Performance of a First-Level Muon rigger with High Momentum Resolution Based on the ALAS MD Chambers for HL-LHC P. Gadow, O. Kortner, S. Kortner, H. Kroha, F. Müller, R. Richter Max-Planck-Institut für Physik, Munich arxiv:5.92v [hysics.ins-det] 3 Nov dσ/d (µbarn/gev) 2 3 4 5 6 c µ b µ t µ W µ Z/γ* µ π/k µ Shower muons Punch-through η µ < 2.7 s = 7 GeV 2 3 4 5 µ (GeV) Fig.. Differential cross-section dσ/d for the dominant muon roduction rocesses as function of the muon transverse momentum at a centre-of-mass energy of s = 7 ev in the seudo-raidity range η µ < 2.7 []. he orange area marks the momentum range which is critical to be suressed by a Level- MD trigger. Abstract Highly selective first-level triggers are essential to exloit the full hysics otential of the ALAS exeriment at High-Luminosity LHC (HL-LHC). he concet for a new muon trigger stage using the recision monitored drift tube (MD) chambers to significantly imrove the selectivity of the first-level muon trigger is resented. It is based on fast track reconstruction in all three layers of the existing MD chambers, made ossible by an extension of the first-level trigger latency to 6 µs and a new MD read-out electronics required for the higher overall trigger rates at the HL-LHC. Data from -collisions at s = 8 ev is used to study the minimal muon transverse momentum resolution that can be obtained using the MD recision chambers, and to estimate the resolution and efficiency of the MD-based trigger. A resolution of better than 4.% is found in all sectors under study. With this resolution, a first-level trigger with a threshold of 8 GeV becomes fully efficient for muons with a transverse momentum above 24 GeV in the barrel, and above 2 GeV in the end-ca region. Index erms HL-LHC, muon drift tube, smd, trigger I. INRODUCION Highly selective first-level triggers are essential to exloit the full hysics otential of the ALAS exeriment at the HL-LHC where the instantaneous luminosity will exceed the LHC Run instantaneous luminosity by almost an order of magnitude. In order to cover the interesting electroweak Fig. 2. rigger efficiency as function of the muon transverse momentum t at the three trigger stages Level-, Level-2 and Event Filter [4]. he black line has been added as illustration for the envisaged Level- MD trigger efficiency. hysics rocesses, the goal for the Level- muon trigger is to maintain a trigger for single muons that is fully efficient at 2 GeV without the need for rescaling. Figure shows the differential cross-section dσ/d for the dominant muon roduction rocesses as function of the muon transverse momentum at a centre-of-mass energy of s = 7 ev in the seudo-raidity range η µ < 2.7. It is obvious that in order to suress the steely rising cross-section for < 2 GeV, a very good momentum resolution for the muon trigger and a shar turn-on of the trigger efficiency is required. he ALAS exeriment lans to increase the accetable trigger rate of the first two trigger levels to MHz at 6 s latency and 4 khz at 3 s latency, resectively. his requires to relace the electronics for the muon trigger decision, as well as the read-out electronics of the muon trigger chambers and the recision monitored drift tube (MD) chambers. he relacement of the recision chamber read-out electronics will make it ossible to include their data in the first-level trigger decision and to increase the selectivity of the first-level muon trigger [2], [3]. he MD-based muon trigger will be imlemented at Level- of the new ALAS trigger system for HL-LHC, which will relace the current Level-. he imrovements on the current ALAS Level- muon trigger efficiency is illustrated in Figure 2, which shows the efficiency at the three trigger stages Level-, Level-2 and Event
Filter. he resolution of the Level- MD trigger is exected to be very close to the one of the Level-2, resulting in a turnon as indicated in the figure and a substantial rate reduction from the existing Level- trigger [5]. wo ossible concets for a Level- MD trigger are currently under study. In the two-station concet, the two outer of the three layers of the MD chambers are used. he muon momentum is determined from the deflection angle in the magnetic field comaring the two measured track segments in the layers. he rate reduction for the two-station concet has been determined using ALAS data at s = 8 ev. It is found to be in the order of 5% across the entire η-coverage of the muon sectrometer [5]. he three-station concet makes use of all three layers of the MD recision chambers and relies on the excellent satial resolution of the MD chambers, which exceeds the angular resolution by a factor of about two. Hence, the erformance of the three-station concet is exected to be comarable to the one from the Level-2 trigger. In this contribution, the resolution and efficiency of the three-station concet is studied, using data from the ALAS data taking at s = 8 ev. II. HE ALAS MUON SPECROMEER he ALAS detector consists of a tracking system in a 2 axial magnetic field u to a seudoraidity of η < 2.5, samling electromagnetic and hadronic calorimeters u to η < 4.9, and the muon sectrometer in a.5 azimuthal magnetic field rovided by a system of air-core toroidal magnets. A detailed descrition of the ALAS detector can be found elsewhere [6]. he muon sectrometer consists of the barrel region with η <.5, and the end-ca region with.4 < η < 2.7. he magnet system is divided accordingly, where both barrel and end-ca toroid magnets consist of eight coils each, resulting in an eightfold symmetry. In the barrel, three layers of MD chambers are installed. In the area between the magnet coils, the so-called large sectors, the distance to the beam axis are 4.9 m, 7. m, and 9.5 m, resectively. Within the coils, in the so-called small sectors, the chambers are laced in a distance of 4.6 m, 8. m, and.6 m, resectively. While the magnetic field strength is higher for the small sectors, muons in this region suffer from multile interactions with the additional assive material of the magnets and their suort structure. he middle and outer layer in the barrel are equied with additional resistive late chambers (RPCs) dedicated to fast triggering for the current Level- trigger. he end-ca consists of three discs with large sectors at a distance of ±7.7 m, ±4.3 m, and ±2.4 m and small sectors at a distance of ±7.3 m, ±3.9 m, and ±2.8 m from the interaction oint. he New Small Wheel (NSW) relaces the innermost layer of the current end-ca of the muon detector for the HL-LHC and will use Micromegas. he middle and outermost layer of ALAS uses a right-handed coordinate system with its origin at the nominal interaction oint (IP) in the centre of the detector and the z-axis along the beam ie. he x-axis oints from the IP to the centre of the LHC ring, and the y-axis oints uward. Cylindrical coordinates (r, φ) are used in the transverse lane, φ being the azimuthal angle around the z-axis. he seudoraidity is defined in terms of the olar angle θ as η = ln tan(θ/2). Fig. 3. Side view of one quadrant of the ALAS detector for illustration of the 3-station concet. Muon tracks are indicated by red lines. he hit clusters and regions of interest in the trigger chambers are marked by blue and yellow markers, resectively. the end-ca are build from MD chambers. hree layers of dedicated thin ga chambers (GCs) for fast triggering are installed around the middle layer of the end-ca. Due to the large size and weight of the detector, some areas in the η-φ sace are not fully covered by muon detectors, in articular the transition between the barrel and the end-ca at.5 < η <.4, as well as the suort structure of the detector at 3.53 < φ < 5.. Hence, these regions have been excluded from the study. III. RIGGER CONCEP he trigger concet is illustrated in Figure 3, which shows a side view of one quadrant of the ALAS detector. he Level- MD trigger relies on the Regions of Interest (RoI) defined by the dedicated existing Level- trigger chambers. he RoIs are built from hits in the RPCs and GCs, which can be extraolated to all three layers of the recision MD chambers using their osition and momentum information. In the barrel, the muon track is measured at the three sace oints around the RoIs. he transverse momentum of the muon is determined from the curvature of the muon track in the middle layer by calculating the sagitta s from the rojection of the track on the sector normal in φ. he sagitta is defined by the shortest distance of the measured track segment in the middle layer with resect to a straight line between the track segments in the inner and outer layer. In the end-ca region, the muon track is measured at three sace oints given by NSW, middle end-ca (EM) and outer end-ca (EO). Due to the osition of the end-ca magnet, the magnetic field is limited to the sace between the inner and middle end-ca layer. Hence, the most sensitive method to determine the transverse momentum of the muon is from the curvature inside those two layers. he measured quantity is the distance L between the track segment in the inner layer, and the extraolated track from the measured track segments in the middle and outer layer of the end-ca. IV. DAA ANALYSIS Data from the ALAS data taking at s = 8 ev, corresonding to an integrated luminosity of 5.5 fb, is used for
this study. he events are reselected by having at least one ositive trigger decision among all the muon trigger items. No requirement on a articular Level- single muon trigger is imosed to minimise the statistical uncertainty on the data. wo different muon reconstruction algorithms are emloyed in this study. he combined algorithm makes use of the combined information from the inner tracking detectors and the muon sectrometer. It has the best transverse momentum resolution and hence is considered as reference algorithm. he standalone algorithm reconstructs the muon transverse momentum with information from the muon sectrometer only. It reresents the benchmark for the trigger algorithm. Quantities measured with the combined and standalone algorithm are indicated by the suerscrits and SA, resectively. Due to energy loss in the calorimeters, the standalone momentum is systematically lower than the combined momentum, therefore the standalone momentum has to be corrected by the most robable energy loss E during the assage from the interaction oint to the muon sectrometer. he most robable energy loss of muons with GeV < < 3 GeV in large barrel sectors is E B = 2.5 ±. GeV, while the most robable energy loss in the end-ca sectors is E EC =.936 ±. GeV. he Level- MD trigger algorithm is studied on basis of muon track segments as reconstructed in the individual layers of the MD chambers. he track segments are required to have at least six hits, and each layer is required to have one track segment in the region of interest. In the overla region between small and large sectors, information from only one sector tye is used. For simlicity, only ositively charged muons with η > are considered. It has been verified that negatively charged muons and muons in the region η < give similar results. Muon tracks with SA > GeV are not considered in the analysis. he transition region between barrel and end-ca as well as the region of the suort structure has been excluded, as described in Section II. For the end-ca, this study focuses on the region in 2. < η < 2.4 as a guide for further investigation. Since the NSW has not been installed yet in the selected data eriod, the information from the inner end-ca of MD chambers is used. V. RESOLUION OF HE SANDALONE ALGORIHM he standalone algorithm makes use of only the muon sectrometer data, hence it can be used to give an estimate for an uer limit of the MD trigger algorithm s erformance. he trigger s efficiency is defined as the ratio of events assing the threshold over all events in a certain momentum range. A trigger can be considered fully efficient once it reaches a lateau of > 99%. For a momentum resolution with a Gaussian shae, the 99% oint is reached at 3σ above the trigger threshold. In order for the trigger to be efficient at the efficiency oint eff = 2 GeV, the corresonding threshold must be set at thresh = eff 3σ eff. () A better momentum resolution translates to a more selective threshold. For the barrel region, the exected resolution of the Events 3 2 5 5 σ =.67 ±.3 = (2 ± ) GeV/c large endca sector charge > 2. < η < 2.4..2.5..5.5..5.2 SA ( - ( + ΔE))/ Fig. 4. Momentum resolution for ositively charged muons in large sectors with 9 GeV < < 2 GeV and 2. < η < 2.4..8.6.4.2.96 at 2 GeV/c SA.99 at 2.3 GeV/c + ΔE 8.4 GeV/c large endca sectors charge > 2.< η < 2.4 5 2 3 [GeV/c] Fig. 5. rigger efficiency for ositively charged muons in large sectors at 2. < η < 2.4 as function of the muon transverse momentum reconstructed using the combined algorithm. A threshold of SA = 8.4 GeV has been alied..8.6.4.2.99 at 2 GeV/c SA + ΔE 7.58 GeV/c large endca sectors charge > 2. < η < 2.4 5 2 3 [GeV/c] Fig. 6. rigger efficiency for ositively charged muons in large sectors at 2. < η < 2.4 as function of the muon transverse momentum reconstructed using the combined algorithm. A threshold of SA = 7.58 GeV has been alied.
.2.4.6 2.2 - (sagitta) [GeV/c].4 3.6 4 - (sagitta) [GeV/c] /sagitta [/mm]..8 5 2 5 2 3 5 3 2 5 2 3. 5 3 2 5 2 3 3 5 4 2.55.6 2.5.55 2 5.45.5 3.4.45 (c).35.4 φ [rad] - (sagitta, φ, η) [GeV/c] - (sagitta, φ) [GeV/c] 2.3.35 (b)..3 [GeV/c] (a) 5 5 [GeV/c] - (sagitta, φ) [GeV/c] 2 4.6 5 4.2.4.6 φ [rad] (d).8 5.2.4.6.8 η η (e) (f) Fig. 7. Iterative method to determine the calibration function (s, φ, η). Data from ositively charged muons in a small sector of the barrel region is used. standalone algorithm for the relevant transverse momentum range around eff = 2 GeV, the resolution is about 4% [6]. he momentum resolution for large end-ca sectors at 2 GeV in the end-ca region 2. < η < 2.4 is shown in Figure 4. Albeit the Gaussian core of the distribution is narrow, with a width of a standard deviation σ =.67 ±.3, there are non-gaussian tails, articularly in the barrel region, resulting from energy loss fluctuations. As the energy loss fluctuations set a fundamental limit on the momentum resolution and hence on the convergence of the trigger efficiency at the lateau, being fully efficient at eff comes at the cost of a reduced rate reduction. One should note that in the end-ca region the combined reconstruction algorithm relies redominantly on the muon sectrometer data, resulting in a non-negligible correlation between the two values and a ossible overestimation of the resolution. he trigger efficiency for the large sectors in the end-ca region 2. < η < 2.4 is shown in Figure 5. he turn-on curve reaches.96 efficiency at 2 GeV and becomes fully efficient at 2.3 GeV. he fact that the trigger is not fully efficient at 2 GeV using the 3σ estimation is caused by energy loss fluctuations, which are resonsible for the non-gaussian tails of the momentum resolution distribution. In order to be fully efficient at 2 GeV a lower threshold of thresh = 7.58 GeV has to be chosen, as shown in Figure 6. Here, the turn-on curve is less stee comared to Figure 5, resulting in a smaller rate reduction. VI. C ALIBRAION PROCEDURE he sagitta s as a measure for the ath s curvature is inversely roortional to the article s transverse momentum, which is exressed by the well-known relation ebl2. (2) 8 As the magnetic field B(φ, η) is not constant over the whole detector, a arametrization of ( s, φ, η) is constructed using an iterated fit rocedure by the means of Equation 2. o account for local inhomogeneities, the barrel region is divided into eight large and eight small sectors evaluated indeendently. In Figure 7a the inverse sagitta is shown against the combined momentum of the muon, which is used as a calibration measure for. A linear function f ( ) = a +a is fitted to the data with the method of χ2 minimization to obtain / s a ( s) =. (3) a After obtaining the fit arameters, the residuals show no strong deendence, as can be seen in Figure 7b. In a second iteration, shown in Figure 7c, the residual ( s) is shown P 4 against φ and a quartic olynomial P4 (φ) = n= n φn is fitted to the data to obtain / s a + P4 (φ). (4) ( s, φ) = a he residuals are shown in Figure 7d, where no strong deendence on φ is observed. he remaining deendence on η is shown in Figure 7e, where the residuals ( s, φ) are shown against η. A quadratic olynomial E2 (η) = P2 n η is fitted to the data to obtain n= n s = / s a + P4 (φ) + E2 (η). (5) a he residuals shown in Figure 7f rove that the arametrisation of in terms of sagitta, φ and η is sound. he same ( s, φ, η) =
Entries 8 6 σ =.49 ±.4 = (2 ± ) GeV/c large barrel sectors charge > < η <.5.9.8.7.6.95 at 2 GeV/c.99 at 23.9 GeV/c standalone t.5 4 2.2.5..5.5..5.2 ( - (sagitta, φ, η))/.4.3.2. (Δs, φ, η) 7.55 GeV/c large barrel sectors charge > < η <.5 5 2 3 [GeV/c] Fig. 8. Momentum resolution using the arametrisation ( s, φ, η) for ositively charged muons in large sectors with 9 GeV < < 2 GeV and. < η <.5. Events 22 2 8 6 4 2 8 6 4 2 = (2 ± ) GeV/c large endca sectors charge > 2. < η < 2.4 φ (, 2.8) (5.3, 6.3) σ =.269 ±.9.2.5..5.5..5 ( - (ΔL, φ, η))/ Fig. 9. Momentum resolution using the arametrisation ( L, φ, η) for ositively charged muons in large sectors with 9 GeV < < 2 GeV, φ (, 2.8) (5.28, 6.28) and 2. < η < 2.4. methodology is alied in the end-ca using L instead of s. VII. RIGGER PERFORMANCE he resolution of the is determined by taking the width of the distribution ( ( s, φ, η))/. In Figures 8 and 9 the distributions for the barrel region and the end-ca region are shown. he resolution is found to be σ =.4 ±.3 and σ =.269 ±.9 resectively. he imroved resolution in the end-ca region with resect to the barrel region can be artially attributed to correlations between the combined and stand-alone reconstruction algorithms. Another contribution is the lower energy loss of muons in large barrel sectors comared to end-ca sectors, resulting in a better momentum resolution in the end-ca region due to less ronounced non-gaussian tails. Setting a threshold of thresh = 7.55 GeV in the barrel region, one arrives at an efficiency curve shown in Figure. For comarison, the curve obtained by using the standalone Fig.. rigger efficiency for ositively charged muons in large sectors at. < η <.5 as function of the muon transverse momentum reconstructed using the combined algorithm. A threshold of SA = 7.55 GeV has been alied using the muon transverse momentum given by the arametrisation ( s, φ, η) and by the energy-loss corrected standalone algorithm..8.6.4.2.97 at 2 GeV/c.99 at 2.6 GeV/c standalone t (ΔL, φ, η) 8.39 GeV/c large endca sectors charge > 2. < η < 2.4 φ (, 2.8) (5.3, 6.3) 5 2 3 [GeV/c] Fig.. rigger efficiency for ositively charged muons in large sectors at 2. < η < 2.4 and φ (, 2.8) (5.28, 6.28) as function of the muon transverse momentum reconstructed using the combined algorithm. A threshold of SA = 8.39 GeV has been alied using the muon transverse momentum given by the arametrisation ( L, φ, η) and by the energy-loss corrected standalone algorithm. momentum is also shown. At 2 GeV the trigger efficiency is.95, while the full efficiency is reached at 23.9 GeV. he efficiency curve in the end-ca region is shown in Figure. It is steeer and almost fully efficient at 2 GeV. Full efficiency is reached at 2.6 GeV. he threshold is chosen = 8.39 GeV. Again for comarison the curve obtained by using the standalone momentum is overlaid. Both curves are very similar in shae, their different sloe follows as a consequence of the aforementioned correlation and reduced energy loss in the end-ca region. to be thresh VIII. SUMMARY It has been shown that a MD trigger can imrove the selectivity of the first-level muon trigger significantly. Based on an iterative fitting method, a arametrisation of the muon s
transverse momentum ( s, φ, η) can be determined. For a threshold of thresh = 7.55 GeV in the barrel region, the trigger is 95% efficient at the efficiency oint eff = 2 GeV and becomes fully efficient at 23.9 GeV. In the end-ca region, setting a threshold of thresh = 8.39 GeV, the trigger is 97% efficient at eff = 2 GeV and becomes fully efficient at 2.6 GeV. REFERENCES [] ALAS Collaboration, ALAS muon sectrometer: echnical Design Reort, CERN-LHCC-97-22. [2] J. Dubbert, S. Kortner, O. Kortner, H. Kroha, R. Richter, Ugrade of the ALAS Muon rigger for the SLHC, Journal of Instr. 5 (2) C26. [3] P. Schwegler, O. Kortner, H. Kroha, R. Richter, Imrovement of the L rigger for the ALAS Muon Sectrometer at High Luminosity, Nucl. Instr. Meth. A78 (23) 245. [4] ALAS Collaboration, Performance of the ALAS muon trigger in collisions at 8 ev, Eur. Phys. J. C75 () 2. [5] ALAS Collaboration, ALAS Phase-II Ugrade Scoing Document, CERN-LHCC--2. [6] ALAS Collaboration, he ALAS Exeriment at the CERN Large Hadron Collider, JINS 3 (28) S83.