows the sequence of the multi-muon trigger chains which were used without a prescale during the 2012 runs.The chain 2mu13 requires two or more muon candidates, each of which passes a single-muon trigger mu13 chain at all three levels of the trigger.The chain mu18 mu8 FS requires at least one muon candidate which passes a single-muon trigger mu18 chain at all three levels of the trigger, and subsequently employs the full-scan algorithm at the EF to find two or more muon candidates with p T > 18 and p T > 8 GeV for leading and sub-leading muons.The choice of the leading p T cut of 18 GeV is driven by computing resource limitations to invoke the full-scan muon finding.The chain 3mu6 requires three or more muon candidates, each of which passes a single-muon trigger mu6 chain at all three levels of the trigger.

Operation in the 2012 runs
The typical maximum L1 trigger rate was 70 kHz, which was reduced at the EF to 700 Hz on average (with peaks of about 1 kHz).Of those rates, the single lepton trigger mu24i was about 8.5 kHz at L1 and about 65 Hz at the EF at an instantaneous luminosity of 7×10 33 cm −2 s −1 .Fig. 2 shows the trigger rates of the single-and multimuon trigger chains.The rates are shown as a function of the instantaneous luminosity, separately for the L1 and EF levels.They are well described by a linear fit with an intercept being approximately zero.This indicates a negligible contribution from effects not related to pp collisions.The rates were reduced by a factor of 28 at L2 (with respect to L1) and by a factor of 4.6 at the EF (with respect to L2) for the mu24i trigger.The rates for the 2mu13 trigger were reduced by a factor of 71 at L2 and by a factor of 1.2 at the EF.
The typical processing time of the HLT was 75 ms/event at L2, and was 1 s/event at the EF.As measured in a typical high luminosity run, the muon HLT algorithms took 5.6 ms/call for L2 SA, 7.7 ms/call for L2 CB (including L2 ID tracking), 260 ms/call for EF CB (including EF ID tracking), and 3 s/call for EF full-scan (including EF full scan ID tracking).
During data taking, the performance of the muon trigger was monitored in two stages.For quick online checks during data taking, the coverage in η-φ space and the distributions of some kinematic variables were produced by the HLT algorithms.A more detailed analysis was performed by calculating efficiencies of trigger chains during the reconstruction stage of the prompt data processing.

Data samples and event selection
Several methods are used to measure the muon trigger performance.This section describes the selection requirements used to define the samples needed for the various methods.

In situ methods to measure trigger performance
The tag-and-probe method relies on a pair of muons.If one muon has caused the trigger to record the event (called the tag muon), the other muon serves as a probe (called the probe muon) to measure the trigger performance without any bias.This method was applied to dimuon decays of Z boson and J/ψ meson candidates.Alternatively, muons contained in events that were recorded by triggers other than the muon trigger can be used as an unbiased sample to evaluate the efficiency of triggering on muons.This method was applied to events with muons from W decay, either from top-quark or W + jets production.A trigger on the missing transverse momentum, as measured with the calorimeter, was used to collect such samples.
Among these four samples, the tag-and-probe method using Z decays provides the most precise determination of the efficiency over a wide range of p T (10 p T 100 GeV).The tag-and-probe method using J/ψ decays provides a coverage for a lower p T region sample (p T 10 GeV).The top-quark and W with jets productions provide supplemental coverage at very high p T (p T 100 GeV).Systematic cross checks on the efficiency dependence due to the underlying physics pro-  cess are evaluated by comparing these different methods.

Data and Monte Carlo samples
Data were considered if recorded under stable beam conditions and with all relevant sub-detector systems fully operational.The trigger performance observed in the data is compared with the ATLAS Monte Carlo (MC) simu-lation, which is the same simulation as used for physics analysis.MC samples were generated and then processed through a simulation of the ATLAS detector based on Geant4 [4,5].The environmental backgrounds due to radiation were not simulated.The simulated events are overlaid with additional minimum-bias events generated with Pythia 8 [6] to account for the effect of pile-up interactions and reweighted to match the distribution of the average number of pile-up interactions in data.
An MC sample of Z boson events was generated using Powheg-box [7] interfaced to Pythia 8.An MC sample of the production of J/ψ mesons decaying to muon pairs was generated using Pythia 8, requiring at least two muons in the final state having p T > 15 and 2.5 GeV.An MC sample of top and antitop quark pair (t t) events was generated using Powheg-box interfaced to Pythia [8].The MC t t sample was normalised to the cross section calculated at next-to-nextto leading order (NNLO) in QCD including resummation of next-to-next-to-leading logarithmic (NNLL) soft gluon terms [9][10][11][12][13][14]. MC samples of single top-quark (single-t) events were generated using AcerMC [15] interfaced to Pythia for the t-channel production, and using Powheg-box interfaced to Pythia for the sand W t-channel production.The single-t production MC events were normalised to the NNLO cross sections [16][17][18].MC samples of W boson production were generated using Alpgen [19] interfaced to Pythia.The MC sample of W events was normalised to the NNLO cross section [20,21].MC samples of dijet events are used for background estimation, and were generated using Pythia 8.

Offline reconstruction
The offline reconstructed muons are constructed by matching tracks found in the MS with those in the ID [22].Muons are required to pass various cuts to ensure a high quality ID track and to be in a fiducial region of |η| < 2.5.The muon momentum is calibrated by comparing the dimuon mass of Z boson candidates measured in data and MC.
The identification and reconstruction of the electrons, jets, jets containing b-quarks (called b-jets), and missing transverse momentum (E miss T ) are necessary for the efficiency measurement with t quarks and W bosons.
Electron candidates [23,24] are required to satisfy E el T > 25 GeV and |η el | < 2.47 excluding 1.37 < |η el | < 1.52, where E el T is the transverse energy, and η el is the pseudorapidity of the cluster in the calorimeter.Candidates are required to be isolated by means of calorimeter-and track-based isolation requirements [25].
Jets are reconstructed using the anti-k t jet clustering [26] algorithm with a radius parameter R = 0.4, running on three-dimensional clusters of cells with significant calorimeter response [27].Their energies have object-based corrections applied as well as corrections for upstream material, non-instrumented material, and sampling fraction.Jets are required to satisfy p jet T > 25 GeV and |η jet | < 2.5, where p jet T is the transverse momentum, and η jet is the pseudo-rapidity of the jet.Jets with p jet T < 50 GeV and |η jet | < 2.4 are required to pass pile-up suppression cuts based on the fraction of the summed track p T that originated from a nonprimary vertex.Duplication between electron and jet objects is avoided by removing the jet closest to an electron if their separation is ∆R < 0.2.
The b-jets are identified among the reconstructed jets with an artificial neural network using variables that exploit the impact parameter, the secondary vertex and the topology of b-and c-hadron weak decays [28].An identification criterion with 70 % efficiency is chosen, as evaluated on jets in a simulated t t sample with p T > 20 GeV and |η| < 2.5.
The E miss T is calculated using the reconstructed jets, electrons, muons, τ leptons, photons, as well as calorimeter energy clusters not associated with these physics objects [29].
In this paper, reconstructed objects (reconstructed using algorithms applied after the event is recorded) are distinguished from trigger objects (objects formed either at L1, L2, or the EF during the fast online reconstruction of the event).

Event selection for the Z sample
Events are required to pass either an isolated singlemuon trigger mu24i or a single-muon trigger mu36.
A pair of oppositely charged muons with invariant mass consistent with the mass of the Z boson, |m Z − m µµ | < 10 GeV, is required.The two muons are required to originate from the same interaction vertex.If one of the two muons has p T > 25 GeV and is isolated, Σ ∆R<0.2 p trk T /p T < 0.1, it is a candidate for the tag muon, and the other muon is a candidate of the corresponding probe muon.From a pair of muons, there can be two candidate tag-and probe-muons.Furthermore, the tag-muon candidate must have a ∆R < 0.1 to an EF CB muon that passes either the mu24i or mu36 trigger.In addition, the probe muon candidate has to be isolated, Σ ∆R<0.2 p trk T /p T < 0.1.The probe muon is matched to a trigger objects if it lies within a distance ∆R < 0.1(0.5)from an EF CB muon (a L1 muon object).The trigger efficiency is defined as the fraction of probe muons that are associated with at least one trigger muon object after applying the above criteria.

Event selection for the J/ψ meson sample
Two special triggers were developed based on the singlemuon trigger for p T > 18 GeV, mu18, as follows.The chain called mu18 J/ψ FS requires mu18 at all three levels and a pair of muons found by the EF full-scan with a mass consistent with that of the J/ψ.It is used to determine the efficiency at L1 and L2.The chain mu18 J/ψ L2 requires mu18 at all three levels and a pair of muons found by L1 and L2 levels with a mass consistent with that of the J/ψ.It is used to determine the efficiency at the EF level with respect to the L1 and L2.Then the total efficiency can be obtained by multiplying these two partial efficiencies.
All combinations of oppositely charged offline muons are considered as J/ψ candidates if each of the muon tracks satisfies |d 0 | < 0.2 mm, where d 0 is the impact parameter distance of the ID track in the transverse plane.The two ID tracks that are associated with the two muon tracks are refitted under the assumption that they originate from the same vertex.The invariant mass constructed from the refitted tracks is required to be consistent with the J/ψ mass, |m J/ψ − m µµ | < 0.3 GeV.To enhance the purity of the selected muons a further requirement is made on L xy , the signed twodimensional decay length of the J/ψ, L xy is defined as with L being the vector originating from the pp.A requirement of L xy < 1 mm is made on the muons.
The requirements on d 0 and L xy are used to suppress non-prompt muons, such as those from the decays of b-hadrons [30].
Due to rate restrictions, samples of J/ψ candidates were selected using an asymmetric dimuon trigger.This implies that decays of J/ψ mesons used in this paper have a large boost and a small spacial distance between the two decay muons.To ensure correct one-toone matching between trigger and offline muons, the distance between them is gauged with the separation of track extrapolations based on their refitted ID track parameters to the locations of the RPC and TGC detectors.If one of the two muons has p T > 18 GeV and its distance from an EF CB muon that passes the mu18 trigger within a distance of ∆R < 0.08, as evaluated by using the extrapolated positions as described above, it is considered as a probe muon.If the other muon is beyond the distance of ∆R > 0.2 from the tag muon, at the extrapolated positions, it is regarded as a probe muon.The ∆R cut value is sufficiently large compared to the typical dimensions of the RoI (L1 trigger segmentation), as described in Section 2.3.A probe muon is matched to trigger objects, if it is within the distance of ∆R < 0.12 from a L1 muon object and a EF CB muon.The distance is evaluated by using the extrapolated positions.

Selection of top quark and W + jets candidate events
Events are required to pass a trigger that requires E miss T (calo) > 80 GeV, where E miss T (calo) is the magnitude of the missing transverse momentum as measured using the calorimeter only.Several cleaning cuts are then imposed to remove events with noise bursts in the calorimeters and those with cosmic-ray showers.
A muon has to satisfy p T > 40 GeV and |z 0 | < 2 mm, where z 0 is the track impact parameter in the zdirection with respect to the primary vertex.The probe muon is required to be isolated by making requirements on the distance from neighbouring jets and energy depositions in the calorimeter.Probe muons are required to satisfy Σ ∆R<0.3 p trk T /p T < 0.05 and ∆R min (jet, muon) > 0.4, where ∆R min (jet, muon) is the minimum It is required that there is no other muon with p T > 25 GeV.
Events are further required to have E miss T > 20 GeV and m W T + E miss T > 60 GeV, where m W T is the transverse mass 5 of the W candidate as defined with E miss T and the muon.For the t sample, there must be at least three jets with at least one b-jet.For the W sample, there must be one or two jets with zero b-jets.Events with an electron are rejected.

Trigger purity
The trigger purity is defined as the fraction of triggers that can be associated to an offline muon.The ∆R distance between the trigger object and the offline muon was used to define this matching.
Fig. 3(a) shows the location of the MU15 trigger at L1 that seeds the mu24i trigger.Separately shown are those that can be associated with an offline muon.No explicit cut on offline muon p T was applied in this association between trigger and offline objects.Fig. 3 shows that the L1 trigger rate is dominated by triggers without associated offline muons (called fake triggers).The overall trigger purity (fraction of L1 trigger rate from true muons ) is 40 %.Most of the fake L1 triggers originate in the end-cap.The cause of these fake L1 triggers 5 Transverse mass is defined as m 2 T = m 2 + p 2 x + p 2 y and has the useful propriety that it is invariant under Lorentz boosts along the beam direction.in the endcap region was extensively investigated [31], and is understood as mainly due to charged particles, for instance protons, produced in large amounts of dense material such as in like toroid coils and shields.Fig. 3(b) shows the MU15 trigger rate as a function of the instantaneous luminosity; again the rate due to fake triggers is shown separately.The error bars show statistical uncertainties only.The rates from the fake L1 triggers scale linearly with the instantaneous luminosity.(b) Rate of isolated single-muon trigger at an instantaneous luminosity of 7×10 33 cm −2 s −1 , as a function of p T threshold for EF CB muons.Black points represent data, while hatched histograms are the predicted components; the one with cyan colour is the MC prediction for W production, the one with yellow colour is the MC prediction for Z production, and the one with dark-green colour is the datadriven estimate for multi-jet production.The working point in the 2012 runs is shown at p T = 24 GeV.tion were evaluated by using MC simulations with their predicted cross sections.Multi-jet production where one or more jets produces a muon from the decay of a heavy quark or from a pion or kaon decay in flight also contribute to this rate.The multi-jet contribution was evaluated in a data-driven approach.
A multi-jet enriched control region (CR) is obtained by using events that are triggered by a single muon trigger with the same p T threshold but without isolation required. 6The CR is defined by inverting the trigger isolation criteria, by requiring at least one jet in an event, and by requiring matching to an offline muon to remove the fake contribution.Then, the multi-jet contribution is evaluated from the data in the CR weighted by the ratio of CR to the signal-region taken from the dijet MC simulation.The uncertainty of this estimation is dominated by the statistical uncertainty in the CR-SR transfer factors from MC simulation, and is shown in Fig. 4(b).The rate was evaluated as a function of the p T threshold on the EF CB muon.The operation point for the 2012 runs, mu24i, corresponds to the one at p T = 24 GeV.About 60 % of the triggered events with mu24i are due to muons from W and Z production.

Resolution
The tag-and-probe method using Z bosons was used to assess the quality of the momentum and position reconstruction compared to the offline reconstruction.The residual of the trigger-reconstructed p T with respect to the offline value is defined as , where p trigger T is the transverse momentum reconstructed by the trigger, and the p T is that of the offline muon.The online algorithms are nearly identical to the offline versions but have some simplifications in the pattern recognition because of timing constraints.Additionally, the offline reconstruction uses updated calibrations and alignment corrections not available at the time the data was recorded.The resolution difference between the trigger and offline reconstructions was defined as the standard deviation of a Gaussian function fitted to the δ pT distribution.Fig. 5 shows the p T resolution differences of the EF SA and EF CB algorithms with respect to the offline reconstruction in the barrel and endcap regions, respectively.The p T resolution difference is about 2 % and 5 % for EF CB and EF SA algorithms.
The resolutions of the η and φ of triggered muons were examined with respect to the offline values similarly by defining the residual as the absolute difference between the trigger and offline reconstructed values.Fig. 6 shows the η and φ resolution differences of the EF algorithms with respect to the offline reconstruction.This shows that the trigger-offline matching criterion used in the efficiency measurements, for instance ∆R < 0.1 for the tag-and-probe method using Z bosons (see Sect. 3.4), is sufficiently loose compared to the η and φ resolutions.

Efficiency measurements with Z boson candidates
For the kinematic region of p T 10 GeV, the efficiency was measured with the tag-and-probe method using the Z boson.The scale factor (SF) is defined as the ratio of the efficiencies in the data and MC simulation, SF(η, φ) = ǫ Z data (η, φ)/ǫ Z MC (η, φ), where ǫ Z data(MC) (η, φ) is the efficiency for muons with (η,φ) measured in data (MC simulation) using Z bosons.The primary usage and motivation of the SF is to obtain correction factors for physics analyses using MC, which corrects for any differences between data and MC trigger efficiencies.Under the assumption that the SF is independent of the process that generates the muons, the SF obtained from one process, Z bosons decaying to two muons, can be adopted for different physics analyses.This assumption is cross-checked later in Sect.8 by comparing the SFs measured with the Z boson, t-quark and W boson samples.

Systematic uncertainty
The following sources of systematic uncertainty were evaluated.The uncertainty numbers quoted in the following are for the efficiency measured in the region of 25 < p T < 100 GeV.
-Dependence on pile-up interactions: The efficiency was measured as a function of the number of reconstructed vertices, separately for data and MC simulation, as in Fig. 7.The efficiency was largely independent of the number of pile-up interactions.The effect was estimated by changing the distribution of the average number of pile-up interactions, resulting in a 0.1 (0.2) % uncertainty in the barrel (endcap) region; -Correlation between tags and probes from Z decays: For medium p T muons, tags and probes tend to be back-to-back in φ.Since the barrel and endcap have 16-fold and 12-fold symmetries, respectively, this can potentially lead to some bias; a tag muon from a Z boson decay inside a highly efficient region of the detector tends to be accompanied by a probe muon in a region of high efficiency.This effect is evaluated by adding a requirement to the tag and probe pairs to prevent them from being back-toback, ∆φ(tag, probe) < π− 0.1, where ∆φ(tag, probe) denotes the azimuthal angle between the tag and probe muons.The estimated uncertainty of the efficiency determination is 0.3% (0.2%) in the barrel (endcap) region; -Matching between probe muon and trigger muon: This effect was estimated by changing the ∆R thresholds of the matching criteria.It was found to be negligible; -Probe muon momentum scale and resolution: This effect was estimated by changing the momentum scale and momentum resolution for the probe muon by their uncertainties, as determined from the calibration using Z bosons.It was found to be a negligible effect; -Probe muon selection criteria: This effect was estimated by changing, typically by 10 %, the cuts in various selection criteria, giving negligible effects; -Background contribution: The amount of background was estimated by using the dijet, t t, and W MC simulations and was found to be negligible [32].Also, varying the Z mass window cut gave negligible effect; -MC modelling: The sensitivity of the efficiency determination to the MC modelling was tested by comparing to a different sample generated with a different MC generator, namely Sherpa [33].It was found to be negligible [32]; -p T dependence: After applying the SF as function of(η andφ any residual deviations of the SF from unity in the pT dependence are taken as systematic uncertainty.This resulted in a 0.4 % effect; 7 -Probe muon charge dependence: It was estimated by comparing the efficiencies measured with positively charged and negatively charged probe muons.The estimated uncertainty is 0.2 % in the endcap region. 7For the SF measurement in bins of (η, φ), it resulted in a 0.4 % effect except for a 3 % effect in a limited endcap region of |η| ∼ 1.2 at p T < 32 GeV.This is because the muons with 25 < p T < 30 GeV and |η| around 1.2 enter into the boundary region between the barrel and endcap MS detectors.However, the muons with p T > 30 GeV at a same |η|, which predominantly determine the SFs in bins of (η, φ) due to Z production kinematics, do not enter this region.The individual systematic uncertainties were added in quadrature to obtain the total systematic uncertainty, resulting in 0.6 % for the efficiency measured in the region of 25 < p T < 100 GeV.

Single-muon trigger: mu24i, mu36
Requiring events to pass either the mu24i or mu36 chain serves as a general-purpose single-muon trigger for many physics analyses.Fig. 8 shows the efficiency to pass either the mu24i or mu36 chain as measured in the barrel and endcap regions, respectively.The efficiency was measured as a function of the p T of the probe muon.The slight excess in simulation in the p T bin centred at 130 GeV was studied in detail.High p T muons from Z boson decays tend to be slightly more forward where there is the largest difference in trigger efficiency between data and simulation.The efficiency turns on sharply around the threshold, reaching a plateau already around p T ∼ 25 GeV.In order to evaluate the turn-on behaviour and its agreement between data and MC simulation quantitatively, a fit was made using a Fermi function f (p T ). 8 From the fit, the low edge of the efficiency plateau region was defined as where the efficiency decreases by 1 % from the plateau value.Table 3 shows these evaluated plateau values and the low edges of the plateaus.The singlemuon trigger that requires either the mu24i or mu36 8 The functional form is a 1+exp {b(c−pT)} , where a indicates the plateau value, b the steepness of the turn-on slope, and c the threshold value.chain exhibits a plateau efficiency for physics analysis with muon p T > 25 GeV.The efficiency plateau is smooth at p T = 36 GeV indicating that there is no inefficiency due to the isolation requirement in this sample.
Fig. 9 shows the efficiency of requiring to pass either mu24i or mu36 chains, as measured separately for the three trigger levels.The error bars indicate statistical uncertainties only.The trigger selection becomes tighter and the efficiency turn-on becomes sharper as the trigger level increases.The plateau efficiency is mostly determined by the L1.The HLT efficiency with respect to the L1 is about 98 -99 %.Fig. 10 shows the measured SFs in bins of (η,φ) for the barrel and endcap regions, respectively.The measurement was done by applying a p T > 25 GeV re- quirement.The bins in (η,φ) were optimised to be fine enough to reflect the hardware segmentation of the L1 trigger detectors and also to be coarse enough to have sufficient statistics in each bin.The typical size of the statistical uncertainty is less than 1 %, except for a few specific areas where the uncertainty is about 3 %.

Other single-muon triggers
Fig. 11 shows the efficiencies of the triggers of mu36 and mu40 SA barrel triggers, together with that of mu24i, as measured in data.The errors in the figure indicate statistical uncertainties only.The turn-on behaviour of mu24i and mu36 are sharp, and it is slower at threshold for mu40 SA barrel.This is because the trigger relies only on the information from the muon detectors, and thus the p T resolution is coarser (see Sect. 5).On the other hand, the requirement of passing either mu36 or mu40 SA barrel resulted in about 2 % higher efficiency in the barrel region than requiring mu36 only, as mu40 SA barrel recovers an inefficiency due to MS-ID matching at the L2 trigger (not shown in the figure).Therefore, requiring that either the mu36 or mu40 SA barrel chains are passed serves as a primary single-muon trigger for any processes that include high p T muons of p T 50 GeV.Fig. 11 also shows the efficiencies of the mediump T single-muon triggers, mu13 and mu18.The plateau efficiency of mu13 is about 6 % higher in the barrel region than that of mu18 and other higher-p T triggers like mu24i.This is because mu13 is seeded from MU10, which requires a two-station coincidence, while mu18 and the others are seeded from MU15 which requires a three-station coincidence (see Sect. 2.3).
A fit using a Fermi function was performed in a similar way to quantify the turn-on behaviour of these medium-p T single-muon triggers.Table 4 shows the evaluated plateau and low edge values for mu13 and mu18.It is seen that the offline cut of muon p T > 15 (20) GeV is sufficient to ensure the mu13 (mu18) trigger efficiency is described by the plateau value.These middle-p T triggers are used in various trigger chains, for instance dimuon triggers 2mu13 and mu18 mu8 FS.The efficiencies of the single-muon triggers mu13 (mu18) are also necessary ingredients to calculate such dimuon trigger efficiencies.

Full-scan muon trigger
As described in Sect.2.6, the chain mu18 mu8 FS is split into the RoI-based single-muon trigger mu18 and the full-scan triggers of mu18 FS and mu8 FS.The fullscan trigger efficiencies were evaluated using the same method and sources as the single muon trigger (see Sect. 6.1).
p T dependence: The uncertainty was estimated by comparing data and MC efficiencies as a function of p T after applying SFs in (η,φ).This resulted in a 0.2 % effect in the barrel and a 0.5 % effect in the endcap region; -Dependence on pile-up interactions: As shown in Fig. 12, the efficiency has a small dependence on the number of pileup events in the end cap region, about 1.0% efficiency loss per 20 vertices.The MC simulation reproduces the effect well.The effect was estimated by changing the distribution of the average number of pile-up interactions, resulting in a 0.1 % uncertainty.
The total systematic uncertainty is obtained by adding them in quadrature.All the other sources gave negligible effects.Fig. 13 shows the mu8 FS efficiency measured separately for the barrel and endcap regions.The plateau efficiencies for the barrel and endcap regions are 98.7 % and 97.6 %, respectively.This results in a higher efficiency in the dimuon trigger than by requiring two RoI-based single-muon triggers.Fig. 14 shows the SFs of mu8 FS in bins of (η,φ), measured by applying p T > 10 GeV cut on probe muons.The SFs are consistent with unity to within 2 % except in two bins where where the difference is as large as 5 %.
7 Efficiency measurements at low p T

Efficiency measurements with J/ψ
For the kinematic region of p T 10 GeV, the efficiency was measured with the tag-and-probe method using J/ψ mesons.An MC study shows that the efficiency is slightly dependent on the measured d 0 .Therefore, the efficiencies of prompt and non-prompt muons can be different due to different d 0 distribution.Predominantly, this effect is removed by the cuts on d 0 and L xy described in Sect.3.5.The residual effect is then suppressed by reweighting the d 0 distribution to that of prompt muons, which is obtained from the events with L xy < 0.
Owing to a very high purity of the offline muon identification, the backgrounds are in most cases also muons with their physics origin not being a J/ψ meson.The background fraction in the J/ψ mass range is about 16 %, ranging between 13 % to 20 % depending on the muon p T .The efficiency was measured by correcting the background effect using the side-bands of the invariant mass.

Systematic uncertainty
The following sources of systematic uncertainty were evaluated.The uncertainty numbers quoted in the following are for the efficiency measured as a function of p T , in the region of 4 < p T < 10 GeV.
-Matching between probe muon and trigger muon: The effect was estimated by relaxing the ∆R criterion from 0.12 to 0.15, and also by relaxing the ∆R distance cut between the two muons from 0.2 to 0.25.The estimated uncertainty is up to 3 % (2 %) at p T = 4 GeV in the barrel (endcap) region, decreasing to 1 % at p T 6 GeV; -d 0 reweighting: The effect was estimated by comparing the efficiency with that obtained by not applying the d 0 reweighting.The estimated uncertainty is 1 % at p T ∼ 4 GeV, decreasing to be negligible at p T 6 GeV; -Probe muon charge dependence: The effect was estimated by comparing the efficiencies measured with positively charged and with negatively charged probe muons.The estimated uncertainty is 1 % at low p T ∼ 4 GeV, decreasing to 0.5 % at p T 6 GeV; -Background contribution: The effect was estimated by not doing the background correction, resulting in a uncertainty of 0.1 %; -Probe muon selection criteria: The effect was estimated by changing typically by 10 % the thresholds of various selection criteria, giving negligible effects; -Dependence on pile-up interactions: The effect was estimated by changing the distribution of the average number of pile-up interactions, resulting in a 0.2 (0.4) % uncertainty in the barrel (endcap) region.
The total systematic uncertainties are obtained by adding them in quadrature.

Low-p T single-muon triggers
Fig. 15 shows the efficiency of the lowest-p T singlemuon triggers, mu4, mu6 and mu8 as a function of the p T of the probe muon.The efficiency of mu4 is about  40 % at the nominal threshold of 4 GeV.The mu4 turnon curve rises slowly until p T ∼ 8 GeV.The plateau efficiency of mu4 is higher by about 3 % in the endcap region, compared to those of mu6 and mu8.This is because mu4 is seeded from MU4, while mu6 and mu8 are seeded from MU6; MU4 requires a three-station coincidence only partially (see Sect. 2.3).
The SFs for mu4 are measured in bins of (p T , Qη) where Q stands for the charge of the muon.Fig. 16 shows these SFs.The SF is significantly lower than unity at Qη ∼ −1.1 for p T values up to ∼ 12 GeV.In the muon spectrometer toroid magnetic field, the muons with Qη > 0 (< 0) bend toward the large (small) |η| direction in the r-z plane.The muons with Qη ∼ −1.1 are thus likely to pass through only one layer of the RPC (see Fig. 1) and hence are not triggered.Fig. 16 shows that this is not well modelled in the MC simulation.8 Efficiency measurements at very high p T

Efficiency measurements with t and W associated with jets
For the kinematic region of p T 100 GeV, the efficiency was measured using muons in t t and W + jet candidate events.Because they are statistically independent of each other and also correspond to background-enriched samples of each other, the efficiencies wuing muons in t t and W + jet events can be obtained by solving the following two equations where ǫ t(W ) is the efficiency in pure t-quark (W + jets) events, and ǫ t(W ),data is the measured efficiency in the t-quark (W + jets) sample.The factors f t,data t and f W,data W denote the fraction of true t-quark (W +jets) events in the t (W with jets) sample, as determined by using MC simulation.

Systematic uncertainty
The following sources of systematic uncertainties were evaluated.The uncertainty numbers quoted in the following are for the efficiency measured using the W + jets sample as a function of p T , in the region of 100 < p T < 400 GeV.
-Muon isolation: To estimate this effect, the efficiency was measured by varying the isolation cut, both by loosening and tightening criteria, as well as changing the ∆R cone size.The estimated uncertainty is typically 0.2 %; -Muon-jet separation: The requirement on muon-jet separation serves also as an isolation cut.This effect was estimated by changing the ∆R criterion in the matching from 0.4 to 0.3 and 0.5.The estimated uncertainty is typically 0.1 % and 0.3 % at maximum; -E miss T reconstruction: The effect was estimated by changing the threshold from 20 GeV to 50 GeV, and also by introducing another tight cut of E miss T (calo) > 120 GeV.The estimated uncertainty is 0.5 % at maximum; -b-jet identification: The effect was estimated by repeating the measurements with a different b-jet identification criterion, namely with 60 % efficiency and 80 % efficiency.The estimated uncertainty is typically less than 0.1 %; -p jet T cut: The effect was estimated by raising the p jet T threshold to 35 GeV.The estimated uncertainty is typically less than 0.1 %; -Background contribution: The number of background events was estimated by using the dijet and Z MC simulations and was found to be negligible at p T > 100 GeV.
They were added in quadrature to obtain the total systematic uncertainties.8.3 Single-muon trigger efficiency at p T 100 GeV Fig. 17 shows the efficiencies measured using t and W with jets events for the single isolated-muon trigger mu24i in the barrel and endcap regions, respectively.The efficiency was measured as a function of the p T of the probe muon, up to p T ∼ 400 GeV.The data and MC simulation agree well up to this very high p T value.
In addition, Fig. 17 shows the ratio between the efficiencies in the data and MC simulation.Those measured with the t and W events are compared, as well as that with the Z tag-and-probe method.These three measurements are in good agreement with each other throughout a large p T range, providing a consistency check on the SF derivation in different physics processes with different experimental techniques.

Conclusions
The ATLAS muon trigger has successfully adapted to the challenging environment at the LHC such that stable and highly efficient data-taking was attained in the year 2012.The transverse momentum threshold for the single-muon trigger was kept at 24 GeV, with a wellcontrolled trigger rate of typically about 8.5 kHz at the Level-1 and 65 Hz at the EF.The processing times of Fig. 17 Efficiency of the mu24i trigger as a function of the probe muon p T , as measured with the t-quark and W +jet events, separately for the barrel and endcap regions.The lower part of each plot shows the ratio between the efficiencies in the data and MC simulation.Also shown is that as measured with the Z decays using the tag-and-probe method.
The error bars for MC simulation indicate the statistical uncertainties only.
the Level-2 and EF muon trigger algorithms were sufficiently short to fit within the computing resource limitations.The purity of the trigger is about 90 % at the EF, of which more than half is due to electroweak bosons production.The efficiencies, as well the scale factors that are defined as the ratios of the data and simulation efficiencies are measured extensively with the proton-proton collision data at a centre-of-mass energy of 8 TeV.The systematic uncertainty in the mea-sured efficiency for the single-muon trigger is evaluated to be about 0.6 % in a kinematic region of 25 < p T < 100 GeV.The efficiency was measured over a wide p T range (a few GeV to several hundred GeV) by using muons from J/ψ mesons, Z and W bosons, and top quark decays showing highly uniform and stable performance.

Fig. 1 A
Fig.1A schematic picture showing a quarter-section of the muon system in a plane containing the beam axis.The MDT chambers in the barrel are arranged in three concentric cylindrical shells around the beam axis.In the endcap region, muon chambers form large wheels, perpendicular to the zaxis.In the forward region, CSC is used in the innermost tracking layer.The RPC and TGC chambers are arranged in three layers (called stations) as indicated in the figure.
Rates of the muon triggers at the L1 as a function of instantaneous luminosity: single-muon triggers of MU15 and MU20, and multi-muon triggers of 2MU10 and 3MU4.The rates of MU4 and MU6 are about 550 kHz and 140 kHz, respectively, at an instantaneous luminosity of 7•10 33 cm −2 s −1 (not shown).Rates of muon triggers at the EF as a function of instantaneous luminosity: single-muon triggers of mu24i, mu36 and mu40 SA barrel, and multi-muon triggers of 2mu13, mu18 mu8 FS and 3mu6.

Fig. 2
Fig.2Trigger rates as a function of instantaneous luminosity.
Distribution of η of the L1 object for events triggered by MU15.The yellow hatched histogram represents all objects, and the cyan histogram shows the component that can be associated with offline reconstructed muons.Rate of MU15 trigger as a function of instantaneous luminosity, separately for the total and the component that cannot be associated with offline-reconstructed muons (denoted as fake).

Fig. 3
Fig. 3 Trigger purity and rate of the L1 trigger MU15.

Fig. 4 (
Fig.4(a) shows the η distribution of the EF trigger objects of the mu24i trigger.The fake triggers are cleaned up by the subsequent HLT decisions, and a purity of about 90 % is achieved.The physics origin of muons at the EF is illustrated in Fig.4(b), which shows the expected composition of the trigger rate of the isolated single muon.The vertical scale gives the trigger rate per bin at an instantaneous luminosity of 7•10 33 cm −2 s −1 .The expectations for W and Z produc-

Fig. 4
Fig.4 Trigger purity and rate of the single-muon trigger mu24i at the EF.

Fig. 5
Fig. 5 Resolution in p T reconstruction by the EF algorithms, as a function of p T of offline reconstruction.Separately shown for (a) the barrel region and (b) the endcap region.

Fig. 6
Fig.6 Resolution in η and φ reconstruction by the EF algorithms, as a function of p T of offline reconstruction.

Fig. 7
Fig. 7 Efficiency to pass either mu24i or mu36 chains, as a function of the number of reconstructed vertices in an event, Nvtx.Separately shown for (a) the barrel region, and (b) the endcap region.The black points are data, while the red bands are MC simulation .The lower plot in each figure shows the ratio of the efficiencies of data and MC simulation.The errors are statistical uncertainties only.

Fig. 8
Fig. 8 Efficiency of passing either the mu24i or mu36 chain as a function of the probe muon p T , separately for (a) the barrel region and (b) the endcap region.The black points represent data, while the band with purple band represent MC simulation.The lower plot in each figure shows the ratio of the efficiencies of data and MC simulation.The error bars include both statistical and systematic uncertainties.

Fig. 9
Fig.9Efficiency of passing either the mu24i or mu36 chain as functions of the probe muon p T , separately for the three trigger levels.The efficiency was measured from data, and is shown separately for (a) the barrel region and (b) the endcap region.The error bars show the statistical uncertainties only.

Fig. 10
Fig. 10 Scale factors of requiring to pass either mu24i or mu36 chains in bins of the probe muon (η,φ), separately shown for (a) the barrel region and (b) the endcap region.

Fig. 11
Fig. 11 Efficiency of single-muon triggers mu13, mu18, mu24i, mu36 and mu40 SA barrel measured in data as a function of the probe muon p T , shown separately for (a) the barrel region and (b) the endcap region.The error bars indicate statistical uncertainties only.

Fig. 12
Fig. 12 Efficiency of the mu8 FS trigger measured as a function of the reconstructed number of vertices in an event, Nvtx.Separately shown for (a) the barrel region, and (b) the endcap region.The points are data, while the bands are MC simulation.The lower plot in each figure shows the ratio of efficiencies of data and MC simulation.The errors are statistical uncertainties only.

Fig. 13
Fig.13 Efficiency of the EF full-scan mu8 FS as a function of probe muon p T , separately for (a) the barrel region and (b) the endcap region.

Fig. 14
Fig. 14 Scale factors of the mu8 FS trigger in bins of the probe muon (η,φ), separately shown for (a) the barrel region and (b) the endcap region.

Fig. 15
Fig. 15 Efficiency of low p T single muon triggers, mu4, mu6, mu8, measured as a function of the probe muon p T , separately shown for (a) the barrel region and (b) the endcap region.For a better view, the error bars for MC indicate the statistical uncertainties only, while those for data indicate both the statistical and systematic uncertainties.

Fig. 16
Fig.16 Scale factors of the mu4 trigger in bins of η multiplied by charge and the probe muon p T , (Qη, p T ).

Table 1
Sequence for the single-muon trigger chains at the L1, L2 and EF levels.The applied p T and isolation cuts are also shown.The superscripts on variables denote the type of the candidate muons, for instance p L2 SA

Table 2
Sequence for the multi-muon trigger chains at the L1, L2 and EF levels.The applied p T cut applied are also shown.The superscripts on variables denote the type of the candidate muons, for instance p L2 SA T denotes the p T of L2 SA muons.

Table 3
Result of fitting a Fermi function to the efficiency turn-on curve for the single-muon trigger.The low edge of the plateau region is defined such that the efficiency decreases by 1 % from the plateau value.

Table 4
Result of Fermi function fit to the efficiency turn-on curve for the middle-p T single-muon triggers.The low edge of the plateau region is defined such that the efficiency decreases by 1 % from the plateau value.