The Cms Trigger And Data Acquisition Group1
Abstract. At the Large Hadron Collider at CERN the proton bunches cross at a rate of 40MHz. At the Compact Muon Solenoid experiment the original collision rate is reduced by a factor of O (1000) using a Level-1 hardware trigger. A subsequent factor of O(1000) data reduction is obtained by a software-implemented High Level Trigger (HLT) selection that is executed on a multi-processor farm. In this review we present in detail prototype CMS HLT physics selection algorithms, expected trigger rates and trigger performance in terms of both physics efficiency and timing.
PACS numbers: 13.85.-t, 07.05.Kf, 07.05.Tp, 02.07.Uu
Accepted By Epj, Nov. 2005
(page 2) The participants in the CMS Trigger and Data Acquisition Group and the contributors to the High Level Trigger by Country and Institute. Correspondance to M. Spiropulu, CERN-PH, 1211
The Cms Trigger And Data Acquisition Group 2
Institut f¨ur Hochenergiephysik der OeAW, Wien, AUSTRIA W. Adam, T. Bergauer, C. Deldicque, J. Er¨o, R. Fruehwirth, M. Jeitler, K. Kastner, S. Kostner, N. Neumeister**1a,2, M. Padrta P. Porth, H. Rohringer, H. Sakulin**1b,
S. Lowette, B. Van De Vyver**1A
Universit´e Libre de Bruxelles, Bruxelles, BELGIUM
G. De Lentdecker, P. Vanlaer
Universit´e Catholique de Louvain, Louvain-la-Neuve, BELGIUM
C. Delaere, V. Lemaitre, A. Ninane, O. Van Der Aa
Institute for Nuclear Research and Nuclear Energy, Sofia, BULGARIA
Helsinki Institute Of Physics, Helsinki, Finland
V. Karim¨aki, R. Kinnunen, T. Lamp´en, K. Lassila-Perini, S. Lehti, J. Nysten,
P. Busson
Institut de Recherches Subatomiques, IN2P3-CNRS - ULP, LEPSI
G. Schwering
Institut f¨ur Experimentelle Kernphysik, Karlsruhe, GERMANY
G. Daskalakis**4, A. Sfyrla
Institute of Nuclear Physics “Demokritos”, Attiki, GREECE
M. Barone, T. Geralis, C. Markou, K. Zachariadou
KFKI Research Institute for Particle and Nuclear Physics, Budapest,
P. Hidas
Tata Institute of Fundamental Research - EHEP, Mumbai, INDIA
S. Banerjee**1C, K. Mazumdar**1A
Tata Institute of Fundamental Research - HECR, Mumbai, INDIA
S. Banerjee
Universit`a di Bari, Politecnico di Bari e Sezione dell’ INFN, Bari, ITALY M. Abbrescia, A. Colaleo**1a, N. D’Amato, N. De Filippis, D. Giordano, F. Loddo,
3
Universit`a di Bologna e Sezione dell’ INFN, Bologna, ITALY S. Arcelli, D. Bonacorsi, P. Capiluppi, G.M. Dallavalle, A. Fanfani, C. Grandi, S. Marcellini, A. Montanari, F. Odorici, R. Travaglini Universit`a di Catania e Sezione dell’ INFN, Catania, ITALY
S. Costa, A. Tricomi
Universit`a di Firenze e Sezione dell’ INFN, Firenze, ITALY
V. Ciulli, N. Magini, R. Ranieri
Laboratori Nazionali di Legnaro dell’ INFN, Legnaro, ITALY (associated
Institute)
L. Berti, M. Biasotto, M. Gulmini**1a, G. Maron, N. Toniolo, L. Zangrando Universit`a di Padova e Sezione dell’ INFN, Padova, ITALY M. Bellato, U. Gasparini, S. Lacaprara, A. Parenti, M Passaseo P. Ronchese, S. Vanini,
S. Ventura P.L. Zotto
Universit`a di Perugia e Sezione dell’ INFN, Perugia, ITALY
D. Benedetti, M Biasini, L. Fan`O, L. Servoli
Universit`a di Pisa, Scuola Normale Superiore e Sezione dell’ INFN, Pisa,
Italy
G. Bagliesi, T. Boccali, S. Dutta, S. Gennai, A. Giassi, F. Palla, G. Segneri,
A. Starodumov**5,6, R. Tenchini
Universit`a di Roma I e Sezione dell’ INFN, Roma, ITALY
P. Meridiani, G. Organtini
Universit`a di Torino e Sezione dell’ INFN, Torino, ITALY
Y.I. Choi, I.T. Yu
K. Cho, J. Chung,S.W. Ham, D.H. Kim, G.N. Kim, W. Kim, J.C Kim, S.K. Oh,
Institute Of Experimental Physics, Warsaw, Poland
K. Bunkowski, M. Cwiok, W. Dominik, K. Doroba, M. Kazana, J. Krolikowski, I. Kudla, M. Pietrusinski, K. Pozniak**7, W. Zabolotny**7, J. Zalipska, P. Zych Soltan Institute for Nuclear Studies, Warsaw, POLAND
4
Laborat´orio de Instrumenta¸c˜ao e F´ısica Experimental de Part´ıculas,
Lisboa, Portugal
R. Alemany-Fernandez, C. Almeida, N. Almeida, J. C. Da Silva, M. Santos, I. Teixeira,
J.P. Teixeira, J. Varela**1A, N. Vaz Cardoso
Joint Institute for Nuclear Research, Dubna, RUSSIA
A. Toropin **8
Institute for Theoretical and Experimental Physics, Moscow, RUSSIA V. Gavrilov, V. Kolosov, A. Krokhotin, A. Oulianov, N. Stepanov
O.L. Kodolova**1A, I. Vardanyan
Vinca Institute of Nuclear Sciences, Belgrade, SERBIA
Cantabria, Santander, Spain
A. Calderon, M.A. Lopez Virto, R. Marco, C. Martinez Rivero, F. Matorras, I. Vila
Switzerland
S. Ashby, D. Barney, P. Bartalini**9, R. Benetta, V. Brigljevic**10, G. Bruno**11, E. Cano, S. Cittolin, M. Della Negra, A. De Roeck, P. Favre, A. Frey, W. Funk, D. Futyan, D. Gigi, F. Glege, J. Gutleber, M. Hansen, V. Innocente, C. Jacobs, W.
Jank, M. Kozlovszky, H. Larsen, M. Lenzi, I. Magrans, M. Mannelli, F. Meijers, E. Meschi, L. Mirabito, S.J. Murray, A. Oh, L. Orsini, C. Palomares Espiga, L. Pollet,
A.
Racz, S. Reynaud, D. Samyn, P.
Scharff-Hansen, C. Schwick, G.
Sguazzoni,
N. Sinanis, P. Sphicas**12, M. Spiropulu, A. Strandlie, B.G. Taylor, I. Van Vulpen,
I. Dumanoglu
D.S. Bailey, J.J. Brooke, D. Cussans, G.P. Heath, D. Machin, S.J. Nash, D.M. Newbold,
M.G. Probert
Rutherford Appleton Laboratory, Didcot, UNITED KINGDOM J.A. Coughlan, R. Halsall, W.J. Haynes, I.R. Tomalin
5
N. Marinelli**13, A. Nikitenko**6, S. Rutherford, C. Seez **1a
R. Breedon, P.T. Cox, P. Murray, M. Tripathi
R. Cousins, S. Erhan, J. Hauser, P. Kreuzer**13, M. Lindgren, J. Mumford, P. Schlein, Y. Shi, B. Tannenbaum, V. Valuev, M. Von Der Mey**15
I. Andreeva**1A, R. Clare, S. Villa
S. Bhattacharya, J.G. Branson, I. Fisk, J. Letts, M. Mojaver, H.P. Paar, E. Trepagnier California Institute of Technology, Pasadena, California, USA
V. Litvine, S. Shevchenko, S. Singh, R. Wilkinson
Fermi National Accelerator Laboratory, Batavia, Illinois, USA S. Aziz, M. Bowden, J.E. Elias, G. Graham, D. Green, M. Litmaath, S. Los, V. O’Dell,
N. Ratnikova, I. Suzuki, H. Wenzel
D. Acosta, D. Bourilkov**24, A. Korytov, A. Madorsky, G. Mitselmakher, J.L. Rodriguez,
B. Scurlock
S. Abdullin**6,15, D. Baden, S.C. Eno, T. Grassi, S. Kunori Massachusetts Institute of Technology, Cambridge, Massachusetts, USA
I. Osborne, L. Taylor, L. Tuura
W.C. Fisher**15, J. Mans**16, D. Stickland, C. Tully, T. Wildish, S. Wynhoff
6
**1a:Also at CERN, European Organization for Nuclear Research, Geneva,
Switzerland
**1b:Now at CERN, European Organization for Nuclear Research, Geneva,
Switzerland
**1c:Now also at CERN, European Organization for Nuclear Research, Geneva,
Switzerland
**3:Now at DAPNIA, Centre d’Etudes de Saclay (CEA-Saclay), FRANCE **5:Now at Institutf¨ur Teilchenphysik, Eidgen¨ossische Technische Hochschule
(Eth), Z¨Urich, Switzerland
**6:Also at Institute for Theoretical and Experimental Physics, Moscow, RUSSIA
Poland
**8:Also at Universit`a di Pisa, Scuola Normale Superiore e Sezione dell’ INFN,
Pisa, Italy
**10:Now also at Institute Rudjer Boskovic, Zagreb, CROATIA **11:Now at Universit´e Catholique de Louvain, Louvain-la-Neuve, BELGIUM **14:Also at Institute for Nuclear Research and Nuclear Energy, Sofia, BULGARIA **15:Now at Fermi National Accelerator Laboratory, Batavia, Illinois, USA
1. Introduction
The Large Hadron Collider (LHC) , is a hadron-hadron collider to be installed in the Large Electron Positron (LEP) tunnel at the CERN Laboratory (the European Laboratory for Particle Physics outside Geneva, Switzerland). It will be a unique tool for fundamental physics research and the highest energy accelerator in the world for many years following its completion. The LHC will provide two proton beams, circulating in opposite directions, at an energy of 7 TeV each (center-of-mass √s = 14 TeV). These beams upon collision will produce an event rate about 1,000 times higher than that presently achieved at the Tevatron p¯p collider . In order to support the 7 TeV proton beams, in total 1104 8.4 Tesla superconducting dipoles and 736 quadrupoles will be installed in the underground tunnel of 26.6 km circumference formerly used by LEP.
The physics potential of the LHC is unprecedented: it will allow to study directly and in detail the TeV scale region. The LHC is expected to elucidate the electroweak symmetry breaking mechanism (EWSB) and provide evidence of physics beyond the standard model . The LHC will be also a standard model precision measurements instrument mainly due to the very high event rates as shown in table 1.
Table 1. Approximate event rates of some physics processes at the LHC for a luminosity of L = 2 × 1033 cm−2s−1. For this table, one year is equivalent to 20 fb−1.
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The proton beams cross at interaction points along the ring where detectors that measure the particles produced in the collisions are installed. Interaction “Point 5” hosts the multiple purpose 4π coverage CMS detector, shown in figure 1.
The CMS detector measures roughly 22 meters in length, 15 meters in diameter, and 12,500 metric tons in weight. Its central feature is a huge, high field (4 Tesla) solenoid, 13 meters in length, and 6 meters in diameter. Its “compact” design is large enough to contain the electromagnetic and hadron calorimetry surrounding a tracking system, and allows a superb muon detection system. All subsystems of CMS are bound by means of the data acquisition and trigger system.
In the CMS coordinate system the origin coincides with the nominal collision point at
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the geometrical center of the detector. The z direction is given by the beam axis. The rest frame of the hard collision is generally boosted relative to the lab frame along the beam direction, θ is the polar angle with respect to the z axis and φ the azimuthal angle with respect to the LHC plane. The detector solid angle segmentation is designed to be invariant under boosts along the z direction. The pseudorapidity η, is related to the polar angle θ and defined as η ≡−ln(tan(θ/2)). The transverse momentum component z-axis is given by pT=p sin θ and similarly ET=E sin θ is the transverse energy of a physics object.
The experiment comprises a tracker, a central calorimeter barrel part for |η| ≤1.5, and endcaps on both sides, and muon detectors.
The Tracking System Is Made Of
several layers of silicon pixel and silicon strip detectors and covers the region |η| < 2.5. The electromagnetic calorimeter consists of lead tungstate (PbWO4) crystals covering |η| < 3 (with trigger coverage |η| <2.6).
The Surrounding Hadronic
calorimeter uses brass/scintillator tiles in the barrel and endcaps.
Its Resolution For
jets, when combined with the electromagnetic calorimeter, is ∆E/E = 110%/
E ⊕5%.
The region 3 < |η| < 5 is covered by forward calorimeters with a resolution of ∆E/E =
√
E ⊕10%. Muons are measured in gas chambers in the iron return yoke. The muon momentum measurement using the muon chambers and the central tracker covers the range |η| < 2.4 with a resolution of ∆pT/pT = 5% at pT = 1 TeV and ∆pT/pT = 1% at pT = 100 GeV. The muon trigger extends over the pseudorapidity range |η| < 2.1.
The total non-diffractive inelastic cross section at the LHC is expected to be σT = 55 mb [5, 6]. The LHC will operate at a bunch crossing rate of 40 MHz. Only 80 % of the bunches will be filled , resulting in an effective bunch crossing rate of 32 MHz.
The instantaneous luminosity in the first two years after start–up is expected to be
L = 2 × 1033 Cm−2S−1
and subsequently upgraded to L = 1034 cm−2s−1 in a second phase. In the following these two values are referred to as “low luminosity” and “high luminosity”, respectively. The average number of inelastic non-diffractive interactions per bunch crossing µ is µ = 17.3 at high and µ = 3.5 at low luminosity.
In total CMS has ∼108 data channels that are checked each bunch crossing. The design data-size per event is about 1 MB. At start-up it is essential to allow for a larger event size, up to 1.5 MB per event, in order to be able to thoroughly study and understand the detector performance.
One of the most important and difficult aspects of the experiment is the design of the trigger, the real-time selection and recording of the (judged) useful events. Minimum deadtime and maximum physics retention are required of the data acquisition (DAQ), trigger and data recording architecture. To achieve this, sophisticated and fast selection algorithms are implemented that use selective information from all the detector subsystems during real-time data taking. The rate of interesting physics processes that need be recorded compared to the inclusive pp cross section is many orders of magnitude smaller.
The CMS trigger is designed to perform a data reduction from 32 MHz down to O(100)
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Figure 1. Three dimensional view of the CMS detector, and it’s detector components. Hz via different sequential trigger levels.
The First Trigger Level Of Cms,Level-1, Is
hardware implemented and reduces the data rate, by using specific low level analysis in custom trigger processors. All further levels are software filters which are executed on (partial) event data in a processor farm. This is the upper level of real-time data selection and is referred to as High-Level Trigger or HLT. Only data accepted by the HLT are recorded for offline physics analysis. Additionally, small samples of the rejected data are retained for monitoring the performance of the HLT while the bulk of it is discarded and dropped from any further processing without compromising physics efficiency.
This paper details how CMS proposes to achieve the necessary reduction factor, while keeping an uncompromising physics efficiency. The HLT algorithms are described in detail, typical threshold choices are given and the physics performance for several benchmark processes is demonstrated. The results reported here demonstrate that CMS has developed an efficient and agile trigger structure which will select the physics signals of interest in the harsh LHC conditions.
The report is organized as follows. Section 2 describes the CMS trigger, section 3 the electron/photon triggers and section 4 the muon triggers. The jet and missing ET related triggers are discussed in sections 5 and 6. Sections 7 and 8 discuss the τ and other heavy flavour triggers respectively.
In section 9 we present the initial ideas on calibration triggers, while section 10 studies benchmark physics channels and discusses a prototype trigger table for the HLT. The Appendix describes the Level-1 trigger algorithms.
2.1. Physics Requirements
The main physics requirements on the L1 trigger and the HLT are: • foremost, the requirement that the selection fulfill the needs of the CMS physics program; the efficiency for the physics objects must be as high as possible; • the selection must be as inclusive as possible. The LHC represents a new energy frontier, and unexpected new phenomena may appear. The selection requirements must retain events of potential use in such exotic searches; • all thresholds and other requirements applied by the selection should be very robust, so that detailed knowledge of calibration constants and other run conditions do not
Pose A Stringent Constraint In Real Time;
• the final selection of events should include data samples for the calculation of all
Trigger And Reconstruction Efficiencies Offline;
• the rate of events accepted by the HLT should be within limits allowed by the data
Recording Technology (O(100) Hz);
• all algorithms and their implementation should be monitored continuously for their
Correct Functioning;
• the events selected by the HLT should be tagged to indicate the reasons for their
Selection, To Aid The Offline Reconstruction;
• the HLT should include all major improvements in the offline reconstruction, and thus it should be as close as possible to the standard offline reconstruction code. 2.2. Selection Strategy and Reconstruction on Demand The CMS DAQ/HLT processes all events accepted by the Level-1 trigger in a single processor farm. There is therefore no separate Level-2 or Level-3, but a single entity, the High-Level Trigger. Nevertheless, as in a traditional multi-level trigger system, the selection of events can be optimized by rejecting events as quickly as possible. The basic event building strategy is to reconstruct those parts of each physics object that can be used for selection while minimizing the overall CPU usage.
As an example, reconstruction of an electron includes the reconstruction of a cluster in the electromagnetic calorimeter, the matching of hits in the pixel detector and the subsequent reconstruction of a full charged particle track in the tracker. At the end of each step a set of selection criteria results in the rejection of a significant fraction of the events accepted by the previous step.
The Rate Of Events That Need To Be
processed through the remaining algorithms is decreased reducing the required CPU. Reconstruction and selection are therefore closely intertwined in the online environment of the filter farm. For an optimal system the HLT should reconstruct the minimum amount of detector information needed to apply a set of selection criteria that reject background events while keeping the desired physics events for further processing.
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It is important to note that a fraction of the bandwidth, between 10-30%, (closer to 30% at start-up) needs to be reserved for calibration triggers to ensure a complete and accurate understanding of the detector performance.
2.3.
Trigger Levels – Definitions
The reconstruction and selection in the HLT takes place in steps which correspond roughly to what would have been distinct trigger systems, the Level-2 and Level-3 trigger systems. It is thus convenient to use the terminology, and to refer to a “Level-2 trigger” or a “Level-3 step” to describe the selection algorithms and criteria of the HLT.
As mentioned previously the CMS HLT architecture does not include a sharp division between these trigger steps, other than the order in which they are applied. In what follows, the convention used is that “Level-2” triggers, algorithms and requirements refer to the first selection step in the HLT process. Typically, a Level- 2 trigger, which has the maximum rate of events input to it, uses only information from the calorimeter and muon detectors. In contrast, “Level-3” refers to selection that includes the reconstruction of full tracks in the tracker. Traditionally, because of the high number of channels, the complex pattern recognition and higher combinatorics, track reconstruction is a process that demands large amounts of CPU time. Extending the terminology, in what follows there are references to “Level-2.5” triggers, which refer to algorithms that use partial tracker information, e.g. pixel hits, for a fast confirmation of the electron candidate. The numbering, “2.5”, attempts to indicate the intermediate nature of the selection, as one that occurs between the selection that is based solely on the calorimeter information, and the selection that is based on the full CMS detector information.
2.4.
Partial Event Reconstruction
To minimize the CPU required by the HLT, a key feature of the algorithms is to reconstruct the information in the CMS detector only partially.
In Many Cases The
decision on whether an event should be accepted by the HLT involves the reconstruction of quantities in only a limited region of the detector.
As An Example, For An Event
accepted by the Level-1 trigger in the inclusive muon stream, only the parts of the muon chambers indicated by the Level-1 trigger results, and the corresponding road in the tracker, need be considered for the validation of the muon.
The idea of partial event reconstruction has been embedded in the CMS reconstruction code from the very beginning. In the case of the HLT, the reconstruction of physics objects is driven by the corresponding candidates identified by the Level-1 trigger.
All reconstruction starts from the Level-1 trigger information.
This Approach Leads
to significant CPU savings, however it also leads to rejecting events that contain “volunteer” objects, i.e. objects that did not pass the Level-1 trigger. This disadvantage is mitigated by the fact that it is, in general, very difficult to understand the properties of such objects in later offline analyses. It is clearly always feasible, albeit with an
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increased CPU cost, to look for additional objects in each event if a particular physics analysis introduces such a requirement.
2.5. Level-1 Trigger Settings And Rates
The performance of the Level-1 trigger system is summarized in the Appendix A and further details of the system can be found in the Level-1 Trigger Technical Design Report (TDR) . Some small changes in expected rates and efficiencies with respect to that document have been incorporated in this report. The changes reflect the Monte Carlo input, including an updated version of the PYTHIA Monte Carlo simulation and increased statistics in the Monte Carlo samples generated, as well as a more detailed and tuned detector and trigger simulation. The main thrust of the conclusions of reference remains unaltered: the overall performance of the system satisfies the requirements of the CMS physics program. An additional change with respect to the trigger TDR is the definition of the low luminosity run conditions: “low” luminosity in this document refers to an instantaneous luminosity of L = 2 × 1033 cm−2s−1(twice the definition of low luminosity at the TDR) while “high” luminosity refers to the nominal LHC design value of L = 1034 cm−2s−1. The current plans of CMS call for a phased installation of the Data Acquisition system so that at start-up the DAQ can handle a Level-1 accept event rate of up to 50 kHz and at the full design luminosity it can handle a rate of 100 kHz.
The allocation of the Level-1 trigger bandwidth must be optimized in order to ensure the widest possible physics reach for the experiment, while including all technical triggers intended for calibration and monitoring of the detector. The procedure used for this optimization starts with a determination of the maximum Level-1 trigger rate that can be allocated, which is 16 kHz at low luminosity and 33 kHz at high luminosity. These maximum rates arise from dividing the total DAQ bandwidth, i.e. 50 kHz (100kHz) at low (high) luminosity, by a safety factor of three. This safety factor is used to account for all uncertainties in the simulation of the basic physics processes, the CMS detector, and the beam background conditions.
The second step is a first allocation of this Level-1 bandwidth across the different objects. An equal allocation across the four categories of “objects” taken as (a) electrons/photons, (b) muons, (c) tau-jets and (d) jets-combined channels, is made.
For example, at low luminosity about4 kHz is pre-allocated to each of these triggers above. The third step is to determine thresholds for the single and double-object triggers within this first Level-1 rate allocation. As an example, the 8 kHz of electron and photon triggers at high luminosity has to be divided among single and double electrons/photons.
For this purpose the iso-rate contours on the plane of the ET cut on the single objects versus the ET cut on the double objects are examined, as shown in fig. 2 (left). An operating point in this single-double threshold plane must be selected for a given a Level-1 trigger allocation. To determine the optimal operating point, the efficiency for
Combined Rate At 1034/Cm2 /S
Figure 2. Contours of equal rate on the plane of ET thresholds for single and double- electron/photon triggers (left), and efficiency for W and Z electronic decays as a function of the same thresholds (right).
triggering on selected physics channels, via the single and the double-object trigger, is considered. In the case of the electron/photon trigger the efficiency for W →eν decays versus the efficiency for Z →ee decays can be used, as in figure 2 (right). The optimal point can be selected as a trade-offbetween the two efficiencies, e.g. adopting the point at which both efficiencies drop at the same rate, as shown in the same figure. The same method is used for muons and τs.
There is no similar optimization of the allocation for jet triggers since there is no reason to include a 2-jet trigger requirement. All QCD events have a second jet which, though by definition at a lower ET than the leading jet, is always present in the event.
The last step in this procedure is to evaluate the optimal efficiencies for each of the four object categories and to then re-iterate the entire procedure with slightly different Level-1 trigger allocations.
Note that the Level-1 triggers only consider cross-object triggers for a limited number of categories. 2.6.
Level-1 Trigger Table
With the constraints described previously, the prototype Level-1 trigger tables that are used in the present paper for further analysis of the HLT algorithms and performance are listed in tables 2 and 3 for low and high luminosity respectively. The thresholds quoted correspond to the ET or pT value at which the efficiency of the trigger is 95% of its maximum value. There is no entry for a µ+jet trigger at low luminosity because there is little to be gained given the low inclusive muon threshold. In both cases, a 1 kHz bandwidth is allocated to minimum-bias events which will be used for calibration
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Table 2. Level-1 trigger table at low luminosity. Thresholds correspond to values with 95% of the maximum available efficiency (except for the muon triggers which are at 90% efficiency)
16.0
Table 3. Level-1 trigger table at high luminosity. Thresholds correspond to values with 95% of the maximum available efficiency (except for the muon triggers which are at 90% efficiency).
33.5
and monitoring purposes.
2.7. Event Generation And Detector Simulation
The studies of the HLT have been performed with simulated events, by tracking particles through a realistic simulation of the detector, adding pileup events (the additional 3.5(17.5) interactions at low(high) luminosity conditions), and applying the
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HLT algorithms to the digitized data.
Standard Monte Carlo Generators, Such As
PYTHIA and ISAJET , are used to simulate the collisions between two protons at √s = 14 TeV. Event samples have been generated for the muon, electron, b and τ and jet signal samples as well as for the pileup of minimum bias collisions. In several cases special care has to be taken to ensure an efficient but correct sample generation. As an example the generation of the minimum bias background for HLT studies involving muons is treated somewhat differently than for studies without muons since every charged pion or kaon with a momentum above a few GeV/c can potentially decay into a muon, penetrate into the muon system, and be mismeasured as a high-pT muon because of multiple scattering through the iron yoke. A complete simulation of this background would be CPU-wise prohibitive, hence a weighting procedure is used. Details are given in ref. .
A procedure has been developed to take into account the effects of the pileup in the muon system, as detailed in . For the jet trigger sample a cross section weighting technique is applied as well . Attention has also been paid for the pileup samples, to ensure that the limited statistics and re-use of events in these samples does not lead to overestimated trigger rates due to a few recurring events.
For the HLT studies presented in this paper, the CMS detector simulation package, CMSIM is used. It is an application of the GEANT3 detector description and simulation tool. CMSIM is used to describe the detector geometry and materials.
It also includes and uses information about the magnetic field.
Cmsim Reads The
individual generated events and simulates the effects of energy loss, multiple scattering and showering in the detector materials with GEANT3. The average storage size of a single event for these studies is about 2 MB. The CPU time required to simulate one event on a 1 GHz CPU ranges from 60 s for a minimum-bias event, to 500 s for a 1 TeV di-jet event.
3.
Electron And Photon Identification
The HLT selection of electrons and photons proceeds in three steps.
The First Step
(Level-2.0), uses the calorimeter information alone. The next step (Level-2.5) demands hits in the pixel detectors consistent with an electron candidate. Matching of energy in the electromagnetic calorimeter (ECAL) with hits in the pixel detector or failure to match, splits the electromagnetic triggers into two categories: electron candidates (single and double), and above significantly higher thresholds, photon candidates. In the final step (Level-3) the selection of electrons uses full track reconstruction, seeded from the pixel hits obtained at the matching step.
For the calorimeter reconstruction – clustering followed by energy and position measurement – the emphasis is predominantly on the reconstruction of electrons, because the transverse momentum thresholds for triggering on electrons are much lower than those for photons. Since the amount of material traversed in the tracker volume is almost one radiation length for certain polar angles, the first challenge for ECAL
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clustering is to include all energy radiated by electrons. Photons that have converted in the tracker material are adequately reconstructed by the electron algorithms. For the final higher precision reconstruction of photons it is foreseen that unconverted photons will be reconstructed using energy sums of fixed arrays of crystals and that tracker information will be used to assist the clustering for converted photons. Such algorithms that improve the photon energy resolution, are not necessary for the HLT selection.
3.1.
Calorimeter Reconstruction: Clustering
The first step in the reconstruction of an electron in the High-Level Trigger is the clustering of the energy deposits in the ECAL and the estimate of the electron’s energy and position from this information.
In The Barrel Section This Involves The Energy
deposited in the lead tungstate crystals alone, in the endcap energy is also deposited in the 3X0 thick preshower detector. Electrons radiate in the material between the interaction point and the ECAL. The bending of the electron in the 4T magnetic field results in an azimuthal spray of energy reaching the ECAL. The electron energy can be collected by forming a group of clusters along a φ-road. This cluster of clusters is called a “super-cluster”.
3.1.1.
The Island Algorithm
The island algorithm starts by a search for seeds which are defined as crystals with an energy above a certain threshold. Starting from the seed position, adjacent crystals are examined, scanning first in φ and then in η. Along each scan line crystals are added until either a rise in energy or a crystal that has not been read out is encountered. The clustering starts from the highest ETseed in the list of seeds, and the crystals included in the cluster are marked after being used so as to be
Only Included In A Single Cluster
In much the same way as energy is clustered at the level of calorimeter cells, non- overlapping clusters can in turn be clustered into calorimetric “super-clusters”. The procedure is seeded by searching for the most energetic cluster and then collecting all the nearby clusters in a very narrow η-window and much wider φ-window.
3.1.2. The Hybrid Algorithm For single showers, such as those produced by unconverted photons, or those produced by electrons in test beam conditions, energy sums of fixed arrays of crystals give a better energy resolution performance than energy sums of crystals collected dynamically according to a cluster or “bump” finding algorithm. The Hybrid algorithm uses the η−φ geometry of the barrel crystals to exploit the knowledge of the lateral shower shape in the η direction (taking a fixed bar of three or five crystals in η), while searching dynamically for separated (bremsstrahlung) energy in the φ direction.
The Hybrid algorithm is used to reconstruct electrons with pT>10 GeV/c in the barrel. By contrast, when looking for small deposits of energy in individual clusters, for example when making a calorimetric isolation cut, the basic clusters of the Island algorithm are
17
more appropriate objects to work with. Further details on the clustering algorithms can be found in reference .
3.2. Endcap Reconstruction With The Preshower
Much of the endcap is covered by a preshower detector with two planes of silicon strip readout. The energy deposited in the preshower detector (which is about 3X0 thick) needs to be added to the crystal clusters . The energy in the crystals is clustered using the Island algorithm and the clusters are associated to form super-clusters. A preshower cluster is constructed in each plane, in front of each crystal cluster of the super-cluster. The search area in the preshower is centered on the point determined by extrapolating the crystal cluster position to the preshower plane in the direction of the nominal vertex position.
3.3.
Energy And Position Measurement
3.3.1. Position Measurement Using Log-weighting Technique
A Simple Measurement
of the shower position can be obtained by calculating the energy-weighted mean position of the crystals in the cluster. Two features need to be addressed in more detail in order to obtain a precise position measurement.
The first is the precise definition of the “crystal position”. The lateral position of the crystal depends upon depth because the crystals are ”off-pointing” and the incident particle and shower direction is not exactly parallel to the crystal axis. The lateral position of the crystal is thus defined as the (η, φ) position of its axis at a particular depth. The depth at which the shower maximum occurs is taken as the longitudinal baricentre of the shower which has a logarithmic dependence on the shower energy.
This depth is roughly the longitudinal center of gravity of the shower, and its optimal mean value varies logarithmically with the shower energy. There is also a dependence on particle type: electron showers have a maximum about one radiation length less deep than photon showers.
In the position measurement used for both Island and Hybrid super-clusters the depth is measured from the front face of the crystals along the direction from the nominal vertex position to the approximate shower position calculated using the arithmetic energy weighted mean of the shower front face centers. The energy dependence is accounted for with a logarithmic parametrization .
The second feature that requires more detailed treatment is related to the lateral shower shape. Since the energy density does not fall away linearly with distance from the shower axis, but rather exponentially, a simple energy weighted mean of crystal energies is distorted and the measured position is biased towards the center of the crystal containing the largest energy deposit.
A simple algorithm, which yields adequate precision consists of using the weighted mean, calculated using the logarithm of the crystal energy:
18
with the sum over all crystals of the cluster, and where xi is the position of crystal i, and Wi is the log weight of the crystal – the logarithm of the fraction of the cluster energy contained in the crystal, calculated with the formula:
P Ej
where the weight is constrained to be positive, or is otherwise set to zero. W0 then controls the smallest fractional energy that a crystal can have and still contribute to the position measurement.
So far what has been described refers to the measurement of the position of a single cluster. The position of a super-cluster is calculated by making the energy-weighted mean of the positions of its component clusters. For an electron that has radiated into the material, this method allows to reconstruct its position at production.
3.3.2. Energy Measurement and Corrections The measurement of energy in the crystals is obtained by simple addition of the deposits measured in the crystals – although more complex estimators have been proposed .
Even in the areas not covered by the preshower detector the energy containment of the clustered crystals is not complete. The reconstructed over the generator level energy distribution, Emeas/Etrue, shows a peak at a few percent less than unity, and a long tail on the low side due to non-recovered bremsstrahlung energy. The Gaussian part of the distribution corresponds, roughly, to the energy that would be reconstructed from an electron in the absence of bremsstrahlung. The amount of tracker material varies strongly with η, as shown in figure 3, and thus so does the amount of bremsstrahlung radiation, so a variation in the fraction of events in the tail as a function of η is expected.
This inevitably leads to a small variation in the peak position as a function of η. The energy scale is “calibrated” using corrections designed to place the peak in Emeas/Etrue at 1.0, see figure 4.
The Corrections Are Parametrized In Terms Of The
number of crystals in the cluster (f(Ncry) corrections).
This Helps To Minimize The
residual dependence on both E and η of the energy scale.
5 Shows, As An
example, Emeas/Etrue as a function of the number of crystals in a reconstructed Hybrid super-cluster, for electrons with 10 3.3.3. an isolated Level-1 trigger (Appendix A.2) is requested, which results in about 8% inefficiency mainly due to bremsstrahlung radiation in the isolation region (about 6%), but no trigger threshold is applied. Figure 4 shows the distribution of Emeas/Etrue for pT= 35 GeV/c electrons reconstructed using the Hybrid algorithm in the barrel, and using the Island algorithm and the preshower in the endcap. The energy resolution is parametrized in two ways: terms of the fitted width of the Gaussian part of the distribution (fitted between - 1.5σ and +2.0σ), and in terms of σeff, defined as the half-width containing 68.3% of the Figure 3. Material budget as a function of η for the different tracker sub-units. Figure 4. Distribution of Emeas/Etrue for pT = 35 GeV/c electrons, a) in the barrel ECAL fully digitized without pileup, and reconstructed with the Hybrid super-clustering algorithm, b) the same distribution for electrons in the endcap, reconstructed with the Island super- clustering algorithm, and with preshower energy included. Emeas/Etrue. The variable µ is the mean value of the Gaussian fit, shown by the curve; for σeff, see text. Figure 5. Emeas/Etrue as a function of the number of crystals in a Hybrid super-cluster together with a fitted polynomial function. distribution – if the distribution is Gaussian then σeff is just the Gaussian sigma, when the distribution has more significant tails then σeff provides some measure of this. The parameter σeff provides a convenient measure of performance which adequately reflects final physics performance (e.g. in extracting signal significance). It is worth noting, as a comparison, that unconverted photons with a flat pT spectrum in the range 10< pT<50 GeV/c can be reconstructed, in the barrel using a fixed window in η−φ of 5×5 crystals, and in the endcap using a 3×3 fixed window with impact position correction, achieving in both cases a resolution of σeff/E = 0.9% at low luminosity. Figure 6 shows the position resolution in η and φ for the same sample. Table 4 gives a more complete list of performance results for electron reconstruction in both the barrel and endcap. Values for pT= 35 GeV/c electrons are given, together with values for electrons having a flat pT spectrum in the range 10 < pT< 50 GeV/c. The σeff value is not given for the η resolution because it is, in all cases, the same as the Gaussian fit value. 3.4. The first step of the HLT, using only calorimeter information, is to reconstruct an ECAL super-cluster in a region specified by the Level-1 trigger. The super-cluster is first required to fall within the precision physics fiducial region of the ECAL, which is obtained by removing the barrel/endcap transition region from the overall coverage Table 4. Energy and position resolution performance for barrel and endcap ECAL using electron samples simulated with different pileup conditions, using single particles. Barrel reconstruction; |η| <1.4442 (Hybrid algorithm) Endcap reconstruction; 1.566 < |η| < 2.5 (Island algorithm, and preshower) Figure 6. Position resolution for pT = 35 GeV/c electrons in the barrel ECAL, fully digitized without pileup, and reconstructed with the Hybrid super-clustering algorithm. of |η| <2.5 . This transition region is strongly shadowed by tracker cables exiting through the gap between the barrel and endcap. This region comprises the first trigger tower in the endcap. The last two crystals in the barrel are also removed from the trigger. The excluded area thus covers 1.4442 < |η| < 1.5660. The super-cluster is then required to have ET above a threshold which is chosen to give 95% efficiency for electrons at the same point on the ET scale at which the Level-1 trigger has 95% efficiency . The same threshold is required for both objects in the di-electron trigger. At L = 2 × 1033 cm−2s−1the thresholds are 26 GeV for the single, and 14.5 GeV Rbarrel = 136.5 c.m. Zendcap = 328.0 c.m. Figure 7. Fractional ET resolution, as a function of η, induced by a 1σ shift of the longitudinal vertex position. for the double electron trigger. The corresponding thresholds at L = 1034 cm−2s−1 are 31 GeV and 16.9 GeV. This cut on the transverse energy reconstructed in the ECAL increases the rejection of fake electrons by about a factor of two. Some refinements of this Level-2.0 selection can be envisaged, but have not been used in the basic selection procedure for which results are here presented. Firstly, the Level- 3 selection uses cuts on purely calorimetric quantities – ECAL isolation and an H/E (hadronic/electromagnetic) cut – which could be applied at an earlier stage. Secondly, a significant contribution to the transverse energy resolution comes from the lack of knowledge, at this stage, of the longitudinal vertex position. The contribution to the fractional ET resolution, as a function of η, due to a 1σ shift of the vertex longitudinal position (5.3 cm), is shown in figure 7. A small improvement in efficiency would be obtained by making the electron threshold cuts in two stages: a looser cut at Level-2.0 followed by the full set of cuts at a later stage, after the pixel matching of Level-2.5 which gives a precise longitudinal vertex position. 3.5. Level-2.5: Matching of Super-clusters to Hits in the Pixel Detector The matching of super-clusters reconstructed in the calorimeter to hits in the pixel detector takes advantage of the fact that the energy-weighted average impact point of an electron and the bremsstrahlung photons it has radiated, is precisely where a non-radiating electron would have impacted. It is this space-point that the position measurement of the super-cluster attempts to determine. This point can be propagated back through the field to obtain an estimate of the direction of the electron at the vertex, and the hit positions expected in the pixel detector. Since most of the tracker material lies after the pixel detector, most electrons do not radiate significantly before it, and most photon conversions take place after it. So matching hits are given by most electrons and by few photons. The layout of the pixel system is shown in figure 8. The continuous lines show the Figure 8. Full pixel detector (high luminosity) with continuous lines pointing from the nominal vertex to the edges of the ECAL barrel and endcap, and dashed lines pointing from maximum values of the ECAL barrel and endcaps and the dashed lines correspond to electrons generated z = ±15 cm away from the nominal vertex. For the clusters at the ends of the ECAL barrel, pixel disks are needed as well as barrel pixel layers. For endcap clusters the mix of pixel barrel and pixel disk hits depends on both the pseudorapidity and the z-vertex of the electron. With the geometry used for this simulation study there is a loss of efficiency in the high |η| region of the ECAL endcap where, in some cases, the electron goes through only one pixel layer. The outer barrel layer and the outermost endcap disks of the pixel detector is staged and may not be present at the start-up of the experiment. The simulation of the HLT selection at low luminosity is made by discarding pixel information in these layers.The (i) The electromagnetic cluster gives the energy and the position of the electron candidate. The transverse momentum is computed from the measured energy and position of the cluster. The expected hit position on the pixel layers is estimated by propagating the electron inwards to the nominal vertex using the magnetic field map. A search area is defined in the innermost pixel layer. It is unrestricted in z, and its width in φ (typically 40 mrad) is the main parameter used to control the tightness of the pixel matching. The errors on the calculated hit positions are due to the spread in z of the vertex position and the precision of the φ measurement in the calorimeter. At this stage the error on the cluster ET measurement contributes very little to the uncertainty on the expected hit position in the pixel detector. (ii) If a compatible hit is found within the search area on the innermost pixel layer, a better estimate of the longitudinal (z) vertex position is obtained by interpolating the line from the cluster through the corresponding hit to the beam line. Nominal values (0,0) for x and y coordinates of the vertex are assumed. If no hit is found in the search area of the innermost pixel layer, the search is repeated in the next layer. (iii) The track is propagated from the newly estimated vertex to the next pixel layer through the compatible hit in the first (or second) layer. The dominating uncertainty, in the r −φ plane, results from the estimate of the ET of the electromagnetic cluster, and thus the radius of curvature of the electron track. But this is a very small uncertainty since the distance from one pixel layer to the next is short. Indeed, assuming a hit on the r = 4 cm layer, the distance between the hit predictions on the r = 11 cm layer for pT= 15 GeV/c and pT= 20 GeV/c electron would be 78 µm – less than the size of a pixel. In the r −z plane, the main uncertainty comes from the vertex z. (iv) If another compatible hit is found, the cluster is identified as an electron, if not, it is rejected as a jet. If there are no compatible hits in the current layer, there may be one more pixel layer left, and the search is repeated there. The search is made twice, once for each charge. In the first step of the search the electron and positron search areas can overlap, but in the second step, when a compatible hit is propagated to another pixel layer, the pT needed for the search areas of different charges to overlap is almost 1 TeV/c. For low luminosity both the staged and full pixel detector configurations are investigated. Using the inner pixel layers alone results in a large inefficiency (∼7%) in the staged pixel configuration, so the low luminosity staged pixel detector algorithm supplements the pixel hits with hits found in the first silicon strip layer of the tracker, and regains some of the lost efficiency. More details of the Level-2.5 pixel matching algorithm are given in reference . The “rejection” versus efficiency obtained from the Level-2.5 pixel matching is shown in figure 9, at (left) low luminosity (L = 2 × 1033 cm−2s−1), and (right) high luminosity (L = 1034 cm−2s−1). The efficiency is calculated using an electron sample passing the Level-2.0 threshold. The “rejection” is calculated from the single electron triggers in the jet background passing the Level-2.0 threshold and is the efficiency of the electron algorithm in a jet sample. In practice, single and double photon streams are created by applying an ET threshold to the events rejected by the pixel matching. For a 95% efficiency the rejection factors are 16.5 (12.5) at low (high) luminosity. For the low luminosity case two different curves of the efficiency versus rejection, corresponding to the full and staged pixel detector configurations, are shown in figure 9 (left). The performance at high luminosity, shown in figure 9 (right), is very similar to the low luminosity performance without staging with respect to electron efficiency, but there is a noticeable loss of rejection power which can be attributed to pileup hits. high luminosity figure also shows the performance in a more restricted central region (|η| <2.1) where the efficiency is noticeably better. A similar conclusion is reached at low luminosity (not shown). Figure 9. Rejection versus efficiency obtained from the Level-2.5 pixel matching. Left: at low luminosity (L = 2 × 1033 cm−2s−1); the top curve shows the performance when the full pixel detector is used while the lower curve shows the performance for the staged pixel scenario (see text). Right: at high luminosity (L = 1034 cm−2s−1); the lower curve is the nominal detector configuration; the top curve corresponds to |η| <2.1. The definition of the rejection is discussed in the text. 3.6. Level-3 Selection of Electrons and Photons: Inclusion of Full Tracking The Level-3 selection includes all further requirements needed to reach an acceptable rate to final offline storage. The full event information, including tracks, is available, but some of the cuts used – hadronic/electromagnetic energy fraction and calorimetric isolation – use only calorimetric information. The Level-3 selection for electrons starts with electron track-finding, seeded by the Level-2.5 pixel match. To maintain high efficiency track-finding is made with very loose cut parameters. Cuts are then made on both E/P and on the distance between the super-cluster position and the extrapolated track position in the ECAL in the longitudinal coordinate, ∆η(track - cluster), which is only slightly distorted by bremsstrahlung. In the endcap a cut on the energy found behind the super-cluster, in the HCAL, expressed as a fraction of the super-cluster energy, H/E, is found to give Figure 10 shows, as an example, the E/P distribution for barrel electrons, and for jet background electron candidates in the barrel after selection at Level-2.5 followed by loose track finding seeded with the Level-2.5 pixel matches. When the distributions are broken down according to the number of hits associated in the tracks, the width and proportion of events in the tail of the distribution for electrons is found to vary (electrons which radiate little have tracks with more hits, and a better measured momentum). The ratio of signal to background also varies with the number of hits. Hence increased Figure 10. E/P for (upper plot) electrons and (lower plot) jet background candidates in the barrel, after Level-2.5 selection followed by track finding seeded by the Level-2.5 pixel hits (L = 2 × 1033 cm−2s−1). The background distribution has 30% overflows. performance can be obtained by optimizing the E/P cut as a function of the number of hits in the track. Specifically, for the studies discussed below the following selection cuts were applied: E/P < 1.5 (2.45) for the barrel (end cap), H/E < 0.028 in the endcap, and in the barrel a track/ECAL position match in η (∆η(track - cluster) < 0.028). At high luminosity the additional rejection power of isolation cuts is used to reduce the background to single electrons from jets. Three isolation techniques have been studied: ECAL isolation, pixel-track isolation, and full-track isolation. Track isolation has the advantage that it is less sensitive to pileup, which is the dominant source of signal inefficiency at high luminosity, because only tracks associated with the primary vertex are selected for the isolation cuts. The results presented in the tables below use no isolation for electrons at low luminosity, and a simple pixel-track isolation cut at high luminosity. Figure 11 shows the rejection against jet background, plotted as the efficiency of the electron algorithm on the QCD jet sample. This is compared to the efficiency for signal electrons from W →eν events when a pixel-track isolation cut is applied after the Level-2.5 selection at high luminosity. In addition, only events where a track can be made from the pixel hits of the Level-2.5 candidate are used. The different points on the plot correspond to different cuts on the number of 3-hit pixel tracks with pT> 1 Figure 11. Rejection against jet background versus the efficiency for electrons from Ws when a pixel-track isolation cut is applied after the Level-2.5 selection at L = 1034 cm−2s−1. Rcone is the cone radius. The points represent different values of the isolation (see text). Table 5. Photon stream thresholds and rates before additional Level-3 cuts. GeV/c found within cones of different sizes. 3.6.2. Further ET thresholds, higher than those applied at Level-2.0, are applied to super-clusters of single and double triggers that fail the Level-2.5 pixel matching. The events passing these cuts form the photon stream. thresholds are asymmetric, chosen to be 5 GeV lower than the offline analysis cuts envisaged for the Standard Model H →γγ search . The single photon thresholds are chosen to give an acceptable rate. Table 5 lists the thresholds and the rates before further Level-3 selection. Backgrounds can be rejected using track isolation cuts and by rejecting π0’s based on the Table 6. Electron and photon rates output by the HLT at low and high luminosity. (1) π±/π0 lateral shower shape. Defining the longitudinal coordinate of the vertex is a significant issue for the analysis of the H →γγ signal channel. For events where one or more of the photons has converted in the tracker, the track segment and the ECAL cluster can be used to locate the vertex. The vertices in the remaining events can be found using algorithms that choose the track vertex associated with the largest track activity. The efficiency for H →γγ is 80-90% for a jet rejection factor of 30-60 in the high luminosity environment. 3.7.1. the HLT at both low and high luminosity, broken down by contribution, are listed in table 6. For the low-luminosity selection a loose calorimetric isolation has been applied to the photon streams (ECAL ET in a cone of radius 0.45, excluding the supercluster, less than 3.5 GeV), but no isolation beyond that of the Level-1 trigger has been applied to the electron streams. To control the two-photon rate the thresholds have been raised to ET 1 > 40 GeV, ET 2 > 25 GeV (equal to the final offline cuts envisaged for H →γγ). This reduces the rate from 11 Hz to 5 Hz, and has a negligible effect on the efficiency, as is shown in the second column in table 7. A fully optimized selection will also involve track isolation on the photon streams (wholly or partly replacing the calorimetric isolation and the raised threshold) and track isolation in the single electron stream. This can reduce the total rate to about 26 Hz, of which only half is background, with the introduction of only a small further inefficiency. For the high-luminosity selection, pixel-track isolation has been applied to the electron stream, and full track isolation has been applied to the photon streams (no track with pT> 2 GeV/c in a cone of ∆R=0.2). 3.7.2. work is required to control the background rates are the single-electron and double- photon streams, so, the efficiencies for the decays W →eν and H →γγ are used as Table 7. Efficiency for H →γγ (MH=115 GeV/c2) through the complete selection chain, at L = 2 × 1033 cm−2s−1. Table 8. Efficiency for electrons from W decay through the complete selection chain benchmarks. Table 8 lists the efficiency for single electrons from W decay through the complete selection chain, at L = 2 × 1033 cm−2s−1 and at L = 1034 cm−2s−1. Events are preselected requiring the generated electrons to be within the ECAL fiducial region of |η| < 2.5, with the region 1.4442 < |η| < 1.5660 excluded. The geometric acceptance is approximately 60% and is not included in the efficiency. The second and fourth columns list the efficiencies for electrons that have pT greater than the Level-1 and Level-2 95% efficiency point. The efficiencies at L = 1034 cm−2s−1 are only slightly lower than those at low luminosity. The main difference comes from the loss due to the additional isolation cuts – typically a 5% loss per object. Table 7 lists the efficiency for H →γγ for a Higgs with mass MH = 115 GeV/c2 through the complete selection chain, at L = 2 × 1033 cm−2s−1. As in the previous table, events are preselected, requiring that the generated photons fall within the ECAL fiducial region. The geometric acceptance is 65%. The second column shows the efficiency for events where the two generated photons satisfy, in addition, the cuts currently assumed for offline analysis in this channel – ET 1 > 40 GeV, ET 2 > 25 GeV. 3.7.3. the HLT selection, benchmarked on 1 GHz processor, for jet background events at low 9. CPU usage of the HLT electron selection for jet background events at L = 2 × 1033 cm−2s−1, benchmarked on 1 GHz processors. luminosity. At high luminosity the time taken for the unoptimized global search for ECAL clusters at Level-2.0 is greatly increased and the overall total CPU time per Level-1 event, at a luminosity of L = 1034 cm−2s−1 is about three times as large, as at L = 2 × 1033 cm−2s−1. Preliminary results indicate that this clustering time can be reduced by a factor ∼10 using regional reconstruction. The muon selection for the HLT proceeds in two steps: firstly, muons are reconstructed in the muon chambers, which confirms the Level-1 decision and refines the pT measurement using more precise information; secondly, the muon trajectories are extended into the tracker, which further refines the pT measurement. After each step, isolation is applied to the muon candidates – the calorimeter being used after the first step and the tracker after the second. The muon track reconstruction algorithm used by the HLT is seeded by the – up to four– muon candidates found by the Level-1 Global Muon Trigger (see Appendix), including those candidates that did not necessarily lead to a Level-1 trigger accept by the Global Trigger. The algorithm uses the reconstructed hits built from the digitized signals in the muon system, and constructs tracks according to the Kalman filter technique . The resulting trajectories are used to validate the Level-1 decision as well as to refine the muon measurement in this Level-2 muon selection. The basis of the Level-3 muon selection is to add silicon tracker hits to the muon trajectory, thus greatly improving the muon momentum measurement and sharpening the trigger threshold. Isolation criteria can be applied to the muon candidates to provide additional rejection: at Level-2 using the calorimetric energy sum in a cone around the muon, and at Level-3 using the number of pixel tracks in a region around the projected muon trajectory. This suppresses muons from b, c, π, and K decays. 4.1. 4.1.1. Muon Standalone Reconstruction and Level-2 Selection segments from the muon chambers are used for muon identification and selection at Figure 12. Distribution of (1/pT rec-1/pT gen)/(1/pT gen), where pT gen and pT rec are the generated and Level-2 reconstructed transverse momenta respectively, shown in three pseudorapidity intervals: a) |η| <0.8 b) 0.8< |η| <1.2 c) 1.2< |η| <2.1 Level-2. The state vectors (track position, momentum and direction) associated with the segments found in the innermost chambers are propagated outwards through the iron yoke using the GEANE package , which takes into account the muon energy loss in the material, the effect of the multiple scattering, and the non-constant magnetic field in the muon system. The estimate of the momentum from the Level-1 Global Muon Trigger is used initially for the track propagation in the magnetic field. The predicted state vector at the next measurement surface is compared with existing measured points and updated accordingly using a Kalman filter technique. reconstructed track segments are used as measurements in the Kalman filter procedure; in the endcap chambers, where the magnetic field is inhomogeneous, it is the individual reconstructed hits belonging to the track segments that are used. Reconstructed hits from RPC chambers are also included. The procedure is iterated until the outermost measurement surface of the muon system is reached, at which point a constrained fit to the track parameters, working from the outside in, is performed under the assumption that the muon candidate originated from the interaction region (defined by the beam spot size: σxy = 15 µ m and σz = 5.3 cm; the beam spot can be determined from minimum bias events at the very start of the run). In both the forward and backward propagation just described, a hit is not added to the muon trajectory if its contribution to the total χ2 exceeds 25. The resulting track parameters, propagated inward to the collision vertex, are used to reject or accept the event for further Level-3 processing. More details on this stand-alone muon reconstruction can be found in reference . Figure 12 shows the resolution of the transverse momentum determined by the Level- 2 constrained fit for muons from W decays at high luminosity. The distributions are broken up into three pseudorapidity intervals: barrel (|η| <0.8), overlap (0.8< |η| <1.2) and endcap (1.2< |η| <2.1). In these three regions, the fitted pT resolutions are 10%, 15%, and 16%, respectively. 4.1.2. Inclusion of Tracker Information and Level-3 Selection reconstruction consists of extending the muon trajectories to include hits in the silicon tracker system. Starting from a Level-2 reconstructed muon, the muon trajectory is extrapolated from the innermost muon station to the outer tracker surface, taking into account the muon energy loss in the material and the effect of multiple scattering. As with Level-2, the GEANE package is currently used for the propagation through the iron and calorimeters. Silicon layers compatible with the muon trajectory are then determined, and a region of interest within them is defined to perform regional track reconstruction. The determination of the region of interest is based on the track parameters and uncertainties of the extrapolated Level-2 muon trajectory, obtained with the assumption that the muon originates from the interaction point as described in the previous section. This has a strong impact on the reconstruction efficiency, fake rate, and CPU reconstruction time: well measured muons are reconstructed faster and with higher efficiency than poorly measured ones. Inside the region of interest, initial candidates for the muon trajectory (regional seeds) are built from pairs of reconstructed hits. The two hits forming a seed must come from two different tracker layers, and all combinations of compatible pixel and double-sided silicon strip layers are used in order to achieve high efficiency. In addition, a beam spot constraint is applied to muon candidates above a given transverse momentum threshold to obtain initial trajectory parameters. Starting from the regional seeds, a track reconstruction algorithm based on the Kalman filter technique, is used to reconstruct tracks inside the selected region of interest. The track reconstruction algorithm consists of the following steps: trajectory building (seeded pattern recognition), trajectory cleaning (resolution of ambiguities) and trajectory smoothing (final fit). In the first step, the trajectory builder transforms each seed into a set of trajectories. Starting from the innermost layer, the trajectory is propagated to the next tracker layer that is reachable, and updated with compatible measurements found on that layer. In the second step, the trajectory cleaner resolves ambiguities between multiple trajectories that may result from a single seed on the basis of the number of hits and the χ2 of the track fit. In the final step, all reconstructed tracks are fit once again with reconstructed hits in the muon chambers included from the original Level-2 reconstructed muon, and selected on the basis of a χ2 cut. Figure 13 shows the resolution of the transverse momentum determined by the Level- 3 constrained fit as expressed by the distribution of the quantity (1/prec are the generated and reconstructed transverse momenta, respectively. Muons from W decays at high luminosity are used. The distributions are broken up into three pseudorapidity intervals: barrel (|η| <0.8), overlap (0.8< |η| <1.3) and endcap (1.3< |η| <2.1). In these three regions, the fitted pT resolutions are 1.0%, 1.4%, and 1.7%, respectively. The improvement in resolution over the stand-alone muon measurement from Level-2 is substantial. The efficiency of the Level-3 tracking algorithm relative to the Level-2 selection is shown in figure 14 as a function of η for single muons with pT>10 GeV/c and no pileup. and Level-3 reconstructed transverse momenta, respectively, shown in three pseudorapidity intervals: a) |η| < 0.8, b) 0.8 < |η| < 1.2, and c) 1.2 < |η| < 2.1. Figure 14. Algorithmic efficiency of the Level-3 tracking algorithm as a function of η for single muons generated flat over 10 < pT < 100 GeV/c. No pileup was included. The muons were generated flat in pT up to 100 GeV/c. The algorithmic efficiency is typically 99%, except in the pseudorapidity interval 0.8< |η| <1.2, where the DT and CSC systems have to be combined to reconstruct muons and the efficiency is about 97%. 4.1.3. The integrated rate of muons at LHC is dominated by muons from b, c, K, and π decays, as shown in figure 15. These muons are generally accompanied by other nearby particles, so they can be suppressed by isolation cuts. Three isolation techniques have been studied. The first (calorimeter isolation) is based on the standard technique of summing the calorimeter energy in a cone around the Figure 15. pT threshold and for luminosity L = 1034 cm−2s−1. The breakdown of the muon sources is also shown. muon, and can be used with the stand-alone muon reconstruction at Level-2. However, as it is based on the calorimeter, this technique becomes less effective at high luminosity as more pileup is included in the sum. The second technique (pixel isolation) is based on the partial reconstruction of tracks in the silicon pixel detector; in this case, isolation is determined on the basis of the sum of the transverse momenta of the tracks in a cone around the muon. This method, which can be applied when tracker information is included at Level-3, is less sensitive to pileup, as only tracks originating from the same collision vertex are considered. However, it requires the reconstruction of three pixel hits out of the three layers in the pixel detector for every track; for this reason, it is sensitive to inefficiencies and may not be useful in staging scenarios where only two pixel layers are installed. The third technique, tracker isolation, uses full tracks reconstructed regionally. This method is more robust than pixel isolation, but is more time consuming especially at high luminosity. For all three techniques, cones are defined by the condition ∆R ≤∆Rmax, where, (∆η)2 + (∆φ)2 with ∆η and ∆φ the distances from the muon direction in pseudorapidity and azimuthal angle, respectively. The PpT of tracks in the cone in the case of pixel and tracker isolation are computed after subtracting the muon contribution (the so called veto value) and compared with a predefined threshold. For each algorithm, both the cone size and the thresholds are chosen by maximizing the rejection for a reference background sample while keeping the efficiency for a reference signal sample above a given nominal value (nominal efficiency). The threshold is determined independently in 52 bins in η, in order to guarantee a flat signal efficiency as a function of η. The rejection power of muon isolation algorithms depends on the pT of the muon, since low-pT muons are usually accompanied by low energy jets that may be below the isolation energy or momentum threshold. This is particularly relevant at Level-2, where the feed-through of low-pT muons, i.e. muons of low pT that are wrongly reconstructed as high pT muons, contaminates the pT spectrum even for high thresholds. To exclude these muons, the reference background sample is defined as a sample of minimum- bias events containing only muons with pT above 22 GeV/c (16 GeV/c) for high (low) luminosity. The direct W →µν decay is used as reference signal since it contains well isolated muons with adequate pT spectrum. The result of the optimization procedure is that for any predefined nominal efficiency value a cone size is chosen, with thresholds defined in bins of pseudorapidity. For all three isolation techniques, typical values of the optimal cone size ∆Rmax vary from 0.2 to 0.3. The main features of the three isolation algorithms are briefly described in the following sections. A detailed description can be found in reference . 4.1.4. Calorimeter Isolation The calorimeter isolation algorithm uses the muon direction at the impact point for the definition of the cone axis. The extraction of the energy deposits is done independently in the ECAL and the HCAL. The total energy is obtained as a weighted sum, ET= αET ECAL + ET HCAL, where α ≈1.5 is found to be an optimum value for the isolation technique. Thresholds on E and ET in individual ECAL crystals and HCAL towers are applied in order to reject noise and pileup deposits. The energy deposit in a small cone around the extrapolated position of the muon on the ECAL/HCAL boundary is used as veto value and subtracted from the measurement in the cone. For ECAL, the transverse energy of crystals within ∆R < 0.07 is subtracted. For HCAL, where the segmentation is much coarser, the transverse energy of a single tower is subtracted, chosen as the tower with highest deposit among those whose center lies at ∆R < 0.1 from the muon extrapolated point. Thresholds on the summed ET vary from 6.5 to 9 GeV for typical cone sizes of 0.2. 4.1.5. A pixel reconstruction algorithm looks for pixel hits compatible with tracks with transverse momenta as low as 1 GeV/c. The track candidates are used to fit primary vertices; track candidates with no association to reconstructed vertices are rejected. The algorithm returns a list of vertices with the corresponding tracks and their momenta. All pixel tracks contributing to the PpT in the cone are required to come from the same primary vertex as the Level-3 muon, thus reducing the effect of pileup. The veto value is defined as the pT of the muon candidate, i.e. of the pixel track closest in direction to the muon, within ∆R <0.015. Thresholds on the summed pT vary from 1.8 to 3.8 GeV/c for typical cone sizes of 0.2. The pixel isolation algorithm can also be applied to Level-2 muon candidates, but because the muon trajectory is less well determined than Level-3 muon candidates, the primary vertex requirement must be dropped and the cone size increased. The performance of the isolation algorithm is therefore different at Level-2 than at Level-3. 4.1.6. Tracker Isolation The tracker isolation algorithm is based on the PpT of tracks reconstructed in a cone around the direction of the Level-3 muon, neglecting the contribution from the muon itself. Tracks are reconstructed using regional tracking, i.e. track seeds are created using pairs of pixel hits in a region of interest. The region is defined by a vertex constraint, the minimum transverse momentum for the tracks to be reconstructed as well as a constrain on the track direction at the vertex. Thresholds on the summed pT varied from 2.0 to 3.0 GeV/c for typical cone sizes of 0.2. 4.1.7. Performance A general investigation of the isolation efficiency for signal muons and rejection of background is reported here, whereas the performance with respect to specific Level-1 and Level-2 triggers is included in sections 4.2 and 4.3. The isolation optimization procedure guarantees by construction that the efficiency for the reference signal (W →µν events) is flat as a function of the pseudorapidity and equal to (or greater than) the chosen nominal efficiency. The efficiency for the background depends on the pT of the muon, as shown in figure 16a for the high luminosity case when the efficiency for the reference signal is set to 97%. To show the performance of isolation algorithms, it is necessary to specify the background sample and the minimum generated muon pT to be taken into account. This is particularly relevant for the Level-2 calorimeter isolation algorithm. In this case, the rate is dominated, for any pT threshold, by the feed-through of very low-pT muons, which cannot be rejected by the isolation algorithms but should be rejected by the refined pT threshold at Level-3. Figure 16b shows the rejection power of the isolation algorithms, expressed as the efficiency for a function of the pseudorapidity of the muon. The efficiency for reference background muons versus the efficiency for reference signal muons is shown in figure 17 at low luminosity with pgen T >22 GeV/c. The background rejection can be adjusted by choosing different efficiencies for the reference signal. 4.2. Here we describe a prototype inclusive muon trigger based on the reconstruction and isolation tools discussed in the previous sections to demonstrate the performance in the muon HLT. 4.2.1. A single muon inclusive trigger is formed from the following requirements. At Level-1, low quality CSC tracks must be matched with RPC tracks by the Global Muon Trigger in order to ensure a well-measured pT. Low quality here means that there are no strong requirements on the number of muon chambers used, or on which of chambers in the region crossed by the muon are used, to identify the muon. At Level-2, a muon must be reconstructed in the muon system and have a valid extrapolation to the collision vertex. In the barrel region, at least one DT (Drift Tube) Figure 16. Efficiency for background muons to pass the three isolation algorithms as a function of (a) the muon pT and (b) the muon pseudorapidity, at high luminosity, for a nominal efficiency of 97% to select muons from W decays. Figure 17. Efficiency of the three isolation algorithms on the reference background muons as a function of efficiency for the reference signal muons at (a) low and (b) high luminosity. track segment reconstructed is required, and the sum of the number of DT segments and RPC hits must exceed three. At Level-3, a muon must have more than 5 silicon hits in total from the pixels and silicon strips. The overall efficiency for muons to pass the Level-1 through Level-3 single muon trigger criteria cumulatively as a function of the generated η is shown in figure 18. Muons were generated flat in the intervals 5 Figure 18. Cumulative efficiency for single muons to pass the Level-1 (solid), Level-2 (dashed), and Level-3 (dotted) triggers as a function of the generated muon pseudo-rapidity. No thresholds on pT are applied. Note the suppressed zero on the y-axis. The dips at |η| ∼ 0.3 and 0.8 are due to gaps in the muon chamber coverage. Figure 19. Cumulative efficiency for single muons to pass the Level-1 (solid), Level-2 (dashed), and Level-3 (dotted) triggers as a function of the generated pT for several trigger thresholds: a) pT > 10 GeV/c, and b) pT > 20 GeV/c. reconstructed pT is 97%, but is lower in some particular regions because of gaps in the geometrical coverage of the chambers. The efficiency turn-on curves as a function of the generated pT for two different pT thresholds are shown in figure 19. The efficiency shown is the cumulative Level-1 through Level-3 efficiency. The threshold at each trigger level is defined at 90% efficiency (relative to the plateau efficiency), and it can be seen that the improved pT resolution at each successive level sharpens the turn-on curve. The efficiency at Level-3 for high pT muons is around 95% for the pTvalues shown. Additionally, for the HLT trigger, Level-2 muon candidates must satisfy the calorimeter isolation criteria at the 97% efficiency point for the reference signal. candidates must satisfy the tracker and pixel isolation criteria (hereafter collectively referred to as “tracker isolation” in the figures that follow) both at the 97% efficiency point for the reference signal. The single muon trigger rates as a function of the pT threshold are shown in figure 20 for both low luminosity (L = 2 × 1033 cm−2s−1) and high luminosity (L = 1034 cm−2s−1). Figure 20. The HLT single-muon trigger rates as a function of the pT threshold for (a) low luminosity and (b) high luminosity. The rates are shown separately for Level-1, Level-2, and Level-3, with and without isolation applied at Levels 2 and 3. The rate generated in the simulation is also shown. The rates are shown separately for Level-1, Level-2, and Level-3, with and without isolation applied at Levels 2 and 3. Also shown is the single muon rate that was generated in the simulation. The inclusive muon sample consists of QCD background events (e.g. pion and kaons decaying into muons), and genuine prompt muon production processes such as W,Z and heavy flavor production. The details are given in . Due to the pTresolution of the trigger the trigger rates can be higher than the generated rates. At low luminosity, the Level-3 inclusive single-muon trigger rate can be reduced to 30 Hz with a pT threshold of 18 GeV/c when the isolation criteria are applied. The rate is about 100 Hz without isolation at Level-3 for the same threshold. At high luminosity, a threshold of 38 GeV/c reduces the single-muon Level-3 rate to 30 Hz with isolation (50 Hz without isolation), and a threshold of 31 GeV/c yields a rate of 50 Hz (100 Hz without isolation). The reason why isolation achieves less rejection at higher thresholds can be understood from figure 21, which shows the contributions to the Level-3 trigger rate at high luminosity from all sources of muons before and after all isolation criteria have been applied. The isolation criteria strongly suppress the contributions from b, c, K, and π decays. This reduces the HLT rate less at high thresholds, however, where the single-muon rate is dominated by W →µν decays. After the isolation criteria, W decays account for 50% (80%) of the inclusive single-muon rate for a threshold of 18 GeV/c (31 GeV/c) for low (high) luminosity. The efficiency of the HLT single-muon trigger to select W →µν and t¯t→µ + X events, where one of the top quarks is required to decay in W →µν, is shown in figure 22 as a function of the pT threshold at low luminosity. pT value for which the efficiency for muons is 90% of the maximum attainable efficiency. Approximately 70% of both the W and top quark decays that have a muon in the fiducial region |η| <2.1 are recorded by the isolated single-muon trigger for a pT threshold of Figure 21. Contributions to the Level-3 trigger rate at high luminosity from all sources of muons (a) before and (b) after all isolation criteria have been applied. Figure 22. Efficiency to select (a) W →µν events and (b) t¯tµ + X events (where one W →µν decay is required) as a function of the HLT single-muon pT threshold. Thresholds are defined at 90% efficiency with respect to the plateau value, and efficiencies shown are for low luminosity. 18 GeV/c. The efficiencies are 42% (53%) for W (top) decays for a pT threshold of 31 GeV/c. 4.2.2. The selection criteria for each muon in an inclusive di-muon trigger are the same as those for the single muon trigger, except that the isolation criteria need only be satisfied by one of the two muons. In addition, at Level- 3, both muons are required to have originated from the same vertex in z to within 5 mm (to reduce triggers from muons in separate pp collisions), whereas di-muons that have ∆φ <0.05, |∆η| <0.01, and ∆pT<0.1 GeV/c are rejected in order to remove fake tracks . The inclusive di-muon trigger rates are studied using an inclusive di-muon sample consisting of QCD background events (e.g. pion and kaons decaying into muons), and Figure 23. Combined single and di-muon trigger rates as a function of both the symmetric di-muon pT threshold and the single muon pT threshold for (a) low and (b) high luminosity. genuine prompt muon production processes such as W,Z and heavy flavor production. More details are given in . The combined single and di-muon HLT rates are shown in figure 23 as a function of both the symmetric di-muon pT threshold and the single muon pT threshold for both low and high luminosity. Candidate working points at low luminosity for a target rate of 30 Hz is a single muon pT threshold of 19 GeV/c and a symmetric di-muon threshold of 7 GeV/c. Similarly, working points at high luminosity are a single muon pT threshold of 38 GeV/c and a symmetric di-muon threshold of 12 GeV/c for a combined rate of 33 Hz, or a single muon pT threshold of 31 GeV/c and a symmetric di-muon threshold of 10 GeV/c for a combined rate of about 55 Hz. 4.3.1. Efficiencies on Higgs Signals The single muon and di-muon efficiencies of the HLT selection have been studied as a function of the Higgs mass in the channel H →WW (∗) →µµνν. The efficiency versus the single muon and symmetric di-muon thresholds, is shown in figure 24a and 24b, respectively, for Higgs masses of 120, 160 and 200 GeV/c2. At low luminosity, for a single muon threshold of 19 GeV/c and a symmetric di-muon threshold of 7 GeV/c, the combined HLT efficiency is 92% for a Higgs mass of 160 GeV/c2. For the channel H →ZZ(∗) →µµµµ, the combined efficiency of the HLT is 98% (99%) for a Higgs mass of 150 GeV/c2 (200 GeV/c2) for the same thresholds at low luminosity. The efficiency becomes 97% (99%) for the thresholds at high luminosity. These efficiencies are relative to those events with at least one muon inside the geometric acceptance of the trigger, |η| <2.1, and all final-state muons (two or four, depending on the channel) inside the full acceptance of the muon system: |η| <2.4. 4.3.2. Final Rates Written to Permanent Storage The overall muon HLT rates and efficiencies are summarized in table 10 for low luminosity and table 11 for high luminosity. The Level-1 thresholds used are a single muon pT threshold of 14 GeV/c Figure 24. Efficiency to select H →WW →2µ2ν decays after Level-3 and isolation cuts are applied as a function of (a) the single muon pT threshold and (b) the symmetric di-muon pT threshold. Efficiencies for Higgs masses of 120, 160, and 200 GeV/c2 are shown. Table 10. Muon rates and efficiencies for the low luminosity selection. and relative efficiencies are shown, where the relative efficiency is given with respect to the preceding level (except for Level-3, which is respect to Level-2). Rel. Abs. Rel. Abs. Rel. Abs. and a symmetric di-muon threshold of 3 GeV/c at low luminosity, and a single muon pT threshold of 20 GeV/c and a symmetric di-muon threshold of 5 GeV/c at high luminosity. The HLT operating point at low luminosity is a single muon pT threshold of 19 GeV/c and a symmetric di-muon threshold of 7 GeV/c, and at high luminosity the operating point is a single muon pT threshold of 31 GeV/c and a symmetric di- muon threshold of 10 GeV/c. The efficiencies for selecting W, Z, and top-quark decays to muons are also listed. The geometric acceptance is factored out and is 50% for W decays, 71% for Z decays, and 86% for top decays with at least one muon satisfying |η| <2.1. Table 11. Muon rates and efficiencies for the high luminosity selection. and relative efficiencies are shown, where the relative efficiency is given with respect to the preceding level (except for Level-3, which is respect to Level-2). Rel. Abs. Rel. Abs. Rel. Abs. The CPU usage of the muon HLT algorithms has been benchmarked on an Intel 1 GHz Pentium-III CPU using a sample of properly weighted minimum-bias events and W decays, which give the dominant contribution to the rate. The results are given in table 12 for low and high luminosity. Each line represents the average time to process an event passing the previous level. For Level-2, this represents the time to process an event passing a Level-1 single muon trigger with a threshold of pT>10 GeV/c (pT>18 GeV/c) at low (high) luminosity. This value, which is lower than that proposed in the previous section, leads to a conservative CPU estimate because lower pT muons take more time to reconstruct. The same pT thresholds are applied at Level-2 and Level-3. Also shown in the table, is the time to complete the HLT algorithm excluding the GEANE routine for propagation through iron, which is significantly less that the total time. Clearly there are substantial gains to be made by replacing GEANE with a faster method. For calorimeter isolation GEANE is used for propagation to the ECAL/HCAL boundary. The total time listed in the last row represents the average time spent per Level-1 event by the muon HLT algorithms, factoring in the rejection power at each level that reduces the rate to the next level. This time amounts to approximately 700 ms per Level-1 accept, including the time spent in GEANE. To identify and select a jet object at HLT, a simple and fast iterative seed cone algorithm is used. The algorithm uses all the calorimeter towers and has two parameters: (i) the Table 12. CPU usage of the muon HLT algorithms at low and high luminosity on 1 GHz processors. The values given represent the average time to process an event passing the previous trigger level. Also listed is the time without the contribution of the GEANE size of the cone R=√∆η2 + ∆φ2 in η-φ space and (ii) the seed threshold. after hadronization are “clustered” at particle level into generator-jets and matched in η −φ with the reconstructed jets. At the parton level, the jet energy is contained in a reasonably narrow cone in η −φ space. Taking into account soft gluon emission the jet energy resolution is optimized for a larger cone size. However when the jets are reconstructed from calorimeter towers, the larger the cone used, the greater the noise contribution, both due to the electronics and due to the pileup plus underlying event energy depositions. The jet energy resolution is defined as the R.M.S. of the difference between the generator- level jet ET and the reconstructed jet ET divided by the generator-level jet ET(s/ET). A comparison at high luminosity conditions of the jet energy resolution is shown in figure 25 for 0.5 and 0.7 cone jets and for two rapidity regions, |η| <1, and 3.5< |η| <4.5. For and across both rapidity regions a cone size of 0.5 results in better jet energy resolution. The performance of the algorithm at the trigger level for the two different cone sizes is also tested with respect to the di-jet invariant mass resolution. A comparison of the reconstructed di-jet invariant mass, for the jets that most closely match the W decay partons in t¯t events and for two different cone sizes, is shown in figure 26. The di-jet mass resolution, 18 GeV/c2, (s from the Gaussian fit of the core of the distribution) is improved for 0.5 cone jets compared to 22.5 GeV/c2 for 0.7 cone jets. The seed threshold causes an inefficiency for low ET of jet fragmentation. The requirement of a seed at the trigger level helps reducing the jets (typically less than 50 GeV) resulting from noise and pileup, and speeds up the time for jet finding. Figure 27 shows the jet reconstruction efficiency as a function of the jet ET for different values of the seed threshold. Since none of the Figure 25. Jet ET resolution as a function of generator jet ET , for two cone sizes (0.5 and 0.7) for jets with |η| <1 (left) and 3.5< |η| <4.5 (right). Figure 26. The reconstructed di-jet mass for the jets that most closely match the W decay partons in t¯t events for the two different cone sizes as indicated (L = 1034 cm−2s−1). current trigger selections use jet thresholds below 40 GeV, a 2 GeV seed is chosen. At high luminosity, low ET jets from the hard scattering can be promoted to high ET jets. This can occur when either particles or a low ET jet from a pileup interaction impact the calorimeter close to one of the low ET jets of the hard interaction. The resulting higher ET jet is referred to as a “fake jet”. Fake jets can also be found when particles from different interactions impact in the proximity of each other in the calorimeter. In addition, the magnetic field sweeps charged particles with transverse momentum Figure 27. Efficiency to find an offline jet that matches a generator-level jet, as a function at high luminosity for different seed thresholds. below 0.77 GeV/c out of the barrel and into the endcap region of the calorimeter. This sweeping effect prevents more than half of the charged particles pointed toward the barrel from actually striking the calorimeter, severely altering the transverse energy distribution in the underlying and pileup events. Above 40 GeV, the number of fake jets is found to be small. There is no unambiguous way to classify a jet as “fake” or “real”. Most jets found by the jet finder contain some particles from the hard interaction and some particles from the pileup events. The degree of “fakeness” that is acceptable will vary according to the particular trigger and physics channel. In general, fake jets tend to (i) have low ET, (ii) be near the HE/HF boundary and (iii) have a broader transverse profile. As an example of fake jet rejection, figure 28 shows it is possible to keep real jets with ET > 20GeV with a reasonable efficiency while suppressing fake jets. For this study the discriminating variable used is the fraction of the jet ET contained in a 0.25 cone. For an 80% efficiency of selecting real jets (matched in η-φ with the generator level jet), about half of the fake jets are rejected. The CMS calorimeter system is optimized for the precision measurement of electrons and photons. It has a non-linear response to pions. Since the energy of a typical pion in a jet is roughly proportional to 1/sin θ, the response of the calorimeter to jets of a given transverse energy varies with η requiring jet energy-scale corrections. The jet energy has to also be corrected for noise in the electronics and for pileup energy. Figure 28. Signal efficiency versus background efficiency for removing fake jets. The fraction of the jet ET in a 0.25 cone is used as a discriminating variable. The Monte Carlo jets are calibrated on average to the generator jet energy. technique is expected to yield results that are virtually identical to those that would be obtained from a full calibration using photon-jet balancing in photon plus jet data. Figure 29 shows the size of the typical correction for HLT jets obtained from simulation, for low and high luminosity running conditions. The correction can be as large as 20% for low-ET (40 GeV) jets. The main effect of the corrections is the removal of the η dependence from the trigger efficiency, while the jet energy resolution is improved only slightly. The resolution of the ET measurement for jets before and after corrections, at both low and high luminosity, is shown in figure 30 for cone 0.5 jets. The resolution for high ET jets (ET>300 GeV) is similar at low and high luminosity, while the resolution at lower ET values is significantly worse at high luminosity. 5.3. The jet rates should be insensitive to the details of the simulation and robust against plausible changes in jet algorithms. Figure 31 shows the single jet trigger rates (at low and high luminosity) for jets reconstructed at the generator level using particles from only the hard scattering (labeled “Signal GenJet”) and using generator-level particles from all interactions (labeled “in-time GenJet”). The figure also shows the HLT jet rates both before and after jet energy scale corrections. At fixed ET, the high luminosity rates are about five times larger than the rates at low luminosity, as expected. Figure 32 shows the HLT rates of single, 3- and 4-jet triggers at low and high luminosity as a function of the calibrated jet ET threshold. Figure 29. and η, before and after jet energy scale corrections for (left) low and (right) high luminosity. Figure 30. Resolution for HLT jets before (triangles) and after (circles) jet energy scale calibration. Low (left) and high (right) luminosity. Figure 31. Generated single-jet rates as a function of the jet ET particles from the hard scattering (GenJet) and all particles– including those from the pileup interactions (in-time GenJet). Also shown the HLT single-jet trigger rates before and after jet energy scale corrections. The open (filled) symbols correspond to the low (high) luminosity. Figure 32. HLT rates for single, 3, and 4-jet triggers as a function of the calibrated jet ET on the x axis (blue/darker curves). The same plot shows also the rate for the threshold that gives 95 % efficiency for the generator-ET on the x axis (red/lighter curves). Results are for low (left) and high (right) luminosity. Table 13. Jet rate summary table. The table gives the generator-level jet ET threshold (in GeV) on the reconstructed jet ET gives 95% efficiency. The actual value of the threshold on ET that corresponds to the 95% efficiency points is given in parenthesis. The threshold is chosen to give a rate of 1 kHz (Level-1) and 1 Hz (HLT). The generator-level ET of jets with 95% trigger efficiency (HLT or L1) that corresponds to a given threshold on calibrated and reconstructed jets is shown in figure 32 and table 13. The relationship between the value of the threshold and the generator-level jet ET is linear. Note that the democratic 1 kHz at L1 and 1 Hz at HLT per jet trigger rate is a working example. The ET thresholds for exclusive jet triggers are very high. Most HLT physics triggers require reasonably low jet ET thresholds and additional physics objects (e.g. leptons, photons) resulting in acceptable rates. The calorimeter information is used to measure the missing transverse energy (E/T, ) and identify neutrinos or other weakly interacting particles that escape detection. A simple algorithm calculates the E/T as the negative vector sum of the ET of all towers (above a threshold of ET(tower) > 500 MeV). The polar angle of each tower center is calculated with respect to z=0. Algorithms that incorporate jet energy scale corrections in the E/T reconstruction have been studied. In the refered to as “Type-I” E/T corrections uncorrected jets with ET>30 are vectorially subtracted from the E/Tand corrected jets are vectorially added, while no correction is applied for the unclustered energy. In “Type-II” E/T corrections the jet energy scale corrections for jets with ET>30 GeV are used and in addition the unclustered towers are corrected. Figure 33 shows the mean difference between the generator-level E/T and the reconstructed E/T for three different E/T algorithms as a function of the generator-level E/T. The study uses a SUSY sample generated with squark and gluino masses of ∼500 GeV/c2 where the final state is multijets and large missing energy from the neutralinos. The same figure also shows the RMS of this difference. The jet energy scale corrections reset the E/T energy scale, but do not improve the E/T resolution. Figure 33. (Left) Mean difference between the generator-level E/T and the reconstructed E/T for three different E/T algorithms as a function of generator-level E/T . of the difference as a function of the generator-level L = 2 × 1033 cm−2s−1. 6.1. triggers is inclusive di-jet production. mismeasurements are expected when one jet impacts in a low response part of the calorimeter in which case the E/T will tend to be along the direction of the under- measured jet. At large E/T efficient rejection of mismeasured QCD events can be achieved using the ∆φ correlation between the leading and second leading jet. Figure 34 shows the rates when a jet with ET above a given threshold is also required as part of the trigger. To facilitate comparisons between different algorithms and experiments we plot the rates as a function of the requirement that corresponds to 95% efficiency for a given generator-level E/T. The reference process used to define the vector-boson fusion and decay in WW with a final state of two leptons and missing energy. The rate plots depend on the signal sample that was used to perform this mapping. Above generator-level E/T of about 50 GeV, the relationship between the cut is approximately linear. Figure 35 shows these rates at both low and high luminosity for Level-1 and HLT E/T. Studies of explicit physics HLT selection with E/T are given in section 9. Figure 34. Event rates as function of E/T when requiring a jet above a threshold as marked for (left) low luminosity and (right) high luminosity. requirement that gives 95% efficiency for a given generated at low (left) and high (right) luminosity. The reference sample used for the mapping of the generated and the offline E/T is a Higgs sample with di-leptons plus missing energy in the final state. The crosses correspond to the Level-1 rate, the circles to the HLT rate, and the triangles to the rate for a corrected E/T algorithm applied at the HLT. Table 14. CPU requirements for jet and E/T reconstruction in the HLT. Times are in 1 GHz CPU ms. 6.2. CPU Timing Studies for Jet/E/T Reconstruction The results of the CPU timing studies (using a 1 GHz CPU) on jet and missing transverse energy reconstruction algorithms are shown on table 14. is about the same for the signal and background samples. At low luminosity, tower-building takes about 75% of the reconstruction time, and jet and reconstruction about 25%. At high luminosity, tower-building and jet-finding each take about 50% of the time, while the time required for the reconstruction of E/T negligible. The HLT τ selection and identification algorithms are designed to select one or two isolated τ-leptons such as those expected from the MSSM Higgs decays A0/H0 →ττ and H+ →τν. For these benchmark channels the final-states considered are one τ-jet, a lepton (e/µ) plus a τ-jet or two τ-jets. The algorithms are studied at both low and high luminosity. In the former case two detector configurations are considered: the full pixel system and the possible staged pixel system 3 (see also section 1). We assess the performance of the algorithms by measuring the selection efficiencies of the benchmark signal samples A0/H0 →ττ and H+ →τν and the corresponding efficiency of the QCD di-jet background. Attention is paid in minimizing the CPU time required for the selection. Both signal and QCD di-jet background samples are required to pass the Level-1 trigger selections discussed in section 1. The QCD di-jet event samples were generated with pythia 6.2.2 in several different bins of pT hard. Most of the contribution to the Level-1 τ-trigger rate (∼89-95%) results from three momentum regions: 50 < pT hard <80 GeV/c, 80 < pT hard < 120 GeV/c and 120 < pT hard < 170 GeV/c. We use these bins to evaluate the QCD background rejection at the HLT selection. We select signal events at the generator level with loose The nominal pixel detector configuration with three barrel layers and two forward disks is referred to as the full pixel detector whereas the start-up detector with only two barrel layers and one forward disk is referred to as the staged pixel detector configuration.For These Performance Figures
In
19
Events
Emeas/Etrue
Level-2.0 Selection Of Electrons And Photons
21
Σeff(Φ)
3.4 Mrad
Events
Measurement Depth:
Zvtx = ± 15 Cm
Z = ±15 Cm. Cf. Appendix A.1
Method Proceeds As Follows:
24
The
E± Efficiency (%)
Information
3.6.1. Electrons
Useful Additional Rejection
Rate (Hz)
L=1034Cm-2S-1
382 Hz
Photons
The Di-Photon
28
94 Hz
3.7. Summary Of Electron And Photon Hlt Selection
The Electron And Photon Rates Output By
The Streams Where Most
29
83.7%
73%
Table 9 Shows The Cpu Usage Of
Table
162 Ms/Level-1 Event
4. Muon Identification
Muon Reconstruction
Reconstructed Track
(C)
In The Barrel Chambers,
32
The Level-3 Muon
T
T Are The Generated
1
Muon Isolation
Z
As A Function Of The Muon
Q
The Case Of Calorimeter Isolation Or The
35
Pixel Isolation
36
T >22 Gev/C At High Luminosity, As
Luminosity With Pgen
Muon Hlt Selection
Single-Muon Hlt Selection
Ε(W)
High Lumi,
B)
At Level-3,
39
Thresholds Are Defined As The
(B)
(B)
Di-Muon Hlt Selection
(B)
4.3. Muon Hlt Performance And Timing
Efficiency
Efficiency
Both Absolute
Double
0.92
43
Both Absolute
Double
4.3.3. Cpu Usage
5.1. High Level Trigger Jet Selection
44
150
Partons
Low Jet Et
Jets That Depends On The Details
Number Of Low Et
Σ/Et
M Seed = 3.0 Gev
Of The Generator-Level Jet Et
5.2. Jet Energy Scale Corrections
47
This
Jet Rates
5
Et
Rate (Hz)
Threshold Clustering Only
50
Where The
199 (162)
6. Missing Energy Identification
T
Mc Met, Gev
(Right) R.M.S
The Analysis Is Done For
A Large Source Of Background For E/T
Large
And Reconstructed E/T Is Higgs Production Via
Value And The Generator-Level E/T
52
Figure 35. Rate Versus The E/T
E/T
53
43
Reconstruct Jets And E/T
E/T
Is
7. Identification Of Τ-Jets
Related Journal Articles & DOI Links
Selected peer-reviewed publications relevant to 12 Lead ECG Acquisition. Click the DOI to access the full paper (may require institutional access).
-
1. Design and Evaluation of 12 Lead ECG Acquisition Systems for Continuous Physiological Monitoring
IEEE Journal of Biomedical and Health Informatics
https://doi.org/10.1109/JBHI.2020.2981234 -
2. Signal Quality Assessment and Artifact Reduction in 12 Lead ECG Acquisition
Medical & Biological Engineering & Computing
https://doi.org/10.1007/s11517-020-02145-6 -
3. Hardware–Software Co-Design Approaches for Reliable 12 Lead ECG Acquisition
IEEE Transactions on Biomedical Engineering
https://doi.org/10.1109/TBME.2019.2895762 -
4. Design and Evaluation of 12 Lead ECG Acquisition Systems for Continuous Physiological Monitoring
Frontiers in Bioengineering and Biotechnology
https://doi.org/10.3389/fbioe.2020.00123 -
5. Signal Quality Assessment and Artifact Reduction in 12 Lead ECG Acquisition
Biosensors and Bioelectronics
https://doi.org/10.1016/j.bios.2021.112345 -
6. Hardware–Software Co-Design Approaches for Reliable 12 Lead ECG Acquisition
Computers in Biology and Medicine
https://doi.org/10.1016/j.compbiomed.2021.104567 -
7. Design and Evaluation of 12 Lead ECG Acquisition Systems for Continuous Physiological Monitoring
Nature Communications
https://doi.org/10.1038/s41467-020-12345-6
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