Design and Simulation of the First Level Global Muon Trigger for the ...

DISSERTATION

Design and Simulation of theFirst Level Global Muon Trigger

for the CMS Experiment at CERN

ausgefuhrt zum Zwecke der Erlangung des akademischen Grades eines Doktors dertechnischen Naturwissenschaften unter der Leitung von

Univ. Doz. tit. ao. Univ. Prof. Dr. phil. Manfred MarkytanInstitutsnummer E136

Institut fur Theoretische Physik

eingereicht an der Technischen Universitat WienTechnisch-Naturwissenschaftliche Fakultat

von

DI Hannes SakulinMatrikelnummer 9131900

Rudolfstraße 106 eA-8010 Graz,Osterreich

Genf, im November 2002

III

Kurzfassung

Fur das Compact Muon Solenoid (CMS) Experiment am Large Hadron Collider (LHC)der Europaischen Organisation fur Teilchenphysik CERN wurde der Globale Myonentrig-ger (GMT) der ersten Triggerstufe entwickelt. Diese dient zur Auswahl potentiell interessanterEreignisse. Mit Hilfe grob segmentierter Daten der Kalorimeter und der drei Myonensysteme inCMS erzielt sie eine Reduktion der Ereignisrate von 40 MHz, der Strahlkreuzfrequenz des LHC,auf 100 kHz, der maximalen Eingangsrate der nachsten Triggerstufe. Der GMT hat die Auf-gabe, unabhangige Messungen regionaler Trigger in jedem der drei Myonensysteme zu kom-binieren und in jeder Strahlkreuzung die besten vier Myonen im gesamten Detektor zu ermitteln.Um Isolationskriterien anzuwenden oder die Messungen der Myonen zu bestatigen, werdendiese zusatzlich mit Regionen im Kalorimeter korreliert. Die Algorithmen des GMT wurdenaufgrund detaillierter Simulationen des Detektors und des Triggersystems entworfen. Basierendauf der Technologie der Field Programmable Gate Arrays wurde das Logik–Design der GMTHauptplatine entwickelt. Um Triggerraten von Dimyonen zu studieren, wurde eine neue Me-thode der Simulation von Triggern entwickelt, die durch dieUberlagerung von im Mittel 17.3Interaktionen pro LHC Strahlkreuzung entstehen. Unter Ausnutzung der Komplementaritat derMyonensysteme kann der GMT die Selektivitat um einen Faktor funf steigern und gleichzeitigdie Effizienz erhohen. Duplizierte Messungen in der Barrel/EndcapUbergangsregion werdendurch spezielle Cancel–Out Einheiten entfernt. Der Gesamtanteil von Triggern durch falscheSpuren (Geister) an der Dimyonentriggerrate kann dadurch auf ca. 15 % reduziert werden. Eswird gezeigt, daß Triggerschranken von 20 bis 25 GeV/c im Einzelmyonentrigger und 4 bis5 GeV/c im Dimyonentrigger bei geplanter LHC–Luminositat vonL = 1034 cm−2s−1 mit dererforderlichen Ratenreduktion kompatibel sind. Dies ermoglicht ausgezeichnete Effizienz furdie meisten Kanale unter den Physikzielen, die von Myonentriggern selektiert werden sollen.

V

Abstract

The present thesis deals with the First Level Global Muon Trigger (GMT) for the Com-pact Muon Solenoid (CMS) Experiment at the Large Hadron Collider (LHC) of the EuropeanParticle Physics Laboratory CERN. The First Level Trigger electronics reduce the event ratefrom 40 MHz (bunch crossing rate of the LHC) to 100 kHz, the maximal input rate of the higherlevel triggers, by selecting potentially interesting events on the basis of coarsely segmented datafrom the calorimeters and the three muon systems in CMS. It is the task of the GMT to combineindependent measurements of regional triggers in each of the muon systems and to determinethe best four muons in the entire detector for each bunch crossing. In order to apply isolationcriteria and to achieve confirmation by the calorimeter the GMT further correlates muon mea-surements with regions in the calorimeter. The GMT algorithms were elaborated with the helpof detailed simulations of the detector and trigger system. The logic design of the main GMTelectronics board was developed based on the technology of Field Programmable Gate Arrays.In order to study di–muon trigger rates, a new method was devised to simulate triggers causedby the pile–up of an average of 17.3 inelastic interactions per bunch crossing at the LHC. Bymaking use of the complementarity of the muon systems the GMT improves background re-jection by a factor of five while increasing over–all efficiency. Duplicated measurements in thebarrel/endcap overlap region are removed by cancel–out units. The total contribution of ghosttriggers to the di–muon trigger rate can thereby be reduced to approximately 15 %. Triggerthresholds of 20 to 25 GeV/c in the single muon and 4 to 5 GeV/c in the di–muon trigger at theLHC design luminosity ofL = 1034 cm−2s−1 are shown to be compatible with the required ratereduction resulting in excellent efficiency for most of the channels among the physics goals tobe selected by muon triggers.

VII

Contents

1 Introduction 1

2 The Large Hadron Collider (LHC) 52.1 Motivation for the LHC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 Design Considerations for the LHC. . . . . . . . . . . . . . . . . . . . . . . 72.3 Parameters of the LHC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.4 Phenomenology ofp− p Interactions . . . . . . . . . . . . . . . . . . . . . . 9

3 Selected Physics Goals at the LHC 113.1 Introduction to Triggering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2 Standard Model Higgs Physics. . . . . . . . . . . . . . . . . . . . . . . . . . 123.3 Supersymmetry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.4 Precision Measurement of Standard Model Processes. . . . . . . . . . . . . . 15

3.4.1 Top-quark Physics. . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.4.2 b-quark Physics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.5 Heavy Ion Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4 The CMS Experiment 174.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.2 The Tracker. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.2.1 The Pixel Tracker. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.2.2 The Silicon Microstrip Tracker. . . . . . . . . . . . . . . . . . . . . . 20

4.3 The Calorimeters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.3.1 The Electromagnetic Calorimeter. . . . . . . . . . . . . . . . . . . . 214.3.2 The Hadronic Calorimeter. . . . . . . . . . . . . . . . . . . . . . . . 22

4.4 The Muon System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.4.1 The Drift Tube Chambers. . . . . . . . . . . . . . . . . . . . . . . . 244.4.2 The Cathode Strip Chambers. . . . . . . . . . . . . . . . . . . . . . . 254.4.3 The Resistive Plate Chambers. . . . . . . . . . . . . . . . . . . . . . 27

5 The CMS First Level Trigger 295.1 The CMS Trigger System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305.2 Level–1 Trigger Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . 315.3 L1 Calorimetry Trigger. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.4 L1 Muon Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.4.1 Requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345.4.2 Drift Tube Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

VIII

5.4.2.1 DT Local Trigger . . . . . . . . . . . . . . . . . . . . . . . 355.4.2.2 DT Track Finder. . . . . . . . . . . . . . . . . . . . . . . . 37

5.4.3 Cathode Strip Chamber Trigger. . . . . . . . . . . . . . . . . . . . . 395.4.3.1 CSC Local Trigger. . . . . . . . . . . . . . . . . . . . . . . 395.4.3.2 CSC Track Finder. . . . . . . . . . . . . . . . . . . . . . . 41

5.4.4 Overlap Region between DT and CSC Track Finders. . . . . . . . . . 435.4.5 Resistive Plate Chamber Trigger. . . . . . . . . . . . . . . . . . . . . 445.4.6 Backgrounds in the L1 Muon Trigger. . . . . . . . . . . . . . . . . . 455.4.7 Performance of the Regional Muon Triggers. . . . . . . . . . . . . . 47

5.4.7.1 Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . 475.4.7.2 Ghosts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.4.7.3 Transverse Momentum Assignment and Turn-On Curves. . 485.4.7.4 Trigger Rates. . . . . . . . . . . . . . . . . . . . . . . . . 595.4.7.5 Resolution inη andφ . . . . . . . . . . . . . . . . . . . . . 605.4.7.6 Charge Assignment. . . . . . . . . . . . . . . . . . . . . . 62

5.4.8 Summary of Regional Muon Trigger Outputs to the Global Muon Trigger64

6 Global Muon Trigger Design 656.1 Requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

6.1.1 Input Requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . 676.2 System Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686.3 Matching Unit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

6.3.1 Default Matching. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 706.3.2 Improved Matching for Variableη-Bin Sizes . . . . . . . . . . . . . . 716.3.3 Pair Logic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.4 Suppression of Ghosts in the Barrel/Endcap Overlap Region. . . . . . . . . . 736.4.1 Cancellation of DT/CSC Ghosts. . . . . . . . . . . . . . . . . . . . . 756.4.2 Cancellation of DT/forward-RPC and CSC/barrel-RPC Ghosts. . . . . 77

6.5 Sort Rank Assignment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 806.6 Exclusion of Very-Low-Quality Unconfirmed Candidates from Certain Trigger

Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 816.7 MIP and ISO Assignment Unit. . . . . . . . . . . . . . . . . . . . . . . . . . 846.8 Conversion of Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 906.9 Muon Merger Unit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

6.9.1 Merging Based on a Merge–Rank. . . . . . . . . . . . . . . . . . . . 906.9.2 Merging Based on MinimumpT Measurement . . . . . . . . . . . . . 916.9.3 Combined Merging Based on a Merge–Rank and the MinimumpT

Measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 926.9.4 Smart Merging ofη Measurements. . . . . . . . . . . . . . . . . . . . 926.9.5 Smart Merging of Charge Assignments. . . . . . . . . . . . . . . . . 956.9.6 Mixing ofpT Measurements. . . . . . . . . . . . . . . . . . . . . . . 956.9.7 Smart Merging of MIP and Isolation Bits. . . . . . . . . . . . . . . . 956.9.8 Merging of Sort Ranks. . . . . . . . . . . . . . . . . . . . . . . . . . 956.9.9 Optional Suppression of Very–Low–Quality Candidates. . . . . . . . 96

6.10 Sorter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .966.11 Summary of the GMT Output. . . . . . . . . . . . . . . . . . . . . . . . . . . 96

IX

7 Global Muon Trigger Hardware Implementation 997.1 Choice of Technology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1007.2 GMT System Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1007.3 GMT Logic Board . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1027.4 Latency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .104

8 Trigger Simulation 1058.1 Simulation Software and Parameters. . . . . . . . . . . . . . . . . . . . . . .1068.2 Samples of Single Muons. . . . . . . . . . . . . . . . . . . . . . . . . . . . .1078.3 Signal Samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1088.4 Monte–Carlo Generation for the Simulation of Trigger Rates. . . . . . . . . . 108

8.4.1 Production of Minimum Bias Events. . . . . . . . . . . . . . . . . . . 1098.4.2 Generated Rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . .1118.4.3 Treatment of Pile–Up. . . . . . . . . . . . . . . . . . . . . . . . . . .1128.4.4 Analytic Method to Treat Pile–Up with Muons. . . . . . . . . . . . . 113

8.4.4.1 Obtaining Trigger Probabilities from the Minimum BiasSamples . . . . . . . . . . . . . . . . . . . . . . . . . . . .113

8.4.4.2 Single Muon Trigger Rates. . . . . . . . . . . . . . . . . . 1148.4.4.3 Di-Muon Trigger Rates with Symmetric Thresholds. . . . . 1148.4.4.4 Di-Muon Trigger Rates with Asymmetric Thresholds. . . . 115

8.4.5 Piling up Single Events with Muons to Form Bunch Crossings. . . . . 1168.4.6 Adding Pile-Up Without Muons. . . . . . . . . . . . . . . . . . . . .1198.4.7 Technical Issues in the Mixing of Bunch Crossings. . . . . . . . . . . 1218.4.8 Generated Di-Muon Rates. . . . . . . . . . . . . . . . . . . . . . . .124

9 Global Muon Trigger Performance 1259.1 GMT Algorithmic Efficiency and Ghosting. . . . . . . . . . . . . . . . . . . 1269.2 Transverse Momentum Resolution and Turn–On Curves. . . . . . . . . . . . 1309.3 Single Muon Trigger Rates. . . . . . . . . . . . . . . . . . . . . . . . . . . .1319.4 Di–Muon Trigger Rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1319.5 Combined Single–Muon and Di–Muon Trigger Rates. . . . . . . . . . . . . . 1359.6 Trigger Efficiency for Selected Signals. . . . . . . . . . . . . . . . . . . . . .137

10 Conclusions 141

Bibliography 145

Acknowledgements 149

Curriculum Vitae 151

Lebenslauf 155

Chapter 1

Introduction

2 1. Introduction

Modern High Energy Particle Physics has made remarkable advances over the last fewdecades like the discovery of the intermediate vector bosonsW± andZ0 by the UA1 andUA2 experiments at the European Particle Physics Laboratory CERN in Geneva in 1983 andthe discovery of the top quark by the CDF and D0 experiments at Fermi National Labora-tory (Fermilab) in Chicago in 1995. The predictions of the Standard Model of particle physicshave been confirmed with excellent precision by the measurements at CERN’s Large ElectronPositron (LEP) collider and the Stanford Linear Collider (SLC) and the Tevatron collider in theUnited States. High precision measurements at the ALEPH, DELPHI, OPAL and L3 experi-ments at CERN’s LEP collider proved that only three lepton generations with light neutrinosexist. Direct violation of combined charge conjugation and parity (CP) invariance has beendemonstrated at the experiments NA48 at CERN and KTeV at Fermilab. Recently indicationsfor the existence a deconfined state of matter, the Quark–Gluon Plasma have been found atCERN’s SPS collider.

In spite of these excellent experimental results, open questions still remain. In the StandardModel the origin of masses is explained by the Higgs Mechanism which predicts a new scalarboson, the Higgs particle. Despite extensive searches at LEP and the Tevatron the Higgs particleso far has not been found and therefore the Higgs Mechanism could not be confirmed. There arestrong reasons to believe that new theories are needed to extend the Standard Model to higherenergy scales. A very elegant extension would be Supersymmetry which predicts many newparticles at the TeV scale, none of which have been observed so far. Other extensions of theStandard Model are possible and also predict new particles at the TeV scale which have notbeen observed so far. Exploration of the TeV scale will allow to determine what extension ofthe Standard Model nature has chosen. The origin of the matter–antimatter asymmetry in theuniverse is one of the most important open questions in cosmology. CP violation is believed tobe one of the necessary ingredients in the asymmetry and its study in the system of the neutralB mesons will give further insights.

Answers to these questions are expected from a new generation of powerful hadron collid-ers. Fermilab’s Tevatron II collider is already in operation and provides proton–antiproton col-lisions at a center–of–mass energy of 2 TeV. CERN is currently constructing the Large HadronCollider (LHC) which will provide proton–proton collisions with a center–of–mass energy of14 TeV operating at luminosities up toL = 1034 cm−2s−1. One of two main multi–purpose ex-periments at the LHC will be the Compact Muon Solenoid (CMS) experiment which is currentlybeing designed and constructed by a collaboration of institutes from over 50 countries involv-ing around 2000 physicists and engineers. The Institute for High Energy Physics (HEPHY)of the Austrian Academy of Sciences, which has a long tradition in collaboration with CERNand already contributed to the UA1, DELPHI and NA48 experiments, is responsible for partsof the tracker and of the first level trigger of the CMS experiment. This thesis on the designand simulation of the First Level Global Muon Trigger has been undertaken as a member of theCMS trigger group of HEPHY.

Triggering is very important at the LHC where due to the high luminosity collisions occurat a rate of 40 MHz, but due to the excessive data volume can only be recorded to data storageat a rate of around 100 Hz. It is the task of the trigger to keep the interesting signals withhigh efficiency while rejecting the large unwanted background. The CMS Trigger System isorganized in multiple levels: the first level has to process data at 40 MHz without dead–timeand is implemented in custom–built electronics while the subsequent levels receive data at areduced rate and are implemented in software running on a large farm of computers. Muonswith high transverse momenta are a part of the signature of many of the processes to be explored

Design and Simulation of the First Level Global Muon Triggerfor the CMS Experiment at CERN

H. Sakulin

3

at the LHC. Due to comparably low background, muons are ideally suited to triggering. CMScontains three independent muon systems which all participate in the trigger. It is the task ofthe Global Muon Trigger to combine muon candidates from these three systems and to findthe best four muon candidates in the detector. By making use of the complementarity of themuon systems it increases efficiency and substantially improves background rejection. It furthercorrelates muon candidates with regions in the calorimeter for the purpose of confirmation bythe calorimeter and the application of isolation criteria.

In the course of this research project the logic design of the Global Muon Trigger waselaborated starting from a preliminary conceptual design. Detailed simulations of the detectorand trigger system were developed in collaboration with the Muon Physics Group and usedto investigate and to improve the performance of the Global Muon Trigger algorithms. Thefunctionality of the Global Muon Trigger was extended in many respects and the extensionswere included in the simulation software used by the Muon Physics Group to study the first leveland higher level triggers. Monte–Carlo generated minimum bias samples provided by the MuonPhysics Group and Production Group were used to study trigger rates and a contribution wasmade by developing a method to treat multi–muon triggers caused by multiple interactions in thesame LHC beam crossing. This method was used by the Muon Physics Group to study multi–muon triggers at all trigger levels. The logic design of the trigger electronics was developed inclose collaboration with the electronics group at HEPHY and in the wider context of the CMSFirst Level Trigger Group.

The thesis is structured as follows: Chapter2 introduces the Large Hadron Collider anddiscusses the phenomenology of proton–proton interactions at LHC energies. Selected physicsprocesses to be studied at LHC are presented in Chapter3 with an emphasis on channels withmuons in the final state. Chapter4 describes the CMS detector and its components. The CMStrigger system is described in Chapter5 with an emphasis on the Level–1 Muon Trigger includ-ing detailed simulation results of the performance of the regional muon triggers. The design ofthe L1 Global Muon Trigger and its algorithms are studied in Chapter6, while Chapter7 brieflydescribes the main features of the hardware implementation. Chapter8 presents the simulationsoftware and techniques used in the trigger studies as well as the signal and background sam-ples. The simulated performance of the CMS Level–1 Muon Trigger after combining the resultsof the regional triggers at the Global Muon Trigger is shown in Chapter9 including the expectedsingle muon and di–muon trigger rates and efficiencies for selected channels of interest. Theresults are summarized in Chapter10.

H. Sakulin Design and Simulation of the First Level Global Muon Triggerfor the CMS Experiment at CERN

Chapter 2

The Large Hadron Collider (LHC)

6 2. The Large Hadron Collider (LHC)

The Large Hadron Collider (LHC) is currently being constructed at CERN in Geneva andis scheduled to start operation in 2006. It will provide proton–proton collisions with a center–of–mass energy of 14 TeV, 7 times higher than the highest energies reached today at Fermilab’sTevatron Collider. The LHC is designed to reach a luminosity ofL = 1034 cm−2s−1 (highluminosity scenario). This is about 100 times higher than the luminosities reached at currentmachines and will allow to collect approximately 100 fb−1 per year. After start–up and forthe first three years of operation the LHC is planned to operate at a luminosity ofL = 2 ×1033 cm−2s−1 (low luminosity scenario), collecting an estimated 10 fb−1 per year in this period.

Additionally, the LHC will be capable of providing collisions of heavy ions such as Pb ionswith a center–of–mass energy of 2.76 TeV per nucleon.

2.1 Motivation for the LHC

The motivations for the construction of a new accelerator, which can reach higher energiesthan accessible today, are many:

The origin of particle masses in the Standard Modelmay be explained by the so-called“Higgs mechanism”, a hybrid of spontaneous breaking of electroweak symmetry andthe principle of local gauge invariance. The mechanism predicts a new scalar boson, theHiggs particle, with a mass which is a free parameter. The heavy vector bosonsW± andZ0 acquire their masses through interaction with the Higgs field. All fermions couple tothe Higgs and acquire a mass proportional to their coupling. The SM predicts all proper-ties of the Higgs particle except its mass. Preservation of unitarity at high energies limitthe Higgs mass to. 1 TeV/c2. So far, the Higgs particle has not been found. The currentlower limit for the Higgs mass is given by LEP II at about 115 GeV/c2. The Tevatron col-lider will be able to discover a Higgs particle withmH < 120 GeV/c2 with an integratedluminosity of 15 fb−1, which should be collected before the start of LHC. If no evidenceof a Higgs particle is found in this mass range, then the LHC will explore the region of120 GeV up to 1 TeV.

Physics beyond the Standard Model.There are strong reasons to believe that the StandardModel is not the ultimate theory of particle interaction but rather a low-energy approxi-mation of some more fundamental theory. An apparent problem in the Standard Model isthe large number of free parameters (26 under the assumption that neutrinos have mass),which are not predicted by the theory. Grand Unification Theories (GUTs) solve thisproblem by assuming that the SU(3)⊗SU(2)⊗U(1) group of the Standard Model resultsfrom the spontaneous breaking of a higher symmetry. GUTs predict that the running cou-pling constants of the electromagnetic, weak and strong forces unify at the GUT scale ofthe order of1015 GeV. However, this is incompatible with the predictions of the StandardModel. A further problem of the Standard Model is the so-called “hierarchy problem”:unless some fine-tuned cancellations took place, the masses of scalar particles would suf-fer extremely high radiative corrections at higher energy cut-offs.An elegant solution to all these problems isSupersymmetry (SUSY), a theory that predictsa universal boson–fermion symmetry. It predicts a large number of new particles —supersymmetrical partners of the known particles and new gauge bosons — at the TeVscale, a scale which is not accessible, today. The LHC will allow to explore this massrange up to about 5 TeV and answer the question if SUSY is really the extension of theStandard Model that nature has chosen.


H. Sakulin

2.2 Design Considerations for the LHC 7

Various other extensions of the Standard Model are also possible. Examples are modelsthat predict a new strong interaction without a scalar Higgs boson and models that assumea sub-structure of quarks and leptons such as string theories. These models also predictnew particles at the TeV scale.

Precision Measurement of Standard Model Physics.Heavy particles such asb andt quarks,andW andZ bosons will be produced in big amounts at the high center–of–mass en-ergies and high luminosity at the LHC. This will allow precision measurement of manyparameters such as mass, coupling and decay properties of the top quark,W mass,αs aswell as the study of CP violation in the System of the neutralB meson.

Heavy Ion Physics.The formation of a deconfined state of hadronic matter, thequark–gluonplasma, is predicted at very high energies. Indications of its existence have been foundat CERN’s SPS collider in 2000 [1]. Heavy-ion collisions with higher center–of–massenergies than available today are required to study the phenomenon in more detail.

2.2 Design Considerations for the LHC

As laid out in the previous section many new physical processes are expected at the TeVscale, a scale which is not accessible with current lepton colliders. Most of the processes ofinterest are characterized by extremely low cross-sections. Hadron colliders, such as the LHC,have clear advantages over lepton colliders in exploring higher energy scales for the followingreasons:

• energy loss due to synchrotron radiation is approximately proportional to1/(particle mass)4 at a given synchrotron radius which limits the maximum beamenergy in conventional electron colliders to approximately 100 GeV per beam; hadronssuffer much less energy loss at the same synchrotron radius allowing to reach muchhigher beam energies;• the cross-sections of the interesting processes typically are higher in strong interactions;• a wide energy range can be probed simultaneously, as the interacting particles — the

quarks and gluons — carry a variable fraction of the total hardon energy leading to awide spread in the actual CM energy.

A certain process, which is characterized by its cross–sectionσ, occurs with a rateR givenby

R = Lσ, (2.1)

whereL is the luminosity of the accelerator. For a collider that collides bunches ofn1 andn2

particles at a frequencyf , the luminosity is given by

L = fn1n2

A, (2.2)

whereA is the area of overlap of the the colliding bunches. In order to maximize rate andstatistics for a rare process, both the luminosity and the cross-section have to be maximized.Figure 2.1 shows the cross sections of several relevant channels forp − p interactions as afunction of the center–of–mass energy

√s as predicted by the simulation software PYTHIA.

The cross-sections of the rare signal processes increase rapidly with higher√s while the over–

all cross–section remains almost constant. It is clearly of advantage to operate at the highestpossible CM–energy.



The luminosity can be maximized by increasing the frequency of collisions and the numberof particles per bunch. There are limits to both, however: operating at a higher frequencyrequires faster detector response and faster electronics; increasing the number of particles perbunch increases the number of interactions occurring in the same beam crossing (pile–up) andtherefore the multiplicity of tracks so that a very good detector resolution is required in order toidentify a potential signal.

2.3 Parameters of the LHC

The Large Hadron Collider will be installed in the existing LEP tunnel at CERN allowingfor optimal re-use of available infrastructure. This choice drives many of its design parameters,which are summarized in Table2.1. The maximum magnetic field that can be reached in thebending magnets using super-conducting technology, will be 8.3 T resulting in a maximumcenter–of–mass energy of 14 TeV inp− p collisions.

The choice of proton–proton collisions over proton–antiproton collisions has the advantageof reducing the dead time needed to accumulate antiprotons (typically several hours). However,it also means that the two beams cannot be bent by the same magnet. Special superconductingtwin–bore dipole magnets have therefore been designed in order to contain the two beams ofcounter–rotating particles of equal charge inside the available space in the LEP tunnel.

Table 2.1: Design Parameters of the LHC forp− p collisions

Parameter valueCircumference 26.659 kmEnergy per beam 7 TeVCenter of mass energy 14 TeVRelativisticγ-factor 7461Injection energy 450 GeVNumber of particles per bunch1.1× 1011

Number of bunches 2808Total number of particles 3.1× 1014

DC beam current 2× 560 mABeam energy 2× 350 MJLuminosity (maximum) 1034 cm−2s−1

Luminosity lifetime 10 hr.m.s. bunch length 53 mmr.m.s. beam radius at IP 15µmBunch spacing 24.95 nsDipole field 8.3 T

The maximum design luminosity of the LHC isL = 1034 cm−2s−1 at a nominal collisionfrequency of 40 MHz. Assuming a total inelastic cross–section ofσT = 55 mb as predictedby PYTHIA for

√s = 14 TeV and taking into account the fact that about 20 % of the bunches

will be empty, an average of 17.3 inelastic interactions (also calledevents) will occur in eachbeam crossing. Each interaction will give rise to an average of 50 charged tracks resulting in


H. Sakulin

2.4 Phenomenology ofp− p Interactions 9

an extremely difficult experimental environment. The LHC detectors must have the capabilityto reconstruct and isolate the signatures of interesting events hidden in this large background.Moreover, as will be discussed in Chapter5, (at least partial) reconstruction and filtering ofevents have to be performed on-line at a rate of 40 MHz in order to reduce the massive amountof data to a manageable rate. Triggering and on–line event selection will therefore be verycomplex and challenging tasks at LHC experiments.

Four experiments will operate at the LHC: two general purpose experiments, CMS [2] andATLAS [3], as well as an experiment dedicated to heavy-ion physics (ALICE [4]) and an ex-periment dedicated to the study ofb-quark physics (LHCb [5]).

2.4 Phenomenology ofp− p Interactions

The total rate ofp − p interactions at high luminosity is expected to beR = σT × L =5 × 108 Hz. The vast majority of these interactions will be due to large distance collisionsbetween two of the incoming protons: in these “soft interactions” only a small transverse mo-mentum (typically less than 500 MeV/c) is exchanged between the protons so that most of thecollision energy escapes down the beam pipe.

The interesting interactions occur in head-on collisions (“hard scattering”) where a largemomentum is transferred: massive particles with high transverse momenta (pT ) can be created.In this case the interaction takes place between two partons (quarks or gluons) inside the in-coming protons so that the effective center–of–mass energy

√s is only a fraction of that of the

protons:

√s =√xaxbs. (2.3)

xa andxb are the fractions of energy carried by the partons in the protons A and B at theinstant of the collision. The probability distributions of thexa,b are a functions of the transferredmomentum and are given by structure functions (parton density functions).xa andxb vary fromone collision to the next so that the effective center–of–mass energy varies from event to eventan the center–of–mass is usually boosted along the beam direction.

The highest rate of high-pT processes comes from QCD jet production with contributionsfrom processes such asgg → qq, qq → gg andqg → qg. These processes are not of pri-mary interest at the LHC and hence constitute a large background. As shown in Figure2.1 therate of QCD jets is several orders of magnitude higher than the rate of the interesting signalswhich makes it almost impossible to detect a signal in channels with only jets in the final state.Channels with leptonic or semi–leptonic final states, in which the background is much lower,will therefore be the most important discovery channels at the LHC which makes measurementand triggering of high-pT electrons and muons a crucial requirement at LHC experiments. Thedrawback of these channels is, however, a lower branching ratio and hence also a lower eventrate.



σ tot

�

� t t

(W )ν�

� z'

�

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m = 175 GeVtop

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nti)p

roto

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LHC

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� gg (mg = 500 GeV)~~ ~

σ

σ

Hσ

σ

σ

σ

σ�

σ�

(H γγ�σ ) m = 120 GeVH

µ

Figure 2.1: Cross sections and event rates as a function of center–of–mass energy.


H. Sakulin

Chapter 3

Selected Physics Goals at the LHC

12 3. Selected Physics Goals at the LHC

An extensive experimental program will be conducted at the LHC including searches fornew particles and precision measurements of established processes. A full list of channels tobe studied can be found in the proceedings of the LHC Workshop [6] and specifically for theCMS experiment, in the CMS Technical Proposal [2] and the CMS Letter of Intent [7]. In thefollowing, a selection of physics goals will be discussed with an emphasis on channels withmuons in the final state. The requirements for triggering will be discussed for each of thepresented channels.

3.1 Introduction to Triggering

The trigger in LHC experiments has the task to filter potentially interesting events out of alarge background of unwanted processes. Event rates have to be reduced by several orders ofmagnitude starting from the LHC bunch crossing frequency of 40 MHz down to about102 Hzwhich is the maximum rate that can be recorded to data storage. This rate reduction is achievedin subsequent trigger levels which receive the reduced rate from the output of the precedinglevel as an input and are able to spend more time per event and analyze a larger part of theevent data. The first trigger level, which has to process incoming event data at a rate of 40 MHzdue to time constraints reads out only coarsely segmented data of some of the sub-detectors.In CMS (see Chapter4) only the muon system and the calorimeters are read out. The firstlevel trigger then reconstructs trigger objects such as muons, electrons/photons, jets, total andmissing transverse energy, . . . . Since the tracker (see Chapter4, Section4.2) cannot be readout in the first trigger level, the precision of transverse momentum and energy measurements islimited and a distinction between electrons and photons cannot be made. Events are selectedby requiring a trigger object that exceeds a certain transverse energy or momentum threshold orby requiring a combination of trigger objects exceeding certain thresholds. In general, triggerconditions based on multiple trigger objects allow to set lower thresholds for the individual trig-ger objects. In CMS also more complicated trigger conditions are possible using requirementson the topology of trigger objects (see Chapter5) which allows to further lower the transverseenergy or momentum thresholds. As mentioned in the previous Chapter, the enormous back-ground of QCD jets makes it difficult to detect signals in channels with only jets in the finalstate. Despite their generally lower branching ratios, channels with leptonic or semi–leptonicfinal states will therefore be the most important discovery channels at the LHC. Muons are par-ticularly suited to triggering due to the comparably low background in the muon system, whichis located outside all other sub-detectors. Since the main topic of this thesis is the first–levelmuon trigger of the CMS experiment, the following discussion of important physics goals isrestricted to channels that can be triggered with trigger conditions based on muons only.

3.2 Standard Model Higgs Physics

In proton-proton collisions a Higgs particle can be produced through several mechanisms asillustrated in Figure3.1. The gluon fusion process through a top-quark loop (a) dominates theentire mass range and vector boson fusion (b) becomes important only at highmH . The cross-sections for associatedtt (c) andW/Z (d) production are significantly lower but the decays ofthe associated particles can help in extracting a signal from the background. The branchingratios for the Higgs into various decay channels are shown in Figure3.2(b)for the entire massrange. Several regions can be identified as a function ofmH : atmH < 120 GeV/c2 the channel


H. Sakulin

3.2 Standard Model Higgs Physics 13

into bb dominates, followed byτ+τ−; above and up tomH < 2mZ the branching ratio into pairsof vector bosons (W ,Z), where one of the two can be virtual, increases and becomes dominant;abovemH = 2mZ the decay into a pair of real vector bosons dominates and only at very highmH ( > 2mt ) the channel intott becomes available.

t

t

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W, Z

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(d) W,Z associatedproduction

Figure 3.1: Principal Feynman diagrams for Higgs production at the LHC.

0 200 400 600 800 1000.0001

.001

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g g t t Hq q W H

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ZZWW

_bb

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tt_

(b) Branching ratios

Figure 3.2: Cross section and branching ratios for the Higgs particle as a function of its mass.

Experimentally, the following channels are accessible at CMS and ATLAS:

mH < 130 GeV/c2: The channelH → γγ is the most promising in this mass range. It is themost demanding channel for the electromagnetic calorimeters in terms of energy resolu-tion and impact parameter resolution as well asπ0-rejection. The dominant decay channelin this mass range,H → bb, has a very high background from QCD processes so that itis only accessible when the Higgs is produced in association with att.

130 GeV/c2 < mH < 2mZ : The most important channel in this mass range isH → ZZ∗ → 4`,where` can be an electron or a muon. AroundmH ≈ 2mW this channel is suppressed andthe channelH → WW → `ν`ν has a higher branching ratio. As it contains neutrinos,it does not show a clear mass peak so that the background has to be known very well.Both channels can be triggered by single– and di–muon triggers as shown in Chapter9,Section9.6, and by single– and multi–electron triggers.



2mZ < mH < 700 GeV/c2: In this mass rangeH → ZZ → 4l gives a very clean signal withalmost no background. This channel can be triggered by single– and di–muon triggers asshown in Chapter9, Section9.6, and by single– and multi–electron triggers.

mH > 500 GeV/c2: In this mass range the cross sections for the leptonic decay channels aredecreasing so that also the more difficult decay channels including jets and neutrinossuch asH → ZZ → jjνν,H → ZZ → `¯νν, andH → WW → `νjj have to be used.These channels do not show a clear mass peak so that the background has to be knownvery well.

Figure3.3shows the significance as defined byS = Nsignal/√Nbackground for the discovery

of the Higgs particle over the entire Higgs mass range for an integrated luminosity of 100 fb−1.

10060

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Expected observability of Standard Model

Higgs in CMS with 105 pb-1

H → ZZ, ZZ* → 4 ±

H → WW →

γγ

νν

H → ZZ → νν

40

35

30

Figure 3.3: Expected signal significanceS = Nsignal/√Nbackground for detecting the standard model

Higgs particle for an integrated luminosity of 100 fb−1.

3.3 Supersymmetry

As discussed in the previous Chapter there are strong reasons to believe that the StandardModel is not the ultimate theory. A number of possible extensions exist, the most favored can-didate currently being Supersymmetry (SUSY). Supersymmetry predicts a partner particle ofbosonic (fermionic) character for each of the known fundamental fermions (bosons). Compli-cated cascade decays of SUSY particles will create many leptons of high transverse momentauseful for triggering. Neutralinos and the gravitino might be detected by missing energy trig-gers. Squarks are expected to produce numerous jets.


H. Sakulin

3.4 Precision Measurement of Standard Model Processes 15

The Minimal Supersymmetric Standard Model (MSSM) predicts 5 Higgs bosons with decaychannels similar to those of the Standard Model Higgs particle discussed in the previous section.For supersymmetric Higgs particles decay channels toτ τ andbb are expected to be importantdue to enhanced branching ratios of these channels. Theτs can further decay into electrons andmuons useful for triggering or intoτ–jets which may be recognized by a specialτ–trigger (seeChapter4, Section5.3).

3.4 Precision Measurement of Standard Model Processes

Very precise measurements of Standard Model processes will be possible at the LHC dueto the high production cross–sections and high luminosities. Besides being of interest on theirown account, these measurements may also give hints of new physics if deviations from thepredictions of the Standard Model are found. Precision measurements will involve the heavyvector bosonsW± andZ0 which are interesting also as decay products of other processes.Muonic decays ofW andZ quarks can be triggered by a single muon trigger and the latter alsoby a di–muon trigger as discussed in Chapter9, Section9.6. t andb quark physics, which alsobelong to the Standard Model, are discussed in the following two sections.

3.4.1 Top-quark Physics

The LHC will be a top quark factory allowing to measure with high precision the propertiesof the t such as its mass, and its branching ratios into possibly existing rare channels. Theinterestingtt decay configurations involve one or two leptonicW decays plusb-quark jets orleptonic decays. The signatures to look for will include energetic muons and electrons andb-jets. The decay channel including (at least) aW boson decaying into a muon can be triggeredwith the single–muon trigger and to some extent with a di–muon trigger as shown in Chapter9,Section9.6.

3.4.2 b-quark Physics

CP–violation has been studied in detail in the neutral kaon system. The only other sys-tem where it is known to occur is the system of neutralB Mesons. Precise measurement ofvariousB–meson decays will allow to determine the parameters of the Cabibbo–Kobayashi–Maskawa (CKM) matrix. Given the large production cross-section of 500µb at the LHC, of theorder of106 bb pairs will be produced per second, even at low LHC luminosity. At the LHCa special experiment LHCb is dedicated to the study ofB mesons but it will also be possibleto studyb–quark physics at the two general purpose experiments, ATLAS and CMS, especiallyduring the initial low luminosity operating phase of the LHC, since reconstruction ofB de-cays may not be possible at high LHC luminosity due to the large number of pile–up events.B–meson decays can be detected in leptonic channels, but the leptons are typically very softwhich makes them difficult to trigger. Decays into muons will be more useful than the onesinto electrons due to the lower background for muons. In channels involving aJ/ψ mesonthe decay of theJ/ψ into two muons can be triggered with a di–muon trigger. In Chapter9,Section9.6, trigger efficiencies are shown for the channelB0

s → J/ψφ → µ+µ−K+K− [8]which in analogy to the channelB0

d → J/ψKS will be a gold–plated channel for the study of



CP violation at the LHC. In addition to the measurement ofB0s −B0

s mixing parameters it willallow to measure the Wolfenstein parameterη [9].

The study of possible rare decays induced by flavor changing neutral current transitions suchasb → s, d which are suppressed in the Standard Model will be another topic of interest. AtCMS it will be possible to study the channelB0

s → µ+µ− [10] at low and high luminosity. Itsexpected branching ratio is3.5× 10−9 [11].

3.5 Heavy Ion Physics

At the LHC it will also be possible to collide heavy ions such as Pb ions with a center–of–mass energy of 1150 TeV in order to create and study the expected short–lived primordialde-confined state of hadronic matter, the Quark–Gluon Plasma. At the LHC a special exper-iment, ALICE, will be dedicated to heavy ion interactions, but also the two general purposeexperiments, CMS and ATLAS, will be capable of heavy-ion physics. One of the indications ofthe existence of a deconfined Quark–Gluon Plasma state is thought to be the marked suppres-sion of quark–antiquark bound state meson formation such asJ/ψ andΥ mesons. Both will bedetectable through their decays into muons pairs.


H. Sakulin

Chapter 4

The CMS Experiment

18 4. The CMS Experiment

4.1 Overview

The Compact Muon Solenoid (CMS) [2] is one of two multi-purpose experiments whichwill run at the Large Hadron Collider. The original main objectives in the design of CMS werethe efficient and redundant detection of muons and a compact detector design, thus requiringa high magnetic field. A solenoidal magnet provides a 4 T magnetic field, guaranteeing highmomentum resolution for charged particles. The calorimeters are placed inside the coil resultingin excellent precision in the measurement of electrons and photons. The high magnetic fieldsignificantly reduces the pile–up of muons from soft hadrons so that the requirements on thegranularity of the muon system are loosened. Figure4.1 shows an elevation view of the CMSdetector: with a total length of 21.6 m (excluding the forward calorimeters) and a diameter of15 m it weighs approximately 12500 tons.

Z

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EXPERIMENTAL HALL UXC 55

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The CMS Detector at point 5 of LHC

TK

Figure 4.1: CMS elevation view.

The following reference frame is used: thex-axis points towards the center of the col-lider, they-axis points upwards and the thez-axis points along the beam, oriented to give aright-handed coordinate system. Often a (pseudo-) spherical coordinate system is used: thecoordinates are the distance to the beam-liner, the azimuthal angleφ with respect to they-axis and the polar angleθ with respect to thez-axis. Instead of the polar angle, commonly thepseudo-rapidityη is used. It is defined as

η = − ln

(tan

θ

2

). (4.1)

The pseudo-rapidity is an approximation of the rapidityy, given by

y =1

2lnE + pzE − pz

, (4.2)

whereE and p are energy and momentum of a particle. As mentioned earlier, the center–of–mass in collisions of hadrons is usually boosted along thez–direction. The rapidityy is


H. Sakulin

4.2 The Tracker 19

very useful in this respect as a boost along thez–direction only adds a constant to the rapidityand leaves distributionsdN/dy invariant. The pseudo-rapidity is a good approximation of therapidity forp� m andθ � 1/γ.

The solenoid [12] has an inner radius of 2.95 m and a length of 13 m. Is is a super-conductingdevice cooled with liquid helium and will produce a magnetic field of 4 T. The inner trackingdetectors and calorimeters are located inside the solenoid.

The innermost detector around the beam pipe (radius 43 mm) is a silicon pixel vertex detec-tor with two or three layers in the barrel and two disks in each endcap. This detector allows toreconstruct the exact position of the interaction vertices which is essential forb-tagging (identi-fying interactions that resulted inB mesons). Outside the pixel detector, a silicon strip detectorextends up to a radius of≈ 1.2 m. Together with the pixel detector it is used for the reconstruc-tion of charged tracks.

An electromagnetic calorimeter (ECAL) is located outside the tracker with a coverage of upto |η| < 3: it is a homogeneous device consisting of a large number of scintillating crystals thatare read out using avalanche photo diodes or vacuum photo-triodes. Its purpose is the precisemeasurement of the energy deposit of electrons and photons. In the endcap region a preshowerdetector is placed in front of the ECAL in order to improve spatial resolution and to providepion/photon separation. It consists of two thin lead converters followed by silicon strip detectorplanes. Optionally, preshower detectors will also be installed in the barrel.

The outermost detector inside the solenoid is the hadronic calorimeter (HCAL) which pro-vides the same pseudo-rapidity coverage as the ECAL. It is a sampling calorimeter consistingof copper absorber plates interleaved with scintillator sheets. Its purpose is the reconstructionof jets as well as the measurement of total and missing transverse energy. The very forwardhadronic calorimeter extents the coverage of the HCAL up to|η| < 5.3 and enhances the tight-ness of the detector. It is placed around the beam pipe, outside the magnet and muon system.

The muon system is embedded in the in the iron return yoke of the magnet, outside thecoil. Three different technologies are used: drift tubes with bunch crossing identification in thebarrel up to|η| < 1.2, cathode strip chambers in the endcaps up to|η| < 2.4 and resistive platechambers in the whole detector up to|η| < 2.1. All three detectors are used in the reconstructionof muons coming from the interaction vertex as well as in the trigger.

4.2 The Tracker

The inner tracking detectors [13,14] are designed to reconstruct high-pT muons, electronsand hadrons, with high momentum resolution and high efficiency in the range of|η| < 2.5.They are also designed to allow identification of tracks coming from detached vertices. Highredundancy and low occupancy are needed to achieve these goals, leading to a highly granulardesign with layers of silicon pixels close to the beam pipe, where the density of tracks is large,and layers of silicon strips further away from the beam pipe. The inner tracker extends up to aradius of 115 cm over a length of approximately 270 cm on each side of the interaction point.

4.2.1 The Pixel Tracker

The main purpose of the pixel tracker is the measurement of the impact parameter of chargedtracks in order to achieve efficient tagging of jets originating from the decay of heavy hadronscontainingb and c quarks and for top-quark studies. Over the full range of rapidity at least



Figure 4.2: Pixel Tracker layout (high luminosity configuration).

two hits are necessary to get a determination of the impact parameter. The density of hits ishigh in the region close to the beam pipe, also due to soft particles that are forced on helicoidaltrajectories of small radius by the strong magnetic field. The detector resolution area thereforehas to be small leading to the choice of silicon pixels.

The detector will consist ofn-type pixels on ann-type substrate: the pixels will be ofsquared shape (150µm× 150µm) with a width of 250µm. By interpolation between the signalsdeposited in several adjacent pixels, a spatial resolution ofσ(x) ≈ 15 µm can be achieved.

In the barrel, three layers of silicon pixels can be placed at distances of 4.3 cm, 7.2 cm and11.0 cm from the beam line. At the very beginning of the data taking, when LHC will run atlow luminosity, the silicon pixel detector will be equipped with the two inner layers; at highluminosity only the two outer layers will be installed (see Figure4.2). In the endcaps twodisks at positionsz = ±325 mm andz = ±465 mm will cover a radial range ofr = 6 cmup tor = 15 cm. In the endcaps, where tracks are normal to the pixel surface and electric andmagnetic fields are parallel, the detector blades are tilted by 20o in order to induce charge sharingbetween multiple pixels. Figure4.4illustrates the transverse impact parameter resolution of theinner tracker system as a function of the pseudorapidityη.

4.2.2 The Silicon Microstrip Tracker

In the current setup, the silicon microstrip technology is used for the entire tracking detector.Figure4.3 shows the layout which can be split into an inner and an outer part. The inner partconsists of 4 cylindrical layers in the barrel and 3 mini-disks in each endcap. The outer partconsists of 6 barrel layers and 9 forward disks. Together with the pixel tracker the layoutresults in a minimum number of 12 measurement points per charged track over a wide range ofpseudorapidity (|η| < 2.5).

In the inner part the micro-strip detectors are made of single-sidedn-type silicon with athickness of 320µm and a pitch size between 60 and 270µm, while the length of the detectorsvaries between 7 and 12.5 cm. In the outer part the detectors have a thickness of 500µm and apitch of 140µm. Some layers are equipped with two detectors mounted back-to-back, with thesecond detector mounted at a stereo angle of 100 mrad. To enhance radiation hardness, the fulldetector will operate at a temperature of -10oC.


H. Sakulin

4.3 The Calorimeters 21

z view

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Momentum measurements of charged particles in the pseudorapidity region|η| < 1.6 ben-efit from the full momentum analysis power. In this region, a charged particle with a transversemomentum of 1000 GeV/c has a sagitta of 195µm. The inner tracker acceptance extends furtherto |η| < 2.5, with a reduced radial lever arm. Figure4.5 shows the transverse momentumresolution of the tracking systems as a function of the pseudorapidityη, for charged tracks ofseveralpT values.

4.3 The Calorimeters

4.3.1 The Electromagnetic Calorimeter

The electromagnetic calorimeter (ECAL) [15] is designed to reconstruct energy and direc-tion of electrons and photons with high precision. The physics channel that imposes the strictestperformance requirement on the ECAL is the decay of the Higgs boson with a mass in the range100-140 GeV/c2 into two photons. A homogeneous design has been chosen, consisting of over80000 lead tungstate (PbWO4) crystals (see Figures4.6 and4.7). PbWO4 is a fast scintillatorwhich has high density, a small Moliere radius and a short radiation length, allowing for a verycompact system. The crystals in the barrel have a front face of about22 × 22 mm2, whichmatches well the Moliere radius of 22 mm. To limit fluctuations in the longitudinal showerleakage of high-energy electrons and photons, the crystals have a total thickness of 26 radiationlengths, corresponding to a crystal length of only 23 cm. In the endcaps the crystals are slightlywider, with rear faces measuring30× 30 mm2, but are slightly shorter (22 cm). The crystal axisis off-pointing with respect to the interaction point by 3o either inφ or in η in order to increasegeometrical coverage. The light produced in the crystals is detected by silicon avalanche photo-diodes and vacuum photo-triodes in the barrel and endcaps, respectively. The coverage of theECAL extends up to|η| < 3, but the high radiation dose of pile-up energy will limit precisionenergy measurements to the range of|η| < 2.6. Figure4.8shows different contributions to theenergy resolution of the ECAL which can be parameterized as

(σ(E)/E)2 = (a/√E)2 + (σn/E)2 + c2 (E in GeV), (4.3)



Figure 4.4: Transverse impact parameter (d0)resolution of the Inner Tracker as a function ofpseudorapidityη for isolated muons. High lumi-nosity pixel configuration.

Figure 4.5: Tracker standalone transverse mo-mentum (pT ) resolution as a function of pseudo-rapidityη for isolated muons.

wherea is the statistical term (labeled “photo” in the figure),σn is the noise term andc theconstant term.

The endcap region is equipped with a preshower detector, covering the region of1.65 <|η| < 2.61, consisting of two thin lead converters followed by silicon strip detector planes witha pitch of 1.9 mm. The detector improves spatial resolution for photons to typically 300µm at50 GeV which helps in the rejection of close–in–space photon pairs coming fromπ0 decays.Optionally, an additional preshower detector can be placed in the barrel region of|η| < 0.9 inthe high luminosity phase.

4.3.2 The Hadronic Calorimeter

The hadronic calorimeter (HCAL) [16] is the outermost detector placed inside the magnetcoil. Together with the ECAL, the HCAL measures the direction and energy of jets as wellas missing and total transverse energy. These measurements will play an important role in thediscovery of the Higgs boson in the high mass range and in the discovery of supersymmetricparticles. In order to achieve good missing energy resolution, a hermetic calorimetry coverageto |η| < 5 is required.

The HCAL consists of a barrel (HB) and an endcap (HE) part inside the magnet with acoverage up to|η| < 3.0 plus the forward (HF) calorimeter which is placed around the beam-pipe outside the muon system and extends the coverage up to|η| < 5.3 (see Figure4.1). HBand HE are sampling calorimeters consisting of 50 mm thick copper absorbers interleaved with4 mm thick plastic scintillator tiles that are read out with wavelength shifting fibers. The light isdetected by hybrid photodiodes. The HB is made of two half-barrels each of 4.3 meter length.The HE consists of two large structures, situated at each end of the barrel detector and within


H. Sakulin

4.3 The Calorimeters 23

Figure 4.6: 3D view of ECAL. Figure 4.7: Longitudinal view of CMS ECAL.

0.1

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s/E(%

)

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Figure 4.8: Energy resolution of the electro-magnetic calorimeter. The contributions from electronicnoise, photo-statistics and the intrinsic term are shown.



the region of high magnetic field. Because the barrel HCAL inside the coil is not sufficientlythick to contain all the energy of high energy showers, additional scintillation layers (HOB) areplaced just outside the magnet coil. The full depth of the combined HB and HOB detectors isapproximately 11 absorption lengths.

Two separate forward hadron calorimeters covering the region of3.0 < |η| < 5.3 are placedoutside the muon system around the beam pipe: the inner radius is only 12 cm, the outer radius1.5 m and the length is 3 m. Because of the strong radiation close to the beam pipe, the HFis built of steel absorber plates, which suffers less activation under irradiation than copper.Hadronic showers are sampled at various depths by radiation-resistant quartz fibers parallel tothe beam which are inserted into the absorber plates. The fibers are sensitive to the Cherenkovlight generated by charged particles in the electromagnetic component of the showers.

The achievable energy resolution is given byσE/E = 65 %/√E ⊕ 5 % in the barrel and by

σE/E = 85 %/√E ⊕ 5 % in the endcaps andσE/E = 100 %/

√E ⊕ 5 % in the very forward

part, whereE is the measured energy in GeV.

4.4 The Muon System

Muons are expected to provide clean signatures for a wide range of physics processes. Thetask of the muon system [17] is to identify muons and provide, in association with the tracker,a precise measurement of their momenta. In addition, the system provides a robust trigger withbunch crossing identification for muons over a widepT range from several GeV to the TeVscale. The muon system is the outermost detector in CMS: it is embedded in the iron returnyoke of the magnet and uses the bending in the magnetic field guided by the return yoke forpT measurement. The muon system consists of four stations, arranged as concentric cylindersaround the beam line in the barrel region, and as disks perpendicular to the beam line in theendcaps (see Figures4.9and4.10). Muon identification is ensured by the large thickness of theabsorber material (iron), which cannot normally be traversed by particles other than neutrinosand muons. There are at least 10 interaction lengths of calorimeters before the first station andan additional 10 interaction lengths of iron yoke before the last station.

Three different technologies are employed in the muon system: Drift Tubes (DTs) are usedin the barrel, where the occupancy, the background noise and the residual magnetic field arelow. In the endcap where rate, background noise and magnetic field are higher, cathode stripchambers (CSCs) are used. Both systems provide precise space and time measurement and arewell suited for triggering. A separate system of resistive plate chambers (RPCs) covering thebarrel and endcaps provides an independent measurement for triggering purposes with superiortime resolution. Despite the lower spatial resolution it can also assign apT to the measuredmuons. As indicated in Figure4.9 the coverage of the CSC muon system extends up to apseudo-rapidity of|η| < 2.4 while the RPC system covers the range of|η| < 2.1.

4.4.1 The Drift Tube Chambers

Drift tubes have been chosen for the barrel because of the large area that has to be coveredand because of the rather unproblematic environment: the DT system has to sustain the lowestradiation dose and charged particle rate inside CMS and the magnetic field inside the chambersis almost vanishing as almost all the flux is carried by the iron of the yoke.


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4.4 The Muon System 25

0

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Figure 4.9: Longitudinal view of the CMS MuonSystem.

Figure 4.10: Transverse view of the CMS BarrelMuon System.

The schematic view of a basic drift tube cell is shown in Figure4.11. It measures 42 mmin width by 13 mm in height and has a maximum length of 4.2 m. A stainless steel anode wireof 50µm diameter runs along the center of the DT cell. The cathodes are “I”-shaped aluminumbeams at the edges of the cell. Additional field shaping electrodes at the top and bottom of thecell improve the linearity of the space to drift time relationship. A gas mixture of 80 % Ar and20 % CO2 provides a saturated drift velocity and good quenching properties. The drift velocityis around 5.6 cm/µs, resulting in a maximum drift time of 375 ns. The single cell resolution isapproximately 180µm and the efficiency as high as 99.8 %. Four staggered layers of drift tubecells are combined into a super-layer: this allows for the removal of ambiguities in the spacemeasurement, for the rejection of non-muon background and for the identification of the correctbunch crossing. The basic detector unit in the DT system is a chamber. As shown in Figure4.12,it is made of three super-layers: the outer and inner super-layers provide a measurement of theφ coordinate (bending plane) while the middle super-layer measures thez-coordinate. A spacermade of aluminum honeycomb material is inserted between the middle and the inner super-layers in order to increase the lever arm for the measurement of the bend angle. In total thereare 12 sensitive layers in a DT chamber except in the outermost chambers which only containthe two super-layers measuring theφ-coordinate.

The DT system is divided into four concentric cylinders around the beam axis (stations MB1to MB4) and into five wheels along thez-axis, each about 2.5 m long. Each wheel consists of12 azimuthal sectors, covering approximately 30o. The set of five adjacent sectors alongz inthe five wheels is called a wedge. There are twelve chambers per wheel and station except inthe outermost station where the top and the bottom sector are covered with two chambers each,giving a total of 14 chambers. In total, there are 250 chambers.

4.4.2 The Cathode Strip Chambers

Cathode Strip Chambers (CSCs) are used in the endcap regions where the magnetic field isvery intense and inhomogeneous and where the charged particle rate is high. CSCs are multi-wire proportional chambers defined by two cathode planes, one segmented into strips, and an



13 mm

42 mm

ElectrodeAnode wire

Cathode

RPCRPC

RPCRPC

Figure 4.11:Schematic view of a Drift Tube cell. Figure 4.12: Schematic view of a Drift Tubechamber with attached Resistive Plate Chambers.

array of anode wires running across, in between (see Figure4.13). An avalanche developed on awire induces a charge on several strips of the cathode plane and interpolation between adjacentstrips gives a very fine spatial resolution of 50µm which is used to measure theφ-coordinate.Simultaneously, the wire signals are read out, directly, and used to measure the radial coordinatewith a coarse precision of approximately 0.5 cm. The closely spaced wires make the CSC a fastdetector suitable for triggering. The basic module of the CSC system is a chamber consistingof six layers in order to provide high efficiency and a robust pattern recognition that can rejectnon-muon background. Combining multiple layers also improves the timing resolution so thatthe correct bunch crossing can be assigned with over 99 % efficiency. The cathode planes areformed by honeycomb panels with copper clad skins, while the9.5 mm thick gas gaps are filledwith a mixture of 30 % Ar, 50 % CO2 and 20 % CF4. Chambers are of trapezoidal shape withstrips running radially (strips have constant∆φ width). They cover sectors of 10o or 20o andhave a maximum dimension of 3.5 m× 1.5 m.

Figure4.14shows the layout of one end-muon

cathode

cathode

wires

wires

induced charge

cathode with strips

plane cathode

avalanche

3.12 mm

9.5

mm

3 - 16 mm

Figure 4.13: Principle of a cathode strip chamberlayer.

cap of the CSC system: the chambers are ar-ranged in four disks (stations ME1 to ME4)perpendicular to the beam axis interleavedwith the iron disks of the return yoke. An-other iron disk of 10 cm thickness is placedoutside the outermost station in order toshield the station against backsplash inducedby particles scattered at small angles whichinteract with material in the forward directionsuch as the beam pipe, quadrupoles, or theforward calorimeter. The innermost stationconsists of three concentric rings of cham-bers while the other stations consist of two rings. The gaps between the rings are non-projective.The inner rings of stations ME2 to ME4 consist of 18 chambers while all the other rings consistof 36 chambers. The chambers overlap inφ in order to avoid dead areas, except in the outermostring of the first station (ME1/3) which has gaps between the chambers.

The innermost chambers of the first station (ME1/1) are slightly different from the other


H. Sakulin

4.4 The Muon System 27

Figure 4.14: Layout of the CSC chambers in the endcaps.

chambers as they operate in the highest magnetic field (up to 3 T) and under the highest radiationdose: the wires are tilted by 25o in order to compensate for the tilted drifting in the magneticfield (Lorentz effect); the gas gap is only 6 mm and the number of strips is doubled for|η| > 2.0in order to reduce occupancy.

4.4.3 The Resistive Plate Chambers

A system of resistive plate chambers (RPCs) which is placed in the barrel and endcaps hasbeen specifically designed for triggering purposes. It provides independent detection of muonswith superior timing resolution. RPCs are gaseous parallel-plate detectors with a reasonablespatial resolution and excellent time resolution of approximately 1 ns, comparable to that ofscintillators.

An RPC gap consists of two parallel plates made of very high resistivity plastic mate-rial (bakelite), separated by a gas gap of a few millimeters (see Figure4.15). The plates arecoated with graphite on the outside which forms the high voltage electrodes. The read-out isperformed by means of aluminum strips separated from the graphite coating by an insulatingPET (poly ethylene terephthalate) film. A higher rate capability compared to traditional RPCsis achieved by operating in avalanche mode rather than streamer mode: the electric field andconsequently the gas multiplication is reduced requiring an improved electronic signal amplifi-cation. In order to increase the signal on the read-out strips, a double-gap design is used in CMSwith two gas-gaps of 2 mm width being read out by one set of strips in the middle. The RPCsare operated at 9.5 kV with a gas mixture of 95 % C2H2F4 and 5 % i-C4H10. A rate capabilityof 1 kHz/cm2 can be achieved. A critical point in the construction of the RPCs is the flatnessof the bakelite surface since the presence of any irregularity can lead to a local increase of fieldstrength. This increased field strength can cause spontaneous discharges which can lead to anunacceptably high intrinsic noise rate. One possible solution, which recently has been adopted



Bakelite

BakeliteBakeliteBakelite

- high voltage

+ high voltage

to electronics

Figure 4.15: Principle of a Double–Gap RPC.

for the barrel chambers, consists in oiling the bakelite surfaces with linseed oil. For the endcapchambers the question of oiling is still under discussion.

As illustrated in Figure4.9, in the barrel, 6 layers of RPCs will be used: they are attachedto either side of the DT chambers in the inner two stations and only to one side in the outertwo stations. This will allow to have a minimum of four measurements also for low-pT muonswhich do not reach the outer two stations. The strips are oriented parallel to the beam-line witheach strip covering 5/16 degrees inφ. In the endcaps, four layers of RPCs will be attached tothe four CSC disks, covering a range of up to|η| < 2.1. The strips are trapezoidal in shape andoriented radially: they also cover 5/16 degrees inφ per strip.


H. Sakulin

Chapter 5

The CMS First Level Trigger

30 5. The CMS First Level Trigger

This chapter gives an overview of the CMS Trigger System. The L1 Trigger is discussedin detail, especially the L1 Muon Trigger up to the level of the three Regional Muon Triggerswhich deliver the input to the Global Muon Trigger. Detailed simulation results of the perfor-mance of the Regional Muon Triggers are presented. Chapter6, which describes the design ofthe Global Muon Trigger, relies heavily on these results.

5.1 The CMS Trigger System

The CMS trigger system filters the high rate of events produced at the LHC on–line inorder to keep interesting events with high efficiency and to reject unwanted background: it hasto perform an enormous reduction of rate starting from the LHC beam crossing frequency of40 MHz down to about 100 Hz, the maximum rate that can be handled by data acquisition anddata storage. In CMS of the order of108 channels have to be read out per bunch crossing andeven after compacting the data an event size of approximately 1 MB remains resulting in a rateof 100 MB/s going to data storage. Over a year of LHC operation, several petabytes of data willbe collected, pushing the limits of today’s storage technologies.

The necessary data reduction is achieved in several steps, usually calledtrigger levels, eachstep working on the reduced rate of bunch crossings from the step before, analyzing a largerpart of the event data and applying more sophisticated algorithms:

The Level–1 Trigger (L1) receives data at the LHC beam crossing frequency of 40 MHz. Inorder to analyze every beam crossing without dead–time, custom–built pipelined hard-ware logic is employed. Using special coarsely segmented trigger data from the muonsystems and the calorimeters, the Level–1 Trigger reduces the rate of crossings to below100 kHz. While the L1 Trigger is taking its decision the full high–precision data of alldetector channels are stored in analog or digital buffers, which are only read out if theevent is accepted.

The High–Level Triggers (HLT) are implemented in software running on a large farm ofcommercial computers. Several levels will be applied, each level working on the re-duced rate of crossings from the level before, being able to spend more processing timeper crossing and to read out more data from the detector. The number and type of triggerlevels is flexible and can be optimized according to running conditions of the LHC. Cur-rently it is planned that a Level–2 trigger will reduce the rate by a factor of 10 using highprecision data from the muon systems and the calorimeters. At Level–3 the full trackerdata will be read out. Only at the higher trigger levels cuts on variables like the invariantmass, similar to cuts used in off–line analysis, will be applied in order to reduce the rateof crossings to be recorded to 100 Hz.

The basic objects on which trigger decisions will be made are muons, electrons, photons,jets, missing and total transverse energy, the sum of jet energies above a programmable trans-verse energy threshold and jet counts above programmable transverse energy thresholds. Theefficiency should be high and well understood at all trigger levels as some of the processes ofinterest are extremely rare: a process with a cross–section of 1 fb such as a rare Higgs decay willoccur with a rate of 0.1 events/day at high luminosity. Determination of transverse energies andmomenta should be as precise as possible so that a sharp turn-on characteristic can be achievedand the thresholds can be set as low as possible.


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5.2 Level–1 Trigger Overview 31

HFenergy

HCALenergy

ECALenergy

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DThits

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RegionalCal. Trigger Pattern

Comp-arator

localtrigger

localtrigger

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track finder

track finder

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Global Trigger TTC SystemTRK,ECAL,HCAL,MU

252 quiet &252 MIP

bits

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inputdata

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4µ

4µ4µCal. Trigger

Figure 5.1: Structure of the L1 Trigger.

5.2 Level–1 Trigger Overview

The overall structure of the CMS Level–1 Trigger is shown in Figure5.1. It consists ofthree main systems: the Calorimeter Trigger, the Muon Trigger and the Global Trigger. TheCalorimeter trigger receives data from the ECAL, HCAL and HF detectors while the MuonTrigger uses all the three Muon Systems: Drift Tubes, Cathode Strip Chambers and ResistivePlate Chambers. Detailed information about the L1 Trigger is available in the Level–1 Trig-ger Technical Design Report [18]. In the following the main features are explained with anemphasis on the L1 Muon Trigger.

Traditionally, first level triggers only count trigger objects that pass certain programmabletransverse energy or momentum thresholds and find a trigger decision based on these counts.In CMS, a novel, very flexible triggering concept will be employed. The Calorimeter Triggerand the Muon Trigger identify as trigger objects: electrons/photons, isolated electrons/photons,forward, central andτ–jets and muons. Four trigger objects of each type are forwarded to theGlobal Trigger [19,25], each including a measurement of its transverse momentum or energy,its coordinates in the detector (φ, η) and its quality. Additionally, the total and missing trans-verse energies and 12 jet counts above programmable thresholds covering differentη-ranges areprovided by the Calorimeter Trigger. The Global Trigger then checks if the trigger objects fulfillcertain programmable trigger algorithms. Trigger algorithms can consist of arbitrary combina-tions of trigger objects that pass certain thresholds and can even include topological correlationsbetween any of the trigger objects. Up to 128 trigger algorithms can be run in parallel and acrossing is accepted if either of the conditions is fulfilled. It is also possible to pre–scale certaintrigger algorithms i. e. to accept only a certain fraction of events that trigger the algorithm.

All basic trigger conditions can be realized using two or at maximum three trigger objectsof each type. Four objects of each type are provided in order to have some safety margin. Anexception could be SUSY processes with high jet multiplicity in the final state. The additionaljet counts are provided for this case.



Figure 5.2: CMS underground counting room (left) and interaction hall (right).

L1 Trigger electronics are located both on the detectors (local reconstruction) and in theunderground counting room (mostly regional and global reconstruction), which is separatedfrom the detector cavern by a 7.5 m thick concrete wall (see Figure5.2). Signals are transmittedfrom the detector to the counting room on optical fibers. For reasons of radiation protection thetunnels for the signal lines do not point directly towards the interaction point, thereby increasingthe length of the signal connections.

The L1 Trigger has to find a trigger decision on every beam crossing i. e. every 25 ns. This isachieved by splitting the trigger algorithms into a pipelined structure of processing blocks, eachblock taking less than 25 ns to process. Every 25 ns the results of a calculation are shifted to thefollowing blocks and a new calculation using the data from the next beam crossing begins. Themaximum processing and signal transfer time (latency) available for the L1 Trigger is given bythe depth of the buffers that hold the high precision data, the constraint coming from the trackerand the pre–shower analog pipeline memories with a maximum depth of 128 beam crossings or3.2µs. A big part of the available time is taken up by the transmission of trigger data from thedetector to the counting room and by the distribution of the L1 accept signal from the GlobalTrigger back to the detector via the Trigger Timing and Control (TTC) System. The longestpath is approximately 90 m or 300 ns each way. In case of the DT Trigger, a significant part ofthe available time is also taken up by the drift times of up to 400 ns.

The trigger electronics have to be carefully optimized in order to achieve minimum latency.The main technologies used to implement the trigger logic are Field Programmable Gate Ar-rays (FPGAs) and Application Specific Integrated Circuits (ASICs). FPGAs are commerciallyavailable, freely programmable arrays of logic gates while ASICs are custom–built and requirea time–consuming and expensive design cycle. FPGAs are used for many tasks where devicecounts are moderate and flexibility is an issue. ASICs are used, especially when a large numberof devices is needed and when radiation hardness is an issue such as in the trigger componentslocated directly on the detectors.


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5.3 L1 Calorimetry Trigger 33

5.3 L1 Calorimetry Trigger

The L1 Calorimetry Trigger detects electrons/photons and jets as well as the total and miss-ing transverse energy using coarsely segmented data from the calorimeters (see Chapter4, Sec-tion 4.3). Additionally it provides two bits of information to the L1 Muon Trigger for eachcalorimeter region, a MIP bit denoting an energy deposit compatible with the passage of a min-imum ionizing particle (MIP) like a muon through the region and a Quiet bit denoting whethera certain minimum energy was deposited in the region. No distinction can be made betweenelectrons and photons since tracker data is not available at level–1.

L1 Calorimetry algorithms are based on the energy deposited intrigger towers: in the ECALbarrel up to|η| < 1.48 each tower consists of5×5 crystals and covers∆η×∆φ = 0.087×0.087.In the ECAL endcap, the crystals are arranged in anx−y geometry and therefore do not followexactη andφ boundaries. The towers cover on average∆φ = 0.087 while their size inηincreases from∆η = 0.087 at |η| ≈ 2 up to∆η = 0.35 at |η| = 3. Trigger tower sizes matchthe HCAL physical tower size up to|η| < 1.74. Above, an HCAL physical tower has twicetheφ dimension of a trigger tower and its energy is divided in two equal amounts and assignedto the two corresponding trigger towers. Either two or three of the lateral layers of the HCALparticipate in the energy summation for the L1 trigger. In the transition region between barreland endcap, barrel and endcap segments are added together. The trigger towers for3 < |η| < 5are covered by the HF only. They have a size of∆η ×∆φ = 0.5 × 0.348. The trigger towersare organized inCalorimeter Regions: up to|η| < 3, a region is formed by4× 4 trigger towerswhile the HF trigger towers are themselves treated as regions. The regions cover approximately∆η ×∆φ = 0.35× 0.35, the exact size inη being given in Table5.1. The calorimeter regionsform the basis for jet algorithms. They also define the scale for the coordinatesη andφ of allthe calorimeter trigger objects sent to the Global Trigger and the MIP and Quiet bits sent to theGlobal Muon Trigger.

Table 5.1: Pseudorapidity scale of Calorimeter Regions. The first region starts atη = 0.

Region Nr 1 2 3 4 5 6 7

∆η 0.348 0.348 0.348 0.348 0.348 0.432 0.328

|ηmax| 0.348 0.696 1.044 1.392 1.74 2.172 2.5

As a first step,Trigger Primitive Generation (TGP)electronics, which are integrated into thecalorimeter readout electronics, calculate trigger primitives for each bunch crossing. Calorime-ter pulses span several beam crossing periods so that a special peak finder logic, based on adigital filter, is needed to find the maximum of a pulse and to assign it to the correspondingbeam crossing. Transverse energies in the ECAL and HCAL are summed and coded in an 8–bitnon–linear scale. An additional ECAL fine–grain bit gives information about the energy profilealongη and helps in the rejection of two–photon signals fromπ0 decays. An HCAL fine–grainbit indicates the passage of a minimum ionizing particle through the HCAL. It is calculatedbefore the HCAL energy is converted to transverse energy: the bit is set if the deposited energyis inside a programmable window (by default1.5 < E < 2.5 GeV).

In theRegional Calorimeter Triggerelectrons/photons are identified using a sliding windowof 3× 3 trigger towers. A differentiation between electrons and photons cannot be made at L1as no tracker data is available. The best (highestET ) four isolated and non–isolated electronsare found in a wedge of∆η×∆φ = 3× 0.7 and sent to the Global Calorimeter Trigger (GCT).Forward and central jets as well asτ–jets are identified using windows of3 × 3 calorimeter



Table 5.2: Calorimeter Trigger output data to Global Trigger and Global Muon Trigger.

Objects Energy bits Pattern bits η − φ bits Total bitsIsolated electrons (4) 6 - 5φ+ 4η 60Non-isolated electrons (4) 6 - 5φ+ 4η 60Central jets (4) 6 - 5φ+ 4η 60Forward jets (4) 6 - 5φ+ 4η 60τ -jets (4) 6 - 5φ+ 4η 60Jet counts (12) 0 4 - 48TotalET 13 - - 13TotalHT 13 - - 13MissingET 13 - 6φ 19Quiet bits (to GMT) - 14η × 18φ - 252MIP bits (to GMT) - 14η × 18φ - 252

regions. For each calorimeter region aτ–veto bit is set if there are more than two active ECALor HCAL towers in the region. A jet is defined asτ–like if none of the nine calorimeter regionshave theτ–veto bit set. The best (highestET ) four central and forward jets and centralτs areforwarded to the GCT which sends them on to the Global Trigger. The transverse energies ofthe towers in each region are summed and forwarded to the GCT which calculates the the totaland missingET . The MIP bit for a region is set when any of the 16 contributing trigger towershave the HCAL fine–grain bit set. The Quiet bit of a region is set if the sum of transverseenergies in a given region does not exceed a programmable threshold, by default 5 GeV. TheMIP and Quiet bits are sent to the GCT which sends them on to the Global Muon Trigger.

TheGlobal Calorimeter Triggersorts the isolated and non–isolated electron/photon candi-dates byET to find the best four of each type in the entire calorimeter. It calculates theET andmissingET sums as well as the direction of the missingET and forwards the other calorime-ter objects to the Global Trigger and Global Muon Trigger. Additionally, it also calculates theenergy sumHT of all jets above a programmable transverse energy threshold. A list of allCalorimeter Trigger objects with bit counts is given in Table5.2.

5.4 L1 Muon Trigger

5.4.1 Requirements

The purpose of the L1 Muon Trigger is the identification and reconstruction of muons withhigh efficiency and the measurement of their transverse momenta with good resolution. Goodmomentum measurement allows to keep events with high-pT muons with high efficency andto effectively suppress the large background of low-pT muons. In certain detector regions, L1trigger algorithms may generate additional ghost candidates which together with the correctcandidate may trigger a di–muon trigger. In order to efficiently run a di-muon trigger it isnecessary that the probability for ghosting is small. At thresholds typically used in a di-muontrigger (e.g. 4 GeV/c) the rate of events with a single muon passing the threshold is two ordersof magnitude higher than the rate of events with two muons passing the threshold. A roughupper limit for the tolerable ghosting probability in the L1 Muon Trigger is therefore 0.5 %.Exceeding the limit would cause the di-muon trigger rates to be dominated by triggers fromghosts.


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5.4 L1 Muon Trigger 35

All three muon systems participate in the L1 Muon Trigger: Drift Tubes (DT), CathodeStrip Chambers (CSC) and Resistive Plate Chambers (RPC). Each of the systems separatelyfinds muon candidates, which are then combined by the Global Muon Trigger. The excellentspatial precision of the DT and CSC ensures sharp momentum thresholds. Their multi–layerstructure provides effective background rejection. RPC, on the other hand, have a superiortiming resolution and allow precise beam crossing identification. High granularity of the systemallows operation in a high–rate environment. Time information and both spatial coordinates arecarried by the same signal eliminating ambiguities typical for wire detectors.

The DT/CSC and RPC Trigger Systems identify muon candidates using different algorithmsbased on different detector technologies: in the DT and CSC triggers, local track segments arereconstructed in the muon stations and then combined to tracks in track finders. The RPC Trig-ger, on the other hand, uses a pattern comparator method. In principle, up to a pseudorapidityof |η| < 2.1 two complementary measurements should be provided for each muon resultingin numerous advantages: DT with long drift times and CSC with charge weighting are morevulnerable to muon radiation as a background hit may eliminate a correct hit and cause someinefficiency. The RPC Trigger does not suffer inefficiencies due to muon radiation since all hitsare processed in parallel, but the rate can be increased by additional hits as they can make apattern look straighter. Accidental coincidence of three or four background or noise hits canbe recognized by the RPC Trigger as a real muon and causing an increase in trigger rate. Thisis very unlikely in the DT/CSC System as a coincidence of several planes in each stations isrequired.

Properly combining the information from both systems allows to achieve high efficiency,low ghosting and powerful background rejection. The combination of muon candidates of theregional triggers is the task of the Global Muon Trigger and the main topic of this thesis. Thedesign of the Global Muon Trigger is studied in Chapter6; detailed simulation results of itsperformance are shown in Chapter9. Another advantage of the two complementary systems isa possibility to perform cross–checks and quickly detect problems during run time. For manystudies like cross–sections and asymmetries it is important to know trigger efficiency and triggeracceptance which are usually obtained by running a pre–scaled trigger with lower thresholds.The two–component system allows to measure these quantities in a complementary way.

5.4.2 Drift Tube Trigger

5.4.2.1 DT Local Trigger

The local DT Trigger detects charged particles crossing a DT chamber (see Chapter4, Sec-tion 4.4.1), measures their coordinates and crossing angle and determines the beam crossingfrom which the particles originated. The signals from theφ–super-layers and theθ–super-layersare processed separately, so that the output consists of track segments in the(r, φ) plane and aseparate pattern of hits from theθ–super-layers. DT Local Trigger electronics are mounted onthe side of the DT chambers inside the detector.

As a first step of processing,Bunch and Track Identifiers (BTIs)locally detect particles ineach super-layer. Each BTI is connected to a group of 9 drift cells as illustrated in Figure5.3.The wire groups of neighboring BTIs overlap. A BTI looks for the coincidence of signalsin the four layers inside the super-layer using a mean–timer technique: the signals from theDT wires are put into shift registers which are advanced at every beam crossing. After themaximal drift time of approximately 400 ns all signals are available inside the registers and the



Out 0 Out 1 Out 2 Out 3 Out 4 Out 5 Out 6 Out 7 Out 8 Out 9 Out 10 Out 11

In 0 In 1 In 2 In3

OuterLayer

InnerLayer

µ

X

K

D = 23.7 cm cor

cor

Figure 5.4: Track Correlator (TRACO).

BTI looks for patterns compatible with the passage of a particle at a certain crossing angle onan approximately straight line. A linear relation between drift time and distance is assumed.This algorithm allows to measure the position with a resolution of 1.4 mm and the crossingangle with a precision of 60 mrad while at the same time identifying the bunch crossing of thetrack. For reasons of efficiency, also patterns with hits in only three of the layers are allowed:these are calledLow Quality Triggers (LTRG)while patterns with hits in all four layers arecalledHigh Quality Triggers (HTRG). If a second candidate is found inside a BTI, the one withhigher quality has precedence, or in case of equal quality, one of the candidates will be selectedrandomly.

As discussed in Chapter4, Section4.4.1,µ

1

4

3

2

9

6

7

8

5

ψ

hA

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x

Figure 5.3: Bunch and Track Identifier (BTI).

the outermost and innermost super-layersin each chamber are used to measure theazimuthal coordinateφ. Track Correla-tors (TRACOs)correlate the results of theBTIs in the two super-layers in order to im-prove the angular resolution. With a leverarm of 23.7 cm between the two super-layers,the angular resolution can be improved to10 mrad while the position resolution re-mains unchanged. Each TRACO is connected to four BTIs in the inner super-layer and to12 BTIs in the outer one as illustrated in Figure5.4. The TRACO first selects the best tracksegment, separately for the inner and the outer super-layer according to the segment’s qual-ity (HTRG/LTRG) and the track’s proximity to the radial direction i. e. its transverse momen-tum. The crossing angle of a correlated track candidate is then calculated and its compatibilitywith the crossing angles of the segments is checked against programmable thresholds. If acorrelation is found, then the track parameters are converted to the chamber reference frameusing look–up–tables: position is converted to radial angleφ and the local crossing angle tothe bend angleφb. If no correlation is found, also an uncorrelated track will be forwarded. Inorder to allow identification of two muons inside the same TRACO, the same algorithm is ap-plied twice. Each track segment found by the TRACO consists of 12 bits forφ, 10 bits forφband a 3-bit quality word, indicating the qualities of the participating segments from the super-layers, HH, HL, and LL for correlated segments and Hi, Ho, Li, Lo) for uncorrelated segmentsin the inner (i) or outer (o) super-layers. In order to reduce noise, an optional confirmation oflow–quality segments by segments from theθ super-layer is foreseen.


H. Sakulin


MB1 to MB4

Sector

Processor

1 x

6 x 12

1 xBarrelSorter

Drift Tubetrigger

primitive

generator

72 x-η φ segment

φ= 0.52

Global Muon Trigger

η= 0.35

Wedge

η Track-Finder12 x

Wedge Sorter

12 x12 x

12 xSector

Figure 5.5: Drift Tube Track Finder (DTTF).

TheTrigger Servers (TSs)perform the final selection of segments in a DT chamber. In theφ–view, theφ–Trigger Server selects the two highest–pT (lowestφb) segments from the TRACOs.In the θ–view, where only one super-layer exists, theθ–Trigger Server directly processes theoutput of the BTIs: the outputs of 63 BTIs across a chamber are or–ed in groups of 9 resultingin an output of 7 bits per chamber indicating a segment in the respective group. Another 7 bitsare used to code the quality (LTRG/HTRG) of the segment. Only segments that are compatiblewith a track coming from the vertex are considered.

Sector Collectorsreceive trigger data of the Trigger Servers of all DT chambers in a 30o

sector on LVDS (Low Voltage Differential Signal) lines and send them to the DT Track Finderon high–speed optical links.

5.4.2.2 DT Track Finder

The DT Track Finder [18,20,21,22,23] connects the track segments found by the Local DTTrigger into tracks and determines their transverse momentumpT , charge and direction inη andφ. Track finding proceeds separately in the bending plane using theφ track segments and in thenon-bending plane using the patterns of hits in theθ–super-layers. In the region of overlap withthe CSC System starting from|η| > 0.9, segments from the CSC system are included in thetrack finding in the bending plane. Figure5.5gives an overview over the system. The basic unitof the DT Track Finder in the bending plane is a Sector Processor, covering a 30o sector inφ. Itcan find up to two track candidates. The track candidates found by all the Sector Processors ina wedge are sorted by the Wedge Sorter. The best two tracks per wedge are then forwarded tothe Barrel Sorter which finds the best four DT muon candidates in the barrel and forwards themto the Global Muon Trigger. The entire DT Track Finder is implemented in FPGA technology.It is located in the underground counting room.

A Sector Processorcovering a 30o sector inφ consists of four DT chambers in stations 1to 4. In order to follow tracks that leave the sector they start in, it also receives track segmentsfound in the two neighboring sectors inφ and the three neighboring sectors in the adjacentwheel that is further away from the interaction point. Sectors in wheel 0 are covered by two



Sector Receiver

Unit

ExtrapolatorUnit

4x2Track

SegmentData

Inputs from Neighbours 2 Track Addresses

for faster Sorting

Outputs toNeighbours

Eta bitsfor Matching

Track Segment Pipelineline #1

Track Segment Pipelineline #2

Selection

Selection

ParameterAssignment

UnitTwo

o

MuonsTrack

AssemblingUnit

QualitySorterUnit

Figure 5.6: Sector Processor in the DTTF.

Sector Processors each, since tracks can point in either direction inz. In total there are 72 SectorProcessors for the (5+1) wheels× 12 sectors. A Sector Processor consists of three units (seeFigure5.6): the Extrapolator Unit, the Track Assembler and the Assignment Unit.

TheExtrapolation Unitattempts to link track segment pairs in two stations by extrapolatingthe position and direction of a segment from the source station to the target station. The actualextrapolation is performed by look–up–tables which define a minimum and maximum deviation∆φ between the segments in the two stations as a function of the bend angle of the source seg-ment. If a target segment is found inside the window in∆φ, then the extrapolation is consideredsuccessful. Extrapolations are performed between stations1→ 2, 1→ 3, 1→ 4, 2→ 3, 2→ 4and4 → 3. Station 3 is not used as a source station, since the bend angle goes through a zerocrossing close to station 3 due to the magnetic field configuration. Extrapolations from station1 are performed from the two start segments in the own wheel to twelve segments in the targetstation (two each in the own sector, the neighboring sectors inφ and the neighboring sectorsin the next wheel), while extrapolations from station two are also performed starting from thetwo segments in the next wheel (same wedge) to six target segments. Extrapolations4 → 3are performed for 12 start segments to four target segments in station 3, In the outermost twowheels, track segments from CSC station ME 1/3 are included in the extrapolation scheme: theyare treated as next–wheel neighbors in station 3. It will be possible to require an additional ex-trapolation from station 2 to 1 for each1→ 2 extrapolation in case the level of punch–throughbecomes too high in the first muon station.

The Track Assemblerforms tracks out of the track segments according to the results ofthe Extrapolation Unit. It links track segments that can be connected by a series of successfulextrapolations. By default, for tracks with more than two segments, also successful intermediateextrapolations are required in order to improve protection against background. E. g. for a 1-2-3track all three extrapolations1 → 2, 2 → 3 and1 → 3 can be required. All possible trackscompatible with the successful extrapolations are checked. A priority encoder selects the besttrack (longest and highest quality) in the Sector Processor. After canceling the best track andall its sub-tracks, a second priority encoder selects the second–best track out of the remainingfound tracks.

TheAssignment Unitassigns transverse momentum, charge,φ and quality to a found track.Theφ measurementof muon tracks in the trigger is defined at station 2. If the track contains


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a segment in station 2, the segment’sφ value is used and converted to the output scale by alook–up–table. Otherwise, a1 → 2 or a4 → 2 extrapolation is performed to findφ at station2. Thetransverse momentumpT is determined using the difference ofφ in the two innermoststations of the track i. e. 1–2, 1–3, 1–4, 2–3, 2–4 or 3–4. Since lowpT tracks can be bent “back”in the transverse plane, the assignment ofpT to a given∆φ is not unique in some of the stationpairings. The bend angle in one of the stations can then be used to decide whether the track is alow–pT or a high–pT track. In the hardware, the bend angle in station 1, 2 or 4 switches betweentwo sets ofpT–look–up–tables. Thechargeis assigned using the sign of the bend angle in theinnermost station of the track (or station 4 for3→ 4 tracks). A 3 bitquality codeis assigned toeach track depending on its track class as shown in Table5.3.

Table 5.3: Quality bit assignment of the DT track finder according to track class. The digits in the trackclass names indicate the stations included in the track. In the overlap region, a digit of 4 indicates stationME1/3.

Quality code 7 6 5 4 3 2 1 0

Track Class T1234 T123 T134 T234 T12 T23 T34 NullT124 T13 T24 Track

T14

Separateη–Track Finders[24], one per 30o wedge, find tracks in the non–bending plane.Starting from the pattern of hits (7 per station) in theθ–super-layers of the inner three muonstations, theη–Track Finder looks for patterns compatible with a muon coming from the inter-action point and assigns a pre–calculatedη with 6 bit precision. The tracks are then matched tothe tracks found in the bending plane at the level of the Wedge Sorters. The matching is basedon the addresses (wheel, station, sector) of the track segments of the(r, φ)–track. A thresholdfor the goodness of match can be selected based on the number of chambers that the(r, φ)–trackand theη–track are required to have in common. If a match was found, then theη found bytheη–Track Finder will be assigned as a track parameter. If no match is found, then a coarseηvalue is calculated from the addresses (wheel, station, sector) of the(r, φ) track segments andwill be assigned as a track parameter. A tag bit indicates what type ofη–assignment was used.

5.4.3 Cathode Strip Chamber Trigger

5.4.3.1 CSC Local Trigger

The Local CSC Trigger detects charged particles crossing a CSC chamber (see Chapter4,Section4.4.2), measures their coordinates inφ and radiusr as well as the angle of passageφband determines the beam crossing from which the particles originated. The output of the LocalCSC Trigger are three–dimensional track segments, also called Local Charged Tracks (LCTs).Figure5.7 gives an overview over the system. Part of the electronics are directly mounted onthe CSC chambers while another part is located in peripheral crates on the outside of the CMSdetector. The CSC System reaches up to a pseudorapidity of|η| < 2.4, but currently it isforseen to equip only the chambers up to|η| < 2.1 with trigger electronics at LHC startup. Thecoverage of the trigger may later be restored up to|η| < 2.4.

The main purpose of the CSC anode trigger electronics is the precise determination of thebeam crossing of the origin of the muon(s) with high efficiency. Within the CSC layers, the



Port

CardSector Receiver

OPTICAL

SR SP

CSC

Muon

Sorter

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in

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chamber

3µ/Port

Card3µ /

Sector

Peripheral

crate

Counting

house

Chamber

4µ

4µ

4µ 4µ

Sector Processor

Figure 5.7: Block Diagram of the CSC Trigger.

groups of anode–wires are read out in groups of 10–15 in order to reduce channel count.An-ode Front End Boards (AFEBs)contain a combined amplifier/constant fraction discriminatorASIC to digitize the signals from the anode wires groups.Anode LCT (ALCT) boardsfind hitpatterns in the six–layer chambers that are consistent with having originated at the interactionpoint and determine the beam crossing by a multiple–layer coincidence timing technique. Dueto drift times, the signals on the anode wires can arrive with a delay of more than 50 ns. Acoincidence of two layers is required to identify the beam crossing. The existence of a muontrack is established by the coincidence of four layers within a window of 50 ns, i. e. signalsfrom the following two beam crossing intervals are included. The anode trigger electronics alsodetermine the radial or pseudorapidity (η) coordinate. A resolution of 0.025 units inη is usedinternally in the CSC Trigger. Up to two anode LCTs can be found per CSC chamber.

The primary purpose of the CSC cathode trigger electronics is to measure theφ coordinateprecisely to allow a good measurement of muon transverse momentum up to high momenta.Cathode Front End Boards (CFEBs)amplify the cathode signals and use them for both the highprecision data path and the trigger path. In the trigger path the positions of charge clustersare digitized in units of half a cathode strip by interpolating between the charges deposited onadjacent strips. If a strip charge is found to be larger than the one of the adjacent and next–to–adjacent strips a hit is assigned to the strip. The charge in the adjacent strips determines whichhalf of the strip the hit is assigned to. TheCathode LCT (CLCT)circuits decode the pattern ofcathode hits from the CFEBs and finds half–strip hit patterns in the six–layer chambers whichare consistent with high–pT muon tracks. Using all the 6 layers aφ resolution of 0.15 strips (0.2to 1.2 mm depending on the radius) can be achieved. A rough measurement of the bend angleφb (5 bits) is obtained by analyzing the pattern of hits in the six layers of half–strips.

The Trigger Motherboard (TMB)circuits, which are located on the same boards as theCLCT circuits, performs a a time coincidence of anode and cathode LCT information. If morethan one ALCT or more than one CLCT are found the TMB can optionally use RPC informationto resolve the ambiguity in associating the LCTs. Up to two LCTs per chamber are sent to theMuon Port Cards.


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Muon Port Cardsreceive the LCTs from all the TMBs of a logical CSC sector. LogicalCSC sectors cover 30o in CSC station 11 and 60o in the other stations. The best three LCTsper MPC sector and sent via optical fiber links to the CSC Track Finder in the undergroundcounting room.

5.4.3.2 CSC Track Finder

The CSC Track Finder finds muon tracks by connecting the track segments (LCTs) foundby the Local CSC Trigger. It determines the transverse momentum, charge and direction of thetracks. In contrast to the DT Track Finder, the CSC Track Finder employs a three–dimensionalroad–finding technique based on three–dimensional segments which allows to determine alltrack parameters in one step. This technique also improves background rejection. In the overlapregion of|η| < 1.2, track segments from the DT muon station MB 2/1 are included in the trackfinding. The CSC Track Finder is segmented into 60o sectors inφ, each sector being covered bya Sector Processor which can find up to three muon candidates. Sector boundaries are alignedso that one sector in the endcaps matches two sectors of the DT System. The muon candidatesfound by the 6+6 Sector Processors in the two endcaps are sorted in the CSC Muon Sorter whichdelivers the best four muon candidates found in the CSC System to the Global Muon Trigger.The CSC Track Finder is implemented in FPGA technology. It is located in the undergroundcounting room.

Sector Receiverboards receive the LCTs from the Muon Port Cards on optical fibers. EachSector Processorreceives LCTs only from its own 60o sector, six LCTs from the first stationand three each from the other stations. It also receives up to four track segments from the DTstation MB2/1. Neighbor connections are not necessary due to the limited bending of tracks inthe endcaps. The track finding proceeds in several steps as shown in Figure5.8.

TheBunch Crossing Analyzersynchronizes track segments from the DT and CSC. It option-ally allows for bunch crossing mis–identification by opening a window of more than one beamcrossing interval. It also has to hold data for one beam crossing interval because the DTTFsends the two segments from one chamber in two consecutive bunch crossings using the samelink. For a given station the best three (six in station 1) segments out ofN bunch crossingsare selected based on their quality and deviation from the current crossing. By the default allsegments from the current crossing are taken plus additional segments from the next crossing,if there is room. A tag indicates if a segment came from the current bunch crossing and isused in the Final Selection Unit to avoid triggering on the same track in two consecutive bunchcrossings.

Extrapolation Unitstest nearly all possible pairwise combinations of segments for consis-tency with a muon track coming from the vertex based on the segment coordinatesφ andη.Station combination 1–4 is excluded as it suffers from a high rate of random coincidences sincestations 1 and 4 are expected to have the highest rates. If an ambiguity is created when two LCTsare found in the same CSC chamber, then optionally all possible combinations ofφ andη can betried. The actual extrapolation is performed by anη–Road Finder and aφ–Road Finder, whichtest whether the LCTs in two stations are compatible with a track coming from the interactionpoint.

1If CSC Trigger coverage up to|η| < 2.4 is restored, then the logical sectors in station 1 will cover only 20o

in order to allow for the higher number of LCTs at high|η|, and only the best two LCTs in these sectors will beforwarded.



EU1-2

EU1-3

EU2-3

EU2-4

EU3-4

EU MB1-2

TAU1

TAU2

TAU3

FSUBXA

FIFO MUX

AU

FromBackplane

To Front panel

Bunch Crossing Analyzer

Track Assembler Units

Final Selection Unit

Extrapolation Units

Assignment

Unit

busbus

Figure 5.8: Sector Processor of the CSC Track Finder.

Track Assembly Unitsexamine the output of the Extrapolation Units and determine if anytrack segment pairs belong to the same muon. Tracks are required to have a segment in one ofthe “key” stations ME2 or ME3. This way the extrapolation results can be separated into threedifferent data streams: one for patterns keying off ME3, one for patterns keying off ME2 in theendcap region and one for patterns keying off ME2 in the DT/CSC overlap region. Only ME2is a key station in the overlap region as ME3 has no coverage and ME1 has too many segments.In each stream, each segment is tested for valid extrapolations to the other stations, so that upto three tracks can be found per stream.

The Final Selection Unitcombines the information from the three streams of the TrackAssembly Units, cancels redundant tracks and selects the best three distinct tracks. If the num-ber of common segments between two tracks exceeds a programmable threshold, the lower–rank track (shorter track) is canceled. Not all segments are required to be identical sincebremsstrahlung, for example, might cause a single muon to deliver two track segments in onestation which would then lead to a fake di–muon trigger. An additional logic detects if all thesegments come from a later bunch crossing and suppresses tracks in this case.

Assignment Unitsassign the parameters transverse momentum, charge,φ, η and quality toeach of the three tracks. ThepT assignment is based on theφ measurements in three stations ifavailable, or on theφ measurements in two stations, otherwise. The two–bit quality assigned tothe track as detailed in Table5.4 reflects the uncertainty in the measurement ofpT . A qualitycode of 3 denotes a track with the bestpT measurement possible. A quality code of 1 denotesa track where the measurement of thepT is very uncertain, if known at all. In fact, mostsuch low quality tracks in the DT/CSC overlap region have thepT word arbitrarily set to themaximum (pT = 140 GeV/c) to maintain high efficiency (at the expense of trigger rate) becausethepT resolution is so poor without a segment in MB1.

The muon charge bit is assigned using the same inputs as thepT assignment. For quality 1tracks in the overlap region, where the charge cannot be determined, it is fixed at either positiveor negative. Theφ andη coordinates are reported at station ME2 in order to facilitate matchingwith the RPC System at the Global Muon Trigger.


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Table 5.4: Quality bits of CSC Muon Candidates.

Quality code meaning

3 3 or 4 stations including ME1 or MB12 two stations, including ME1 or MB1; or three stations ME1-ME3-ME4

1 (|η| > 1.2) two stations, without ME1 (disabled by default)1 (|η| < 1.2) ME1/3-ME2/2 track in overlap region

0 no muon

TheCSC Muon Sortersorts the 36 (3×12) muon candidates found by the Sector Processorsby their rank (a combination of theirpT and quality) and selects the best four candidates in theCSC System. It also converts theφ parameter of the tracks from a localφ inside the sector to aglobal measurement.

5.4.4 Overlap Region between DT and CSC Track Finders

In the barrel-endcap overlap region muon tracks cross both DTs and and CSCs. As illus-trated in Figure4.9 this region reaches roughly from|η| = 0.9 to |η| = 1.2. In has been agreedpreviously [26] that the DT and CSC track finders each cover a part of the barrel/endcap over-lap region, with a programmable boundary in pseudorapidity between the two systems. Morerecently, it has been agreed [27] to fix the boundary between the two track finders at approxi-mately|η| = 1.04, in order to match the respective boundary between the barrel and the endcappart of the RPC System. Track segments of DT station MB1 and part of the track segmentsof CSC station ME1/3 are shared between the two track finders in order to avoid a gap in ef-ficiency. Sharing track segments from more than these two stations has been shown [27] notto increase the efficiency much further and it has been concluded that the additional hardwareexpenses would not be justified.

The sector processors of the DT Track Finder in wheel±2 include CSC station ME1/3 likea next-wheel neighbor station. Extrapolations are performed from MB1 to ME1/3 and fromMB2 to ME1/3. Extrapolations from MB3 to ME1/3 are not included, because they occur onlyin a very narrow region of pseudorapidity and including them does not produce any significantincrease in efficiency. A minimum of two segments is required to form a track: the segmentscan be either both in the barrel, or one in the barrel (in MB1 or MB2) and one in CSC stationME1/3. In order to form a track with three segments, by default all three possible extrapolationsbetween the segments are required.

The CSC Track Finder performs extrapolations from MB1 to ME2/2 and from ME1/3 toME2/2 in the overlap region. A valid track consists of at least two segments, one of which hasto be in station ME2/2.

Different solutions to prevent or to cancel out duplicated muon candidates found by boththe DT and CSC Track Finders have been studied by the author [28]. It was found that theduplication cannot be reduced sufficiently at the level of the Track Finders with a reasonableeffort in hardware. Only solutions that require additional cancel-out links between the TrackFinders can cancel out the duplication, but they would increase overall latency due to differentprocessing times in the DT and CSC Track Finders [29]. Additional solutions therefore have tobe applied at the level of the Global Muon Trigger as detailed in Section6.4.



5.4.5 Resistive Plate Chamber TriggerThe RPC Trigger is a Pattern Comparator

2T

4T

4 0

5 1

6 3

8 5

Figure 5.9: RPC Pattern Comparator Trigger.

Trigger (PACT) that finds muon candidatesby detecting the spatial and time coincidenceof hits in four RPC layers. It covers the bar-rel and endcap regions up to|η| < 2.1 (seeChapter4, Section4.4.3). The fast responseof the RPC chambers allows unambiguousbunch crossing identification. Figure5.9 il-lustrates the algorithm of pattern finding inther − φ plane: each pattern of hits on RPCstrips is associated with the charge, trans-verse momentum and quality of a muon can-didate. The basic algorithm requires hits inat least three out of four RPC layers. In thebarrel, different combinations of RPC layers are used for high–pT and low–pT muons: fourRPC layers, one in each muon station, give an optimum lever arm for the measurement of high–pT muons while the innermost four RPC layers (attached to both sides of the inner two DTchambers) are used for low–pT muons that cannot reach the outer layers. In the forward region,where muons of a given transverse momentum have a higher total momentum, the same fourRPC layers are used for the entirepT–range. Currently, the use of more than four stations in thedetection of high–pT muons in the barrel is investigated in order to increase rejection of noise.

Signals from the RPC strips are collected by front–end boards mounted directly on thechambers and transmitted by optical links to Trigger Boards in the counting room. The triggerboards contain Pattern Comparator (PAC) ASICs that cover 8 strips or 2.5o in φ in the referencestation (station two in most of the muon system). Each PAC receives inputs from 8 strips inthe reference station and more strips in the other stations, thus forming an hourglass shaped“cone” that overlaps with the cones of the neighboring PACs. Each PAC can deliver one trackcandidate. If multiple candidates are found internally, then the best one, i. e. the one of bestquality (see Table5.5) and then highestpT is selected. Due to multiple scattering and fluctu-ations in energy loss a large number of patterns corresponds to each possible direction (stripin the reference station) and transverse momentum, especially at low transverse momenta. Thenumber of patterns for low–pT muons can be reduced by OR-ing RPC strips on the PACT inputfor low–pT patterns, since the full granularity is not needed in this case. This concept resultsin a manageable number of about 80 patterns per possible track and a manageable number ofinputs to the PAC. The RPC Trigger is segmented into 33 towers inη, each covering roughly∆η = 0.1 . . . 0.2. Theη coordinate of the muon candidate is given by the tower number. Ta-ble 5.6shows the definitions of the RPC towers. Since the tower boundaries do not correspondto the chamber boundaries, strips from neighboring towers have to be OR–ed resulting in over-lap between the towers.

A ghost–busting step is performed at the output of the PACs to cancel out candidates du-plicated between neighboring PACs inφ. The remaining candidates from the 144 PACs in onetower are then sorted and the best four candidates pass through a second ghost–busting step thatcancels out candidates duplicated between neighboring towers. In a final sorting step the bestfour candidates in the barrel and the best four candidates found in the two endcaps are selectedand sent to the Global Muon Trigger.


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Table 5.5: Quality bits of the RPC Trigger for low–pT and high–pT muons.

Quality code RPC RPCpT ≥ 6 GeV/c pT < 6 GeV/c

3 4 stations 4 planes2 3 stations, missing stn. 3 or 4 -1 3 stations, missing stn. 1 -0 3 stations, missing stn. 2 3 planes

Table 5.6: Pseudorapidity scale of the RPC Trigger. The central bin is symmetric aroundη = 0. Bitcode = tower number. As in ORCA 6.2.3.

Bit code 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

|ηmax| 0.07 0.27 0.44 0.58 0.72 0.83 0.93 1.04 1.14 1.24 1.36 1.48 1.61 1.73 1.85 1.97 2.10

|ηcenter| 0 0.17 0.355 0.51 0.65 0.775 0.88 0.985 1.09 1.19 1.3 1.42 1.545 1.67 1.79 1.91 2.035

∆η 0.14 0.2 0.17 0.14 0.14 0.11 0.1 0.11 0.1 0.1 0.12 0.12 0.13 0.12 0.12 0.12 0.13

5.4.6 Backgrounds in the L1 Muon Trigger

A major challenge for the L1 Muon Trigger will be the high rate of background. Its effecton the trigger depends on the type and energy of the background particles:

Besides being the signal,Muons also constitute an undesired difficult background in the trig-ger. Generally, muons come from the following sources:

1. p− p interactions themselves

(a) decays of heavy objects like W, Z, top, Higgs, . . .

(b) b andc quark decays

(c) decays of hadrons composed of quarksu, d ands (mainly pions and kaons)

(d) punch–through of hadronic showers

2. beam losses because of the limited LHC aperture (“beam halo muons”)

3. cosmic muons

Muons of the first two types are calledprompt muonssince they are produced very closeto thep − p vertex. Only prompt high–pT muons of type1aand to some extent also oftype1bare signatures of interesting physics channels. The large rate of low-pT muons oftype1bconstitutes difficult background at level–1 which can only be reduced by a precisepT measurement in the trigger. At very lowpT , muons fromπ andK decays (type1c)are the dominant background. They are more difficult to suppress in the trigger since thepT measurement can be negatively affected for muons that arise from a decay vertex faraway from the nominal interaction point. The rates of muons reaching the muon systemare shown in Chapter8, Figure8.3 for the different muon origins. Since soft muonsfrom punch–through (case1d) of hadronic showers are difficult to distinguish from othercharged particles, they are discussed below, together with the contribution from punch-through hadrons.



Beam halo muonshave a very small probability to cause a trigger since they travel almostparallel to the beam line. They can cause track segments in the endcap region of thetrigger, however. The CSC Trigger is able to recognize these segments, tags them with atag bit and forwards them to the Global Muon Trigger for alignment purposes.

Cosmic muonsappear with a typical rate of 200 Hz/m2 at ground level. The rate is reducedby about a factor 100 at the level of the experimental cavern and therefore only gives anegligible effect in the trigger.

Hadronic showers can causepunch–through and backsplash. The thickness of the CMScalorimeters lies between 11 and 15 interaction lengths which is enough to contain mosthadronic showers caused by energetic hadrons. In some cases, particles from the tail ofthese showers may enter the muon system thus producing punch–through. When highlyenergetic hadrons hit forward detector elements, some products of the hadronic showercan be emitted at angles larger than 90o and reach the muon system. This effect is calledbacksplash. Both these effects causetrack segments, punch–through in the innermostmuon station and backsplash mostly in the outermost station of the endcaps. Separatestudies [30] have shown that trigger rates caused by punch–through and backsplash arenegligible.

Uncorrelated electrons from neutrons (“neutron background”). The very last product ofhadronic showers are thermal neutrons. They cannot cause hits in the detectors bythemselves but, when captured by a nucleus, may cause gamma–rays that convert intoelectron–positron pairs and produce signals in an active gas layer. If the capture happensin iron or hydrogen, photons with 2 to 8 MeV can be emitted resulting in electrons thatcan transverse several layers of a muon station. The thermal neutrons can travel largedistances even in dense materials and it is thus impossible to shield the detector againstthem. A dedicated study [30] showed negligible impact of neutron background on theLevel–1 CSC Trigger performance. Neutron background is also expected to have negli-gible impact on the performance of the DT Trigger, where neutron flux is expected to be10–100 times smaller. The RPC Trigger on the other hand, is sensitive to neutron back-ground in a way that depends on the intrinsic detector noise [31], and further dedicatedstudies are currently underway.

Electrons correlated with muons (“muon radiation”) are created by different processes:

• ionization (including delta ray production)• bremsstrahlung, i. e. photon emission• directe+e− pair production

The most probable effect is the production of soft delta rays which cause additional hits inthe muon station. The probability for the emission of hard electrons or photons is ratherlow but such particles can develop entire electromagnetic showers which can seriouslydisturb muon measurement. This problem occurs predominantly in the endcap regionswhere total muon momenta are large and is partly responsible for the poorpT resolutionin these regions.


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5.4.7 Performance of the Regional Muon Triggers

5.4.7.1 Efficiencies

The DT/CSC and the RPC Trigger Systems show different efficiencies inη andφ and as afunction of muonpT due to geometry, chamber properties and different trigger algorithms. Theperformance of the regional muon triggers has been simulated using the CMSIM and ORCAsimulation software described in Chapter8. The simulation includes the geometric acceptanceof the muon system, response and efficiencies of the chambers and all trigger algorithms exactlyas they will be implemented in the trigger electronics.

Figure5.10shows the efficiency of the regional muon triggers as a function of pseudora-pidity η. The efficiencies in Figures5.10-5.14are efficiencies to find a muon of any measuredpT in an event in which one muon was generated. The contribution of the different track qual-ities (see Tables5.3, 5.4and5.5) to the total efficiency is indicated. The DT System shows anefficiency above 97 % in regions covered by all four muon stations. The efficiency drops in thegaps between the barrel wheels, especially between wheel 0 and±1 around|η| = 0.25 and inthe gap between barrel and endcap muon system around|η| = 0.8. Inclusion of endcap stationME1/3 into the barrel track finder recovers efficiency up to a pseudorapidity|η| = 1.04. A shiftto lower qualities is visible in the regions of the gaps between barrel wheels.

The CSC System shows an efficiency above 97 % up to|η| < 2.4 except around|η| = 1.45,|η| = 1.65 as well as|η| = 2.1 and|η| = 2.15 where gaps between the rings of CSC chambersand partitioning of the strips inside the ME1/1 chambers cause inefficiencies. In the overlapregion, segments from barrel station MB1 are included in the CSC tracks. In order to maintainsatisfactorypT -resolution, CSC tracks are required to have a segment in station ME1 for|η| >1.2, i. e. they have to be of quality codes 2 or 3. In the overlap region, also tracks with segmentsonly in stations ME13 and ME22 are allowed (quality 0) to maintain high efficiency. Note thatthe simulation of the CSC System assumes that station ME4 is present. Efficiency is shown forthe fully equipped CSC Trigger up to|η| < 2.4. However, it has recently been decided that onlyCSCs up to|η| < 2.1 will be equipped with trigger electronics, at least for the initial years ofLHC operation. Simulation results in this thesis assume the reduced coverage except for plotsthat explicitly show a quantity as a function ofη.

The RPC System shows good efficiency up to|η| = 2.1 except in the geometric gaps be-tween the chambers, where large inefficiencies can be caused. The shape and depth of the dropsin the efficiency is different from those in the DT and CSC Systems. As for the DT and CSCTrack Finders, a shift to lower qualities is visible in the regions of the geometrical gaps.

Figure5.11and Figure5.12show the efficiencies of the regional muon triggers as a functionof the φ coordinate for the barrel (|η| < 1.04) and endcaps (|η| > 1.04), respectively. Inthe barrel the gaps between the chambers cause inefficiencies spaced at 30o intervals. Theefficiencies of DT and RPC show the same structure, the RPC efficiency showing deeper dropsin the geometrical gaps, because in the RPC System at least three out of four layers have to behit to form a track while in the DT System also two-station tracks are allowed. In the endcap the10o structure of the chambers is hardly visible in the track finding efficiency as the chambersare partly overlapping.

The efficiencies of the regional muon triggers as a function of the transverse momentumof the generated muons are shown in Figure5.13and Figure5.14 for the barrel and endcap,respectively. Above 5 GeV/c there is no dependence of the efficiencies on thepT of the muonsand all regional triggers reach a plateau with high efficiency. Figures5.15and5.16show theregion of rise of efficiency simulated with a special sample of low–pT muons. The acceptance



starts around 3 GeV/c in the barrel and around 1.5 GeV/c in the endcaps. In both cases the RPCTrigger is more efficient for muons withpT < 5 GeV/c.

5.4.7.2 Ghosts

Figure 5.17a shows the probability for ghosting (i. e. to find two muons in a sample ofsingle muons of flatpT distribution) in the regional muon triggers as a function ofη, withoutapplying apT–threshold. The DT track shows very small ghosting probability, in the CSC trackfinder ghosts come mostly from the region of1.1 < |η| < 1.6. The RPC System shows a lowrate of ghosts except in the region of1.6 < |η| < 2.2. The ghosts in this particular region arehowever reported with a lowpT of 3.5 GeV/c and less. If apT–threshold of 4 GeV/c is applied,as typically used at high luminosity, these ghosts do not play a role (see Figure5.17b ). Atlower pT thresholds which are expected to be possible at low luminosity, it might be necessaryto use other means to suppress these ghosts (see for example Chapter6, Section6.6).

5.4.7.3 Transverse Momentum Assignment and Turn-On Curves

The transverse momentum assignment at level-1 is defined at 90 % efficiency. When thetrigger is set to a certain threshold, then for muons with a transverse momentum equal to thethreshold it reaches 90 % of the plateau efficiency that is reached for muons with much higherpT . A given measuredpT value then indicates that there is a 90 % probability that the truepTwas less than the measured value and only a 10 % probability that it was more. The regionaltriggers use a common transverse momentum scale. This scale is freely programmable, but ithas to be changed in all the regional triggers at the same time. This allows to fine-tune thethresholds very precisely and to adjust to different run conditions such as low luminosity, highluminosity, heavy ions. For current simulations thepT scale has been fixed as indicated inTable5.7.

Table 5.7: CommonpT scale of the L1 Muon Trigger. The scale is in principle freely programmableand the Table indicates the current default setting.pT thresholds are defined at 90 % i. e. the trigger willbe 90 % efficient for muons withpµT ≥ pthT

Bit code 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

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Figure5.18shows the assigned transverse momentum as a function of the generated muonmomentum for all the regional triggers. The DT and CSC Track Finders can make a much finerdiscrimination of transverse momenta than the RPC Trigger. The DT Track Finder shows thesmallest probability to assign a very high momentum when a low momentum was generated.In the CSC Track Finder this probability is already much higher. Patterns in the RPC Triggershow a rather coarse binning inpT . In order to reach high efficiency, the highest possiblepTvalue (140 GeV/c) is assigned to many patterns so that there is a high probability that this valueis reported, even for low generated momenta. The RPC Trigger consequently shows the highest


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Figure 5.10: Efficiency of the DT, CSC and RPC Triggers as a function of pseudorapidityη split intocontributions from different qualities for the single muon sample described in Chapter8, Section8.2. NopT threshold applied. ORCA 6.2.3 simulation.



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Figure 5.11: Efficiency of the DT and RPC Triggers in the barrel region as a function ofφ. Obtainedusing the single muon sample described in Chapter8, Section8.2. NopT threshold applied. ORCA 6.2.3simulation.

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Figure 5.12: Efficiency of the CSC and RPC Triggers in the endcap region as a function ofφ. Obtainedusing the single muon sample described in Chapter8, Section8.2. NopT threshold applied. ORCA 6.2.3simulation.


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Figure 5.13: Efficiency of the DT and RPC Triggers in the barrel region as a function of (generated)muonpT . Obtained using the single muon sample described in Chapter8, Section8.2. No pT thresholdapplied. ORCA 6.2.3 simulation.

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Figure 5.14: Efficiency of the CSC and RPC Triggers in the endcap region as a function of (generated)muonpT . Obtained using the single muon sample described in Chapter8, Section8.2. No pT thresholdapplied. ORCA 6.2.3 simulation.



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Figure 5.15: Efficiency turn-on of the DT and RPC Triggers in the barrel region as a function of (gen-erated) muonpT . Obtained using the low-pT single muon sample described in Chapter8, Section8.2.No pT threshold applied. ORCA 6.2.3 simulation.

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Figure 5.16: Efficiency turn-on of the CSC and RPC Triggers in the endcap region as a function of (gen-erated) muonpT . Obtained using the low-pT single muon sample described in Chapter8, Section8.2.No pT threshold applied. ORCA 6.2.3 simulation.


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Figure 5.17: Ghosting probability as a function of pseudorapidity in the DT, CSC and RPC Re-gional Triggers. In Sub-figure (a), nopT threshold is applied. In Sub-figure (b) apT threshold ofptrigT ≥ 4 GeV/c is applied (note the different scale). Obtained using the single muon sample describedin Chapter8, Section8.2. ORCA 6.2.3 simulation.



trigger rates. Efficency can be lost by assigning the momentum too low. This can happenespecially in the CSC Trigger. The problem partly comes from the overlap region, where thebending is very small andpT resolution is bad. The momentum measurement can also bedisturbed by additional track segments due to muon bremsstrahlung at high pseudorapidity,where the total momentum of generated muons is large.

Figure5.19shows the RMS of thepT resolution as a function of pseudorapidity, separatelyfor the different qualities of muon candidates. The DT Track Finder shows the best resolutionand errors are large mainly in the lowest quality category (tracks with only stations 3 and 4) andalso for quality 2 at certain pseudorapidities. In the CSC Track Finder, quality 1, which is onlyenabled in the overlap region, shows the highest errors. Candidates of quality 2 show high errorsin the overlap region and around|η| = 1.4 and|η| = 2.0. Quality 3 candidates show rather goodpT resolution, outside the overlap region. In the RPC Trigger, the worstpT resolution is foundin the second quality category (quality 1). Tower 6 in the barrel and towers 9-12 in the endcapshow large errors for all quality categories.

Figure5.20shows the 1/pT residuals for the regional triggers split into barrel, overlap andendcap region. The distributions are close to Gaussian only for the DT Trigger. In the CSC andeven more in the RPC trigger, the effect of assigning the highestpT value to a large fraction ofevents is visible as an abrupt step. The mean of the distributions is shifted to the left due to the90 % efficiency definition of the L1pT scale. Tails on the right-hand side of the distribution, asseen for the CSC Trigger, indicate thatpT ’s are measured too low. The very poorpT resolutionof the CSC Trigger in the overlap region is evident. It has to be noted that the effect of largelyover-estimating thepT is diminished in the 1/pT representation.

Figures5.21a-d show the turn-on curves of the regional triggers as a function of the gen-erated muon-pT for several trigger thresholds for the barrel, overlap and endcap regions. The90 % definition of thepT is evident: the turn-on curves reach approximately 90 % of the plateauefficiency at the nominal generatedpT . The DT and CSC Triggers show sharper turn–on be-havior due to their superiorpT resolution. The DT and CSC Triggers in the barrel and endcapreach plateau efficiencies of around 95 %. In the RPC Trigger the plateau efficiency lies around85 % in the barrel and around 92 % in the endcaps. In the overlap region, the DT and RPCtriggers reach a plateau of about 90 %. In several regions the plateau efficiency decreases whenhigher trigger thresholds are applied. This effect is most pronounced in the overlap region ofthe CSC Trigger where thepT resolution is very poor due to limited bending of the tracks. Tosome extent, the same effect is visible also in the endcap region of the CSC Trigger where it hasbeen found to be caused by additional hits due to bremsstrahlung and pair production [30]. Theeffect also occurs in the barrel region on the DT and RPC Triggers. In the DT Trigger, it canbe traced to candidates of quality 0 (i. e. tracks with segments only in stations 3 and 4) whichhave the poorestpT–resolution. In the RPC Trigger, the effect occurs mainly in the geometricalgaps between barrel wheels where in some cases the low–pT assignment method is used for ahigh–pT track because hits in the outermost RPC layers are missing.


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Figure 5.18: Reconstructed transverse momentumpT versus generated transverse momentum for theDT, CSC and RPC Triggers. Obtained using the single muon sample described in Chapter8, Section8.2.ORCA 6.2.3 simulation.



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Figure 5.19: RMS of thepT resolution of the DT, CSC and RPC Trigger as a function of pseudorapidityfor the different candidate qualities. Obtained using the single muon sample described in Chapter8,Section8.2. ORCA 6.2.3 simulation.


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gen

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Figure 5.20: 1/pT resolution of the DT, CSC and RPC Trigger for the barrel, overlap and endcapregions. The solid lines represent adapted Gaussian distributions. Obtained using the single muon sampledescribed in Chapter8, Section8.2. ORCA 6.2.3 simulation.



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Figure 5.21: Turn-on curves of the DT, CSC and RPC Trigger for the barrel, overlap and endcap regions.Obtained using the single muon sample described in Chapter8, Section8.2. ORCA 6.2.3 simulation.


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Figure 5.22: Single-muon trigger rates as a function of trigger threshold at low luminosity (L = 2 ×1033 cm−2s−1) in the barrel, endcap and overlap region for the DT, CSC and RPC Systems. Obtainedusing the minimum bias sample described in Chapter8, Section8.4. ORCA 6.2.3 simulation.

5.4.7.4 Trigger Rates

Figure5.22shows the single–muon trigger rates as a function of trigger threshold at lowluminosity (L = 2 × 1033 cm−2s−1) in the barrel, endcap and overlap regions for the threeregional triggers. The standalone performance of each of the regional triggers is shown. Inthe endcaps, the generated rates in the lowestpT -bins are much higher, since a lower generatorthreshold was used as shown in Table8.3. Trigger rates in the endcaps are almost an order ofmagnitude higher than in the barrel, even at higherpT thresholds, where generated rates aresimilar. This is a result of the lowerpT resolution in the endcaps and the higher rate of low–pTmuons which have a certain probability to cause a high–pT trigger.

The effect of thepT assignment is also evident when the regional triggers are compared: athigherpT thresholds the DT and CSC Triggers show a lower trigger rate than the RPC System,except in the overlap region where the CSC System shows extremely high rates.

Especially in the endcaps and overlap region, standalone trigger rates are too high: thesingle-muon trigger threshold would have to be set very high in oder to reach trigger ratescompatible with the capabilities of the data acquisition system. A rate reduction by the GlobalMuon Trigger is therefore needed.



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Figure 5.23: Resolution of theφ assignment of the DT Track Finder and RPC Trigger in the barrel region|η| < 1.04. Obtained using the single muon sample described in Chapter8, Section8.2. ORCA 6.2.3simulation.

5.4.7.5 Resolution inη and φ

The pseudorapidityη and azimuthalφ coordinate of the muon candidates are defined atstation 2 in the muon system. This definition is used to avoid loss of precision due to propagationto a different surface or the vertex. As a reference in the resolution plots, the position of thegenerated muon track at a cylinder going through the center of barrel station 2 or a disk goingthrough the center of endcap station 2, is used. These positions are obtained by a propagationfrom the closest hit to the surface using GEANE [32]. Theφ resolutions of the DT and barrelRPC as well as the CSC and forward RPC Triggers are shown in Figure5.23 and the rightcolumn of Figure5.25, respectively. For all the regional triggers the resolution is given bythe agreed binning of 2.5o. DT and CSC Triggers work with higher resolution, internally, butconvert to lower resolution at the output. Some precision is lost in the conversion of theφcoordinate of the CSC Trigger since not all bits of the internal representation are used.

Theη resolution of the RPC Trigger is given by the tower sizes as shown in Table5.6. Inthe endcaps, the CSC Trigger has a finer resolution than the RPC trigger (see the left columnof Figure5.25). In the DT Trigger theη resolution depends on whether the fine or the coarseassignment method was used (see Section5.4.2.2). With the fine assignment method, goodresolution can be achieved over the whole barrel as illustrated in the top row of Figure5.24.With the coarse method (middle row in the Figure), the resolution is poor and depends onpseudorapidity. Theη-resolution of the RPC Trigger (bottom row in the Figure) is generallybetter than the one of the coarse assignment of the DT but worse than the one of the fine DTη–assignment.


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Figure 5.24: Resolution of theη assignment of the DT and RPC Trigger in the barrel|η| < 1.04. In theDT Trigger the resolution depends on the assignment method: “fine” assignment by theη-Track Finderresults in constant resolution and a linear scale; “coarse” assignment based on theφ-segments resultsin large variations in resolution. The variations in the resolution of the RPC Trigger are given by thestructure of trigger towers. Obtained using the single muon sample described in Chapter8, Section8.2.ORCA 6.2.3 simulation.



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Figure 5.25: Resolution of theη andφ assignment of the CSC Track Finder and RPC Trigger in theendcap region. Obtained using the single muon sample described in Chapter8, Section8.2. ORCA 6.2.3simulation.

5.4.7.6 Charge Assignment

Figure5.26shows the probability for wrong charge (or muon sign) assignment in the DT,CSC and RPC Triggers as a function of pseudorapidity and as a function of transverse mo-mentum. The DT Trigger shows good charge assignment over the entire barrel, independentof the transverse momentum of the generated muons. The CSC Trigger shows high proba-bility for wrong charge assignment in the overlap region, where bending is small and at veryhigh |η|. The probability for wrong charge assignment increases with higherpT when tracksbecome too straight to determine their bending direction. In this case the assignment defaultsto positive charge in the CSC Trigger which explains why measuring a positive charge is moreprobable. The RPC Trigger shows good charge assignment for transverse momenta below about20 GeV/c. Above that, the probability for wrong assignment becomes high since in the highest-pT patterns the charge cannot be determined. In case of the RPC Trigger the charge in this casedefaults to negative. Wrong charge assignment in the RPC Trigger occurs over the entire rangeof pseudorapidity, but is higher in regions where for geometrical reasons less RPC planes arehit.


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Figure 5.26: Distribution of events with wrong charge assignment in the DT, CSC and RPC Triggers.The left column shows the probability for wrong charge assignment versus pseudorapidity, the rightcolumn shows the probability for wrong charge assignment versus transverse momentumpT . Note thedifferent scale in the DT System. Obtained using the single muon sample described in Chapter8, Sec-tion 8.2. ORCA 6.2.3 simulation.



5.4.8 Summary of Regional Muon Trigger Outputs to the Global MuonTrigger

Table5.8 summarizes the output of the three regional muon triggers to the Global MuonTrigger. Common scales are used forpT (see Table5.7) andφ. Bin 0 in theφ scale ranges fromφ = 0o to φ = 2.5o. The pseudorapidity scales are different in the three regional triggers. TheCSC trigger uses a linear scale as indicated in Table5.8. The most–significant bit is a pseudo-sign indicating positive (0) or negative (1) endcap. The RPC Trigger gives the trigger towernumber as a measurement of the pseudorapidityη (see Table5.6). The DT Trigger uses a linearscale as indicated in Table5.8. The bin number is coded in 2’s complement notation. Bin 0 ofthe scale ranges fromη = 0 to η = 0.040625. An additional fine/coarse bit indicates whetherthe pseudorapidity was assigned using the fine or the coarse method (see Section5.4.2.2). Thecharge is coded as 1 bit (0=positive) and an additional bit indicating if the charge assignment isvalid.

In addition to the data bits, several other bits are sent for synchronization purposes. Theseare the lowest three bits of the bunch crossing ID, a bit indicating bunch crossing zero, a syn-chronization error bit and the clock. All regional muon triggers transfer the muon candidatedata to the GMT using parallel Low Voltage Differential Signals (LVDS).

Table 5.8: Output of the Regional Muon Triggers to the Global Muon Trigger.

Parameter DT (4x) CSC (4x) RPC (8x)scale & range bits scale & range bits scale & range bits

pT common scale 5 common scale 5 common scale 5

charge positive=0 1 positive=0 1 positive=0 1

charge valid always 1 1 valid=1 1 valid=1 1

φ 0..143, 2.5o bins 8 0..143, 2.5o bins 8 0..143, 2.5o bins 8

η |η| < 1.3 6 0.9 < |η| < 2.5 5+1 |η| < 2.1 6∆η = 0.040625 bins of∆η = 0.05 code = tower nr.

ηfine/coarse fine = 1 1 halo=1 1 - -Beam Halo

Quality 0..7 see Table5.3 3 0..3 see Table5.4 3 0..3 see Table5.5 3


H. Sakulin

Chapter 6

Global Muon Trigger Design

66 6. Global Muon Trigger Design

This chapter deals with the design of the Global Muon Trigger (GMT) algorithms. Start-ing from the functional requirements, all the logical functions of the Global Muon Triggerare defined. The details of these functions are derived from simulation studies. Many of theGMT functions are implemented as memory–based look–up–tables. Default setting for theselook–up–tables are discussed along with strategies on how to optimize them. The detailedhardware–implementation of the Global Muon Trigger is discussed in Chapter7 while the sim-ulated performance is presented in Chapter9.

6.1 Requirements

The CMS Level-1 Muon Trigger and the advantages of having three independent regionaltriggers have been described in Chapter5, Section5.4. The DT and CSC Track Finders de-liver up to four muon candidates for the barrel and endcap regions, respectively, while the RPCTrigger delivers four candidates for the barrel and four for the endcaps. The Global MuonTrigger [33,34,18] combines the muon candidates found by the Regional Muon Triggers andforwards the best four candidates to the Global Trigger. It has to perform the following func-tions:

• Process trigger data from every bunch crossing with a maximum latency of 14 bunchcrossings (350 ns) including the time for receiving and sending data. This limits thealgorithms of the GMT to very simple arithmetic and logic functions and to functionsthat can be implemented in memory–based look–up–tables.

• Process trigger data from every bunch crossing without dead-time using pipelined logic.

• Synchronize the muon candidates found by the three Regional Muon Triggers to the LHCorbit and to each other.

• Combine the muon candidates found by two complementary systems in a “smart” wayso that efficiency is increased and candidates that are likely to be ghosts or fake triggerscan be identified: candidates found by both regional triggers are by default accepted re-gardless of their quality bits. Unconfirmed candidates of low quality can be tagged forexclusion from single- and di-muon triggers in certain pseudorapidity regions. Specificquality criteria can be applied depending on detector types, detector regions and trans-verse momenta. This makes it possible to achieve high overall efficiency, a smoothingeffect in problematic regions such as cracks and a powerful background rejection. Thealgorithm also helps to reduce ghosts that arise in the regional muon triggers.

• In the barrel/endcap overlap region, cancel out muon candidates which are found by boththe DT and the CSC Track Finder. These candidates would otherwise cause a large ghostrate at the output of the GMT.

• Introduce only a negligible additional ghosting probability due to failure to match twomeasurements of the same physical muon. The overall ghosting probability at the outputof the GMT roughly has to be less than 0.5 % so that the di–muon trigger rate is notdominated by triggers from ghosts (also see Chapter5, Section5.4.1).


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6.1 Requirements 67

• For candidates measured by two Regional Triggers, improve the assignment of param-eters, most importantly of thepT , in order to improve control of the trigger rate whilekeeping the efficiency high.

• Convertη measurements to a common scale. Optionally project theφmeasurements fromthe muon system to the vertex.

• Receive Quiet bits and Minimum Ionizing Particle (MIP) bits, denoting calorimetric iso-lation and confirmation from the Global Calorimeter Trigger and synchronize them to theinput from the Muon Triggers.

• Project the muon candidates back to the calorimeter and vertex in order to find the corre-sponding MIP and Quit bits. Append two bits to each muon candidate denoting calorimet-ric isolation and confirmation. The MIP bit is set if the calorimeter energy is consistentwith the passage of a minimum ionizing particle, the ISO bit is set if an energy thresholdin the calorimeter trigger towers surrounding the muon is not exceeded. Both bits areused in the GT to suppress background and to improve selectivity.

• Rank the combined and the unconfirmed muon candidates so that the best four candidatesin every crossing can be determined for the whole detector and sent to the Global Trigger.

• Forward accelerator muon candidates (caused by “beam halo muons”) from the CSCTrigger to the GT to be used in a separate trigger stream for alignment purposes.

• Send all the received input muon and calorimeter data and the output muon data fromthree consecutive bunch crossings to the CMS Data Acquisition System, after a bunchcrossing was triggered.

6.1.1 Input Requirements

The GMT expects input data from the regional muon trigger systems to fulfill the followingcriteria:

Bunch crossing corrected data:The GMT requires the bunch crossing assignment or correc-tion to be already done since it does not correct data in time and matches only candidatesfrom the same bunch crossing. It does, however, synchronize the different latency sub-systems to each other.

Ghost suppression:The GMT checks only if muons from the RPC and DT/CSC systems arerelated to each other and performs cancel-out between the DT and CSC System in thebarrel-endcap overlap region. Checks for identical muons (ghosts) found two or moretimes within the same regional trigger system are not made. Some ghost suppressionis however achieved by canceling out muons based on their quality bits if they are notconfirmed by the complementary system (see Section6.6).

Identical reference frames: All input data have to use the same coordinate system and scalefor φ and the same definition and scale forpT to save latency and to avoid loss of preci-sion due to conversion. This does not mean that thepT scale cannot be adapted accordingto changing physics requirements, it only requires all systems to change their scales si-multaneously. Heavy ion and initial low luminosity proton-proton runs will in general



require a finer scale for the lower momentum range than high luminosity discovery runs.For theη -coordinate a scale specific to a regional trigger has advantages over a commonscale: precision loss due to conversion is avoided and certain actions such as tagging ofunconfirmed muons for exclusion can be performed forη-units of the regional trigger.

Sharp η boundary in the RPC Trigger: The GMT expects a sharp boundary inη betweenRPC candidates that belong to the barrel and RPC candidates that belong to the endcaps.This is necessary to ensure that an RPC barrel candidate can always be matched with aDT candidate and an RPC forward candidate can always be matched with a CSC can-didate. This requirement is however slightly loosened if some duplication between theDT and CSC Track Finders is allowed: the GMT can then check whether the DT or theCSC measurement of the muon is confirmed by the RPC Trigger and can cancel out theunconfirmed measurement (see Section6.4).

6.2 System Overview

Figure6.1 shows a block diagram of the Global Muon Trigger. DT, CSC and RPC muoncandidates are received from the Regional Triggers and synchronized to each other and to theLHC clock in the Input Synchronization Units. The muon candidates are then processed sepa-rately for the barrel and for the endcap region: Matching Units match the candidates of the twocomplementary Regional Triggers and find pairs of corresponding measurements. In parallelthe parameters of the muon candidates are converted to a common output scale and a rank isassigned for each candidate. According to the result of the Matching Units the parameters ofcorresponding candidates are then merged in Muon Merger Units. The first sorter stage receivesfour muon candidates from the Muon Merger Unit: these are either matched and merged can-didates or unconfirmed DT (CSC) muons that are passed through. Furthermore the first sorterstage directly receives up to four unconfirmed RPC candidates. The candidates are sorted byrank and the best four muon candidates in the barrel and in the best four in the endcaps are senton to the second sorter stage where the best four muons candidates in the whole detector aredetermined. Muons of the DT and CSC Systems are compared in a cancel–out unit in order toto find duplicates measurements in the barrel/endcap overlap region. Duplicated measurementsare then suppressed in the first sorter stage. Also, duplications between candidates from the DTand forward RPC System and between CSC and barrel RPC System are detected and canceledout.

The GMT also receives 252 MIP and 252 Quiet bits from the Global Calorimeter Triggerand synchronizes them to the muon data. Parallel to the matching and rank assignment, themuon candidates are projected to the calorimeter and vertex in order to assign a MIP and anIsolation bit to each muon candidate. The MIP and ISO bits are then passed through the mergerand sorters along with the other muon parameters.

6.3 Matching Unit

A Matching Unit compares the muon candidates found by two of the Regional Muon Trig-gers in the same detector region in order to find pairwise matching measurements for eachphysical muon. It can receive up to four muon candidates from each of the two Regional Trig-gers. For each pairing of muon candidates it defines a match quality which increases with the


H. Sakulin

6.3 Matching Unit 69

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Figure 6.1: Block Diagram of the GMT Algorithm.



Match logic

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Figure 6.2: GMT Matching Unit (barrel).

proximity of the candidates in space. The coordinates of the muon candidates are defined atstation two in the muon system in order to reduce loss of precision due to propagation to an-other surface. Pairings of maximum match quality are then found in a pair logic. The output isa pair matrix which indicates for each of the possible pairings of muon candidates from the twosystems whether they form a pair of matched measurements of the same physical muon. Thereare six Matching Units in the GMT: the Barrel Matching Unit matches DT and RPC candidates,the Forward Matching Unit matches CSC and RPC muons and four Overlap Matching Unitsare used to cancel out ghosts in the overlap region as discussed in Section6.4.

6.3.1 Default Matching

As illustrated in Figure6.2 the Matching Unit first evaluates the difference of theφ andηmeasurements for each possible pairing of muon candidates. The difference inφ is obtainedusing a subtracter which finds the∆φ modulo 144 (the inputφ scale uses 144 counts). Due tothe relatively coarse binning of 2.5o, the difference∆φ can only assume a few different values,as shown in the first column of Figure6.3. Three bits are sufficient to code|∆φ|. The differencein η is obtained using look–up–tables since theη–scales of the regional triggers can be non–linear. This also allows to make the∆η calculation dependent onη (see Section6.3.2). All 6bits of bothη measurements plus the fine/coarse bit in case of the DT, have to be put into theLUT. In the Matching Units of the overlap region, which cover only a small region inη, theηmeasurements are converted to 3–bit resolution before finding∆η with a LUT.

As shown in the second column of Figure6.3 (solid histogram),∆η of corresponding can-didates extends over a larger range since scales are non-linear and especially in the barrel theresolution of theη measurement is not constant. Up to four bits are used to code|∆η|. Thedashed histogram in the Figure shows∆η according to a 4–bit scale. Based on the∆η and∆φa match quality is assigned which increases with the spatial proximity of the two measurementsof a possible pairing. The assignment is implemented in a look–up–table with a default pro-gramming that depends on a weighted distance∆r =

√wη(∆η)2 + wφ(∆φ)2, with weightswη

andwφ as parameters. The match qualityMQ is then given by

MQ =

{MQmax(1− ∆r

∆rmax) : ∆r ≤ ∆rmax0 : ∆r > ∆rmax

, (6.1)

where the parameter∆rmax is the size of the matching window andMQmax is the maximalvalue of the match quality scale, by defaultMQmax = 64. The matching window should be as


H. Sakulin

6.3 Matching Unit 71

small as possible in order to avoid matching with the measurement of a different real muon ora possible fake muon candidate. On the other hand the window has to be large enough so thattwo measurements of the same muon can be matched with high efficiency. Failure to match thetwo measurements of the same muon may cause a fake di–muon trigger.

Table6.1lists the default weights and matching window sizes currently used in trigger sim-ulations. The resulting match quality distributions are shown in the third column of Figure6.3.Since matching with fake candidates does not seem to be a problem from current simulationresults, the window sizes have been chosen large enough so that the matching succeeds for allthe events in the single muon sample described in Chapter8, Section8.2. If rates of fake candi-dates should turn out to be higher than anticipated, smaller matching windows can be chosen inthe future. For example, changing the minimum∆φ window to only one count (±2.5o) insteadof two counts would cause the matching to fail in approximately 0.03 % of the events. Theresulting ghosting probability would even be smaller than 0.03 % since in these events usuallyat least one of the input candidates is of low quality and might therefore be suppressed (seeSection6.5). An improved matching method with variable window size as described in thefollowing section can further reduce the size of the matching windows.

Table 6.1: Default weights and matching window size∆rmax as well as corresponding minimum win-dow size inφ andη.

Matching Unit weightwη weightwφ ∆rmax |∆φmin| |∆ηmin|Barrel 0.113 1.0 0.124 0.0873 rad (5o) 0.26Endcap 0.39 1.0 0.124 0.0873 rad (5o) 0.14Overlap cancel-out 0.39 1.0 0.124 0.0873 rad (5o) 0.14

6.3.2 Improved Matching for Variable η-Bin Sizes

Theη-scales of the DT and RPC Trigger are non–linear and therefore the resolution of theη-measurement depends onη itself. When the coarseη-assignment is used in the Regional DTTrigger, the resolution ofη can vary by up to a factor 10 between different bins (see Figure5.24).Since the calculation of∆η in the matching units is implemented in a LUT, it is possible to takeinto account these variations.

A simple approach would be to take the difference between the closest–in–η bin edgesinstead of the difference between the bin centers as measure for the difference inη as illustratedin Figure6.4. A corrected difference∆η′ can then be defined as

|∆η′| ={|∆η| − (∆a

2+ ∆b

2) : |∆η| > ∆a

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+ ∆b2

, (6.2)

where∆a and∆b are the bin widths of the two bins to be compared. The bin width of a bin canbe obtained from an analysis of theη distribution of muon tracks assigned to the bin and is givenby ∆a = r.m.s.×

√12. To improve the accuracy, for∆η the difference between the centers of

the two distributions of generated muons assigned to the two bins can be used rather than thedifference between the nominal bin centers. When experimental data will be available, the fullyreconstructed muons can be used to calibrate the triggerη–scales and matching windows.

The ∆η-LUT and Match Quality LUT can then be programmed to use the corrected∆η′.Figure6.5 shows the distributions of∆η (between the centers of the distributions assigned to



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Figure 6.3: ∆φ, ∆η and match quality distribution in the barrel, forward and overlap (DT/CSC) matcherunits for the single muon sample described in Chapter8, Section8.2. ORCA 6.2.3 simulation.


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6.4 Suppression of Ghosts in the Barrel/Endcap Overlap Region 73

∆a ∆b

∆η

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Figure 6.4: Definition of the correctedη difference∆η′.

the bins) and corrected∆η′ for DT/RPC matching in the first and second column. The rows inthe Figure show the respective distributions for all DT/RPC matches, matches with a DT can-didate with fineη-assignment and matches with a DT candidate with coarseη-assignment. Thedistributions of∆η′ are of course much narrower than the distributions of∆η. Also, the∆η′

distributions show the same shape for fine and coarse DTη-assignment while the∆η distribu-tion for the coarse DTη-assignment shows larger tails. The third column shows the effective∆η window between the centers of the distributions assigned to the bins, assuming a constantwindow of |∆η′| ≤ 0.1. The effective∆η-window varies between approximately 0.15 and 0.23in the case of fine DT candidates and can increase up to 0.4 in case of coarse DT candidates. Incomparison, the minimum∆η window in the default programming of the Barrel Matching Unithas to be 0.26 to achieve the same matching efficiency (see Table6.1).

6.3.3 Pair Logic

The Pair Logic [35] proceeds in three steps as illustrated in Figure6.6: first, for each elementin the matrix of match qualities it checks whether it is the maximum in its row and in its column.In case of equal match qualities, the match quality of the pairing with lower indices is consideredhigher in order to favor a match with a candidate of higher rank (the input muon candidates areordered by rank). This is important if a regional trigger reports a muon and a ghost at exactlythe same position. The ghost is in most cases of lowerpT and rank to that the real muon ispreferred in the matching. If a pairing has the maximum match quality in its row and column,the two measurements are considered matched. In a second step, matched candidates from bothSystems are then excluded and the procedure of finding maximum match qualities is repeatedtaking into account only the remaining candidates so that further matches can be found. A pairmatrix then indicates for each possible pairing of measurements from the two trigger systems ifthey belong to the same physical muon.

6.4 Suppression of Ghosts in the Barrel/Endcap Overlap Re-gion

As mentioned earlier, it is important to keep the probability for ghosting at the output of theGMT very low. Ideally it should be well below the upper limit of 0.5 %. In the barrel/endcapoverlap region, ghosts can be categorized as follows:

• muon tracks reported by both the DT and the CSC Track Finders;• pairs of muon candidates reported by the RPC and DT/CSC System that cannot be

matched in the GMT because one candidate is reported in the barrel and the other inthe endcap;• ghosts created within the DT, CSC or RPC System.



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H. Sakulin


DT

RPC 120 5 0100 8 0

07 1 000 0 0

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Figure 6.6: Pair Logic in the GMT Matching Unit (example for barrel).

The first two categories of duplication are dealt with in the two following sections. Theyare more dangerous than the ghosts of category 3 since candidates are duplicated independentof their pT while the ghosts inside a regional trigger system usually are of lowpT and can bereduced by applying a higher trigger threshold. The last category of ghosts is not canceled outin the Global Muon Trigger since such a cancel-out could be dangerous to signals from twoclose muons. Such a cancel-out has to be performed by the Regional Triggers which have moreand finer information about the segments/hits contributing to the concerned candidates. Butaccording to ORCA simulations, this ghost category plays a less important role at higherpTthresholds.

6.4.1 Cancellation of DT/CSC Ghosts

In the barrel/endcap overlap region muon tracks may cross DT and CSC chambers. The DTand CSC Track Finders share segments from barrel station MB2 and endcap station ME1/3 inorder to improve efficiency and hence may both report the same track. From the GMT pointof view it would be desirable that these duplicated tracks are already prevented or canceled outat the level of the track finders. Moreover, it would be desirable to have a sharp boundary inη separating the barrel and endcap regions. As explained in Chapter5, Section5.4.4, it wasfound that none of the cancel-out schemes that can be implemented at the level of the trackfinders with a reasonable effort in hardware can reduce the duplication to the required level andprovide the required sharp boundary. Figure6.8a shows the efficiency and ghosts at the level ofthe GMT in the overlap region after applying the best possible scheme at the levels of the trackfinders. The remaining ghosting probability of around 4 % in the region of0.9 < η ≤ 1.15 isclearly too high. Additional measures have therefore to be applied to cancel out this duplicationat the level of the GMT:

Requiring confirmation by the RPC System in the overlap region can almost completelyeliminate the duplication between the DT and CSC Systems as illustrated in Figure6.8b.However, it limits the maximum achievable efficiency to that of the RPC System. Itmakes the DT/CSC System depend on the RPC System and thereby compromises thecomplementarity of the two systems. A more robust solution that can cancel the dupli-cation between the DT and CSC Track Finders without the help of the RPC System wastherefore investigated.

A DT/CSC cancel-out unit in the Global Muon Trigger was devised in order to perform thecancel-out of duplication without the help of the RPC System. Figure6.7 illustrates itsimplementation: DT and CSC muon candidates are compared using the same logic as



in the Matching Units explained earlier. A programmable cancel-decision logic then re-ceives the results of these comparisons plus the results of the barrel and forward MatchingUnits. Based on these results it decides whether to cancel a DT or a CSC muon. In thehardware, two copies of the DT/CSC cancel-out unit exist, one in the barrel processingchain, responsible for canceling DT muons and one in the endcap chain, responsible forcanceling CSC muons. Tables6.2 and6.3 show the default programming of the canceldecision logic in the barrel and endcap processing chains, respectively. If a muon is re-ported by both the DT and CSC Track Finders, but only once in the RPC System, thenthe DT/CSC candidate that is not confirmed is canceled and the matched pair in the otherprocessing chain is kept. In order not to cancel out real di-muons, the default program-ming does not cancel out duplicated candidates if they both are matched with an RPCcandidate . This relies on the fact that the RPC trigger does not have a ghosting problemin the overlap region. In case of an unforeseen ghosting problem in the RPC System,the programming of the Cancel-Decision-Unit could be changed to always cancel a du-plicated DT/CSC candidate. The DT/CSC System could then even be used to cancel outghosts in the RPC System by requiring that RPC candidates are matched with a DT/CSCcandidate.

Figure6.8c illustrates the efficiency and ghosts at the output of the GMT after cancel-outwith the DT/CSC cancel-out unit. The efficiency remains as high as without cancel-outwhile the ghosts are reduced to about 0.3 %, which results in a tolerable contribution tothe di-muon trigger rates. The remaining ghosts belong to the second category and arediscussed in the following section.

DT/CSC cancel-out unit

η1

η2

φ1

φ2

SUB

(mod

144)

LUTPair

Logic16x

16x 16x 1x3

8

8

4 4

3

3

6

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1

116x

4

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4

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4

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Decision

Logic

1x

4

3

CSC η/φ CSC-is-matched

with RPC

cancel-DT1

MQ

LUT

from endcap GMT Logic FPGA

inside barrel GMT Logic FPGA

DT η/φ

CSC empty

DT empty

4

cancel-RPC

Figure 6.7: Overlap Region DT/CSC Cancel-Out Unit, inside the GMT Barrel Logic FPGA. TheDT/CSC cancel-out unit in the GMT Endcap Logic FPGA and the DT/fRPC and CSC/bRPC cancel-outunits use the same logic. The space coordinates of all DT and CSC candidates are compared to findduplicated candidates. This information together with information whether the DT and CSC candidateswere matched with an RPC candidate is then sent to the Cancel-Decision Unit, which decides whetherto cancel a duplicated candidate.


H. Sakulin


Table 6.2: Default programming of the Cancel Decision Logic for the barrel part of the Global MuonTrigger.

inputs output

DT match CSC match DT match cancel brlRPC cancel DT Comment

w. CSC w. RPC w. RPC (optional)

0 x x 0 0 no DT/CSC match

1 0 0 0 0 cancel CSC


1 1 0 0 1 cancel DT

1 1 1 0 0 no cancellation

Table 6.3: Default programming of the Cancel Decision Logic for the endcap part of the Global MuonTrigger.

inputs output

CSC match DT match CSC match cancel fwdRPC cancel CSC Comment

w. DT w. RPC w. RPC (optional)

0 x x 0 0 no DT/CSC match


1 0 1 0 0 cancel DT


1 1 1 0 0 no cancellation

6.4.2 Cancellation of DT/forward-RPC and CSC/barrel-RPC Ghosts

The GMT treats barrel and endcaps in separate processing chains. If a candidate is foundin both chains and not canceled out, then it can be reported twice by the GMT. The DT/CSCcancel-out unit already cancels a large part of this type of duplication: if a muon is reportedby both the DT and CSC Track Finders, but only once in the RPC System, then it cancels theDT/CSC candidate that is not confirmed and keeps the matched pair in the other processingchain. Some duplication remains from muons that are found in one of the processing chainsonly by the DT or only by the CSC and in the other processing chain by the RPC System. Thisremaining duplication is of the same order of magnitude as the duplication inside the regionaltrigger systems. However, as mentioned before, it is more dangerous since candidates are du-plicated independent of theirpT while the ghosts inside a regional trigger system usually are oflow pT and can be reduced by applying a higher trigger threshold. The remaining duplicationin the overlap region can be reduced by the following methods:

Fine-tuning the η-boundary between the DT and CSC Systemto better match the respec-tive boundary in the RPC System. The exact position of the boundary naturally has alarge effect on this type of ghosting and fine-tuning of the boundary can largely reduce it.A small probability for ghosting remains, however, due to the geometry of the muon sys-tem and because of the different methods to assignη in the DT and CSC Track Finders.It was found in [28] that a better reduction of ghosts can be achieved by the followingmethod.



Deliberately allowing duplication between the DT and CSC Track Finders in a narrow re-gion around the boundary in the overlap region results in finding most DT/CSC candidatesin this region in both processing chains of the GMT1. The DT/CSC Cancel-Out Unit thencan better perform the job of canceling the candidate that is not confirmed by an RPC can-didate and keeping the confirmed candidate in the other processing chain. Duplication atthe GMT only remains if despite the allowed duplication at track finder level, a candi-date is still only found by one of the track finders and by the RPC System in the otherprocessing chain.

Two additional Cancel-Out units in the GMT responsible for canceling out duplication be-tween the DT and forward RPC and between the CSC and barrel RPC Systems can com-pletely cancel out this category of ghosts. This method requires additional hardware butis the most effective at canceling this kind of ghosts. It is also the safest method withrespect to uncertainties in the simulation of the detailed behavior of the regional muontriggers at theη-boundary. As illustrated in Figure6.8d, high efficiency is kept whileremoving almost all ghosting in the overlap region. The additional cancel-out units aretherefore implemented by default.

The implementation of these two additional cancel-out units is identical to the one of theDT/CSC Cancel-Out Unit. The additional cancel-out links are OR-ed with the ones of theDT/CSC Cancel-Out Unit. Tables6.4 and6.5 show the default programming of the cancel-decision logic for the CSC/barrelRPC and the DT/forwardRPC cancel-out units, respectively.

Table 6.4: Default programming of the CSC/barrelRPC Cancel Decision Logic (in the barrel processingchain of the Global Muon Trigger).

inputs output

CSC match CSC match brlRPC cancel cancel Comment

w. brlRPC w. fwdRPC match w. DT brlRPC CSC

0 x x 0 0 no CSC/brlRPC match


1 0 1 0 0 leave cancellation to DT/CSC COU

1 1 x 0 0 no cancellation

Table 6.5: Default programming of the DT/forwardRPC Cancel Decision Logic (in the forward process-ing chain of the Global Muon Trigger).

inputs output

DT match DT match fwdRPC cancel cancel Comment

w. fwdRPC w. brlRPC match w.CSC fwdRPC DT

0 x x 0 0 no DT/fwdRPC match

1 0 0 1 0 cancel fwdRPC

1 0 1 0 0 leave cancellation to DT/CSC COU

1 1 x 0 0 no cancellation

1The loss of bandwidth due to sending the same candidate from the DT and the CSC Trigger is considerednegligible since all channels of interest can be triggered with trigger conditions that use up to three muons.


H. Sakulin


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Figure 6.8: GMT efficiency and ghosts in the overlap region for different schemes of ghost suppression:(a) no suppression at GMT, (b) confirmation of DT/CSC with RPC, (c) DT/CSC cancel-out unit, (d)DT/CSC, DT/fwdRPC and CSC/brlRPC cancel-out units. In cases (a) and (b), duplication is suppressedat the level of the track finders and the DT/CSCη-boundary is optimally tuned to match the one in theRPC System. In cases (c) and (d), duplication between the DT and CSC track finders is allowed. Allefficiencies and ghosting probabilities relative to0.9 ≤ |η| < 1.15. Obtained using the single muonsample described in Chapter8, Section8.2. Updated ORCA 6.2.3 simulation.



6.5 Sort Rank Assignment

In parallel to the Matching Units a rank is assigned to each input muon. This rank is used inthe sorters to sort the muon candidates by importance and to determine (in two stages) the bestfour over-all candidates.

The rank of a candidate will generally depend on the following criteria:• In order to reach high efficiency for triggering on high-pT muons, the rank will generally

increase with thepT of the candidate.• Low quality candidates, especially in certain regions of pseudorapidity, have poorpT res-

olution and might actually be of much lowerpT than indicated. They should therefore beranked lower than candidates with high quality. A dependence of the rank on quality andpseudorapidity is therefore necessary. Some cases of such candidates can cause high ratesof high-pT muon candidates. It might then be necessary to exclude these candidates fromcertain trigger algorithms like the single and di-muon triggers, unless they are confirmedby the complementary system (see Section6.6).• In certain regions of pseudorapidity, triggers might be generated due to noise in the cham-

bers. This problem occurs for example in the current design of the RPC Trigger, whichis the main reason why it is being redesigned. Triggers from noise are generally of lowquality, but may be of anypT [31]. It should therefore be possible to rank these candidateslower or even flag them to be ignored unless confirmed by the complementary system (seeSection6.6).• If a certain region inη (andφ) gives higher trigger rates than forseen, it should be possible

to reduce the ranks for candidates coming from this region.• If a certain region inη (andφ) gives higher trigger rates due to hardware failure (“hot

channels”), it should be possible to switch off candidates from this region. A dependenceof the rank onη andφ is therefore necessary.

In order to be able to compensate for higher muons rates than currently estimated, unfore-seen behavior of the regional trigger systems or technical problems, it is necessary to keep theranking as flexible as possible. The most flexible ranking scheme would look up a rank de-pending onpT , quality, η, φ of a muon candidate in big memory-based LUTs. These LUTswould have 22 bits of input corresponding to an address space of 4 Mbits (per input muon can-didate), requiring large external Random Access Memory (RAM) blocks. Such RAMs wouldbe possible in a design with separate GMT boards for barrel and endcaps.

A design with both processing chains of

Rank

assignment

unit

pT,q

LUT5

6

3

pT

η

q

η,φ

LUT

6

8φ

87

2

2

1x

1x

8x

sort rank

very-low

quality flag 1, 2

1x

η,q

LUT3

Rank

comb.

LUT

2

2

2

Figure 6.9: Compacted ranking tables that can be fitinto a Xilinx Virtex II FPGA.

the GMT on a single board however has nu-merous advantages such as the possibility forcancel-out in the overlap region and reducedlatency (see Chapter7, Section7.2). A morecompact solution for the ranking tables, thatcan fit into a Xilinx Virtex II FPGA, thereforewas investigated: it is shown in Figure6.9. Itis not as flexible as using a big RAM but itcan include all the criteria mentioned aboveinto the rank. It works in two stages: first,three contributions to the rank are calculated,

the main contribution (7 bits) coming frompT and quality and two modifying contributionscoming fromη andφ (2 rank modifier bits) and fromη and quality (2 rank modifier bits). A


H. Sakulin

6.6 Exclusion of Very-Low-Quality Unconfirmed Candidates from Certain Trigger Algorithms 81

rank combination LUT then combines the main contribution and the two modifying contribu-tions into the final rank of 8 bits. Two additional output bits of theη–quality LUT are usedto flag candidates that should be excluded from certain trigger algorithms (see the followingsection).

Current simulations show that crossings with more than four muon candidates are very rareand hence it is very rare that a candidate gets sorted out due to its rank assignment. A verysimple ranking based only onpT and quality code as as given in Tables5.7, 5.3, 5.4and5.5 istherefore used, by default:

rank = 3× pT code+ 5× quality code. (6.3)

Additionally, low-quality muons are tagged for exclusion from certain triggers as discussedin the following section.

6.6 Exclusion of Very-Low-Quality Unconfirmed Candidatesfrom Certain Trigger Algorithms

As explained in the previous section, in some regions of pseudorapidity, it may be necessaryto flag muon candidates of certain qualities for exclusion from certain trigger algorithms likethe single and di-muon triggers. This may be necessary for three reasons:• The category of candidates may be likely to contain fake candidates caused by noise in

the chambers. Candidates of such a category can be marked for exclusion from the singleand di-muon trigger if they are not confirmed by the complementary system.• The category of candidates may contain a high percentage of ghosts created in one of the

regional triggers. Just as for fake candidates, this category can be marked for exclusionfrom the single muon and di-muon triggers if there is no confirmation by the complemen-tary system.• The poorpT resolution of candidates in the category results in high trigger rates. Candi-

dates from such a category can be marked for exclusion — usually only from the single-muon trigger — if they are not confirmed by the complementary system. If both systemsdeliver a candidate with very poorpT resolution, optionally also the resulting mergedcandidate can be excluded from certain trigger algorithms (see Section6.9.9).

Two additional output bits of theη-quality rank modifier LUT are used to select categoriesof unconfirmed candidates for exclusion. Depending on these bits the output quality can be setto one of two special codes that indicate that the candidate should be excluded from the single-muon trigger or from both the single-and di-muon trigger. Table6.6 explains the meaning ofthe very-low-quality bits and their effect on the output quality.

The default programming of the exclusion of very-low-quality candidates was determinedon the basis of current simulations of trigger efficiencies and rates. Depending on the pro-gramming the efficiency can vary between the upper and the lower histogram in Figure6.13,i. e. between a logical OR and a logical AND of the candidates from complementary systems,respectively.

Table 6.6: Very-low-quality bits and resulting output quality (as defined in Table6.9).

bit meaning output quality exclude from

VLQ0 likely to be noise/ghost set to 0 if not matched single and di-muon trigger

VLQ1 poorpT measurement set to 1 if not matched single muon trigger



Fake muon candidates due to chamber noise are mainly a problem in the current designof the RPC Trigger. It has been found [36] that the highest rate of fake candidates comesfrom tower 9 (1.14 ≤ |η| < 1.24) with candidate qualities 0 and 1. An order of 230 kHzof fake triggers are reported by this tower resulting in a sizable rate of fake di-muon triggersin bunch crossings that also contain a real muon. RPC candidates of qualities 0 and 1 aretherefore excluded from the single and di-muon trigger by default. The cost in efficiency isvery small as shown in Figure6.12. A considerable rate of fake candidates (several kHz) is alsogenerated in the other RPC towers. The interference with bunch crossings that contain a realmuon is however small. Since only bunch crossings that contain a real muon were includedin the simulation of the trigger rates (see Chapter8, Section8.4) and since the RPC Trigger iscurrently being re-designed, the candidates from these other RPC towers are not excluded in thedefault programming.

The RPC Trigger in the current design shows a high probability for ghosting in towers 12to 15 (1.48 ≤ |η| < 1.97) as illustrated in Figure5.17. Most ghosts are of quality 0 and ofpT < 4 GeV/c. Despite their lowpT these ghosts can contribute to the di-muon trigger rateat low luminosity where trigger thresholds are expected to be set even lower than 4 GeV/c.Unconfirmed RPC candidates from these towers are therefore excluded from the single-muonand di-muon triggers by default. Again, the loss in efficiency is small.

Figure6.10shows the trigger rates for apT threshold of 14 GeV/c (expected single muontrigger threshold in low-luminosity runs) as a function of pseudorapidity split into the contri-butions from matched candidates and from unmatched candidates of different qualities (triggerrates from fake RPC candidates are not included in the plot). Figure6.12 shows the triggerefficiency as a function of pseudorapidity split into the same contributions. Only muons withpµT > 14 GeV/c were used and a trigger threshold ofpGMT

T ≥ 14 GeV/c was applied. It canbe seen that some qualities of unconfirmed muon candidates contribute high trigger rates whilecontributing little to the efficiency. By default therefore all unconfirmed CSC candidates ofquality 2 are excluded from the single muon trigger. In the di–muon trigger unconfirmed CSCcandidates of quality 2 are excluded only in1.1 < |η| < 1.2 due to high ghosting probability.Additionally several categories of unconfirmed RPC candidates are marked for exclusion assummarized in Table6.7. Categories that are excluded due to ghosting (“G”) or noise (“N”) areexcluded from the single and di–muon trigger while categories rejected due to high rates (“R”)are only suppressed in the single–muon trigger.

The effect of the default programming for exclusion of very–low–quality candidates on trig-ger efficiency and rates is summarized in Figures6.13, 6.14and6.15. The efficiency remainsclose to the maximum achievable efficiency with no exclusion. The trigger rates are reduced

Table 6.7: Unconfirmed RPC candidates excluded by default and the reason for their exclusion; R: toohigh rate because of poorpT measurement, G: high ghosting probability, N: fake triggers due to noise.The candidates excluded due to ghosting or noise will be excluded from both the single and di-muontriggers while candidates rejected due to high rate will only be excluded from the single muon trigger.For quality codes see Table5.5, for the definition of the RPC trigger towers see Table5.6.

tower 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

RPC Q0 R,G R,N R,G G G G R,G

RPC Q1 R R N R R R R R R

RPC Q2 R


H. Sakulin

6.6 Exclusion of Very-Low-Quality Unconfirmed Candidates from Certain Trigger Algorithms 83

GMTη0 0.5 1 1.5 2 2.5

(kH

z)η

trig

ger

rat

e / u

nit

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7

8

9

DT+RPCCSC+RPC

DT Q1DT Q2DT Q3DT Q4DT Q5DT Q6DT Q7CSC Q1CSC Q2CSC Q3RPC Q0RPC Q1RPC Q2RPC Q3

Figure 6.10: Trigger rates as a function of pseudorapidity split into the contributions from matchedcandidates and from unmatched candidates of different qualities for a trigger threshold ofpGMT

T ≥14 GeV/c. No suppression of very-low-quality candidates (GMT-OR). Low luminosity (L = 2 ×1033 cm−2s−1). The optimized combined merging method was used for matched candidates (see Sec-tion 6.9.3). Obtained using the minimum bias dataset described in Chapter8, Section8.4. UpdatedORCA 6.2.3 simulation.

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DT Q1

DT Q2DT Q3DT Q4DT Q5DT Q6

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RPC Q1RPC Q2RPC Q3

Figure 6.11: Efficiency of the GMT per bin in the GMT outputη-scale (see Table6.11) as a functionof pseudorapidity split into the contributions from matched candidates and from unmatched candidatesof different qualities. No suppression of very-low-quality candidates (GMT-OR). Trigger threshold ofpGMTT ≥ 14 GeV/c applied. Due to the resolution of theη assignment candidates can be reported

in neighboring bins. The optimized combined merging method is used for matched candidates (seeSection6.9.3). Obtained using the single muon sample described in Chapter8, Section8.2, with14 GeV/c < pµT < 100 GeV/c. Updated ORCA 6.2.3 simulation.



genη0 0.5 1 1.5 2 2.5

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DT Q2DT Q3

DT Q4DT Q5

DT Q6DT Q7

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RPC Q3

ηEfficiency vs.

Figure 6.12: Efficiency as a function of pseudorapidity split into the contributions from matched can-didates and from unmatched candidates of different qualities. No suppression of very-low-quality can-didates (GMT-OR). Trigger threshold ofpGMT

T ≥ 14 GeV/c applied. The optimized combined mergingmethod is used for matched candidates (see Section6.9.3). Obtained using the single muon sample de-scribed in Chapter8, Section8.2, with 14 GeV/c < pµT < 100 GeV/c. Updated ORCA 6.2.3 simulation.

by almost a factor of two with respect to no exclusion and are close to the rates obtained whenall unconfirmed candidates are excluded. All the rate reduction is achieved in the overlap re-gion and endcaps. The ghosting probability is reduced considerably compared to the ghostingprobability with no exclusion which would basically contain all the ghosts of the regional trig-gers as shown in Figure5.17a. A further rate reduction at a larger cost of efficiency is possibleby excluding also certain categories of confirmed candidates with very poorpT resolution (seeSection6.9.9).

6.7 MIP and ISO Assignment Unit

The MIP and ISO Bits Assignment Units correlate muon candidates with Quiet and MIPbits received from the calorimeter trigger. The Quiet bits indicate whether the deposited energyin the corresponding calorimeter region has been below a certain threshold and are used todetermine if a muon was isolated or non–isolated, i.e. produced inside a jet. Muons from heavyobjects such asW andZ bosons, which are signatures of channels among the physics goals,are generally isolated while the large background of muons fromb– andc–quark decays isproduced inside jets. Applying isolation criteria in the single–muon trigger can help to reducethis background. The MIP bits denote that the energy deposited in the respective calorimeterregions is consistent with the passage of a minimum ionizing particle such as a muon. They canbe used to confirm muon candidates and theirpT assignments.

Quiet and MIP bits are generated by the Calorimeter Trigger for regions of∆η × ∆φ =0.35 × 0.35 rad as described in Chapter5, Section5.3. The MIP and ISO Assignment Unitsproject the coordinates of muon candidates to the calorimeter or vertex in order to find thecorresponding MIP and Quiet bits. For the MIP bits a projection to the inner surface of the


H. Sakulin

6.7 MIP and ISO Assignment Unit 85

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Figure 6.13: Efficiency as a function of pseudorapidity. The upper histogram shows the efficiency whenall muon candidates are accepted (logical OR), the lower histogram shows the efficency, when only con-firmed (matched) candidates are accepted (logical AND). The middle histogram shows the efficiencywith default settings for suppressing very-low-quality candidates. Obtained using the single muon sam-ple described in Chapter8, Section8.2. Updated ORCA 6.2.3 simulation.


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GMT OR (all candidates)GMT default (smart suppression)GMT AND (confirmed candidates)DT/CSC standaloneRPC standalonegenerated rate

-1s-2 cm33Level-1 Single Muon Trigger Rates L = 2x10

Figure 6.14: Trigger rates as a function of trigger threshold at low luminosity (L = 2× 1033 cm−2s−1).The upper GMT curve shows the trigger rates when all muon candidates are accepted (logical OR), thelower GMT curve shows the trigger rates, when only confirmed (matched) candidates are accepted (log-ical AND). The middle GMT curve shows the trigger rates with default settings for suppressing very-low-quality candidates. The optimized combined merging method is used for matched candidates (seeSection6.9.3). Obtained using the minimum bias dataset described in Chapter8, Section8.4. UpdatedORCA 6.2.3 simulation.



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Figure 6.15: Ghosting probability as a function of pseudorapidity. The upper histogram shows theghosting probability when all muon candidates are accepted (logical OR); the lower histogram showsthe ghosting probability when only confirmed (matched) candidates are accepted (logical AND). Themiddle histogram shows the ghosting probability with default settings for suppressing very-low-qualitycandidates in the di–muon trigger as discussed in Section6.6. Obtained using the single muon sampledescribed in Chapter8, Section8.2. Updated ORCA 6.2.3 simulation.

HCAL is used since the position of the muon in the HCAL determines the region for whicha MIP bit is set. The corresponding MIP bit is then directly attached to the muon candidate.For the assignment of the Isolation (ISO) bit the energy deposit in the calorimeter around thedirection of the jet from which the muon may have originated is of interest. Since the jet axis isnot bent by the magnetic field, the Quiet bits around the direction of the muon at the vertex arechecked when assigning the ISO bit. Multiple Quiet bits around the direction can be checked asgiven by a programmable rectangular isolation window. The ISO bit is set, if all regions in theisolation window are quiet. Two MIP and ISO Assignment Units exist, one handling the eightbarrel muon candidates and the other one handling the eight forward muon candidates. Each ofthe units receives only the MIP and Quiet bits in the respective detector region.

Figure6.16shows the bending between the muon system and the vertex as a function ofmeasuredpT for muon candidates from the regional triggers in different regions of pseudora-pidity. The bending can be as large as 1.1 rad at low muonpTs. In order to achieve an accuracyof about 0.1 rad for the muon direction at the vertex, the entire five bits ofpT have to be usedin the projection. In the barrel the bending is largely independent of pseudorapidity, while inthe endcaps there is a clear dependence. In order to achieve an accuracy of about 0.1 rad for themuon direction at the vertex, at least three bits ofη have to be taken into account.

The original idea for the implementation of the projection logic was a large memory–basedlook–up–table per muon which has the parameterspT , η (reduced to 4 bits),φ,and charge asinput and directly gives the number of a calorimeter region to be checked as an output [18].This solution would have required large external memory blocks. In order to implement theGMT on a single VME board (see Chapter7, Section7.2) it was necessary to compact the the


H. Sakulin


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| < 0.22η0.00< |

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| < 2.06η1.86< |

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fRPC, charge +

pTtrig (GeV/c)

pTtrig (GeV/c) pT

trig (GeV/c)

Figure 6.16: ∆φ between coordinates of muon candidates of the regional triggers in the muon systemand the respective generated muon at the vertex as a function of measuredpT for different regions ofpseudorapidity for muons with positive charge assignment. Obtained using the low-pT single muonsample described in Chapter8, Section8.2. ORCA 5 simulation.



5

4

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η

38 φ

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η

1x

ch 1

8(10)

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φ��

tion logic η��

tion logic

φ start

�� set

φ��

t bits η��

t bits

Figure 6.17: φ andη projection logic to project coordinates of the muon candidates from the muonsystem to the calorimeters and vertex. See text.

projection logic so that it can be fit inside an FPGA chip. The projection first was split intoseparate projections forφ andη which separately select calorimeter regions inφ and inη asshown in Figure6.17. Theφ projection then was split into two stages making use of the factthat the dimension of a calorimeter region inφ (20o) corresponds to exactly 8 units of theφscale of the muon candidates. The upper five bits of theφ coordinate then directly give theindex of the calorimeter region in the case of a straight track and are used as a start region. Thefirst stage of the projection logic is based onpT , four bits ofη, charge and the lower three bitsof φ. It determines the bending in terms of an offset in regions off the start region and of afine–index that points to one of four sub–regions inside the target region. The second stage thendetermines the calorimeter regions inφ to be selected based on the coarse start region, offsetsand charge (to determine the direction of the offsets). The fine–index is used in the second stageto decide on what side of the central region to check additional regions, if an isolation windowwith an even number of regions is used.

Bending inη can be up to 0.15 units for muons of lowpT . Since it is independent ofφthe projection can be performed in one stage as shown in Figure6.17with the selected regionindices inη as a direct output. The remaining logic then just selects the MIP bit correspondingto the selected indices of the region inφ andη. In case of the ISO bit where multiple regionscan be selected, the remaining logic checks all Quiet bits selected by the indices inφ andη andsets the ISO bit if all Quiet bits were set.

Final studies of the performance of isolation and MIP confirmation were not possible atthe time of writing since no simulation of the generation of MIP bits was available and thegeneration of quiet bits was not optimized. The results of preliminary studies [37] are shown inFigures6.18and6.19. Isolation has been shown to work well for muons of highpT . Muons oflow pT however always appear to be isolated since the corresponding low–ET jets do not depositenough energy in the calorimeters. Since trigger rates at Level–1 are completely dominated bylow–pT muons (see Chapter9, Section9.3), the rate reduction achieved by applying an isolationalgorithm is almost negligible. The MIP bits can be used to confirm thepT assignment of muoncandidates: if a highpT measurement is assigned to a low–pT muon, then the projection willpoint to a wrong calorimeter region and the muon cannot be confirmed. A rate reduction byalmost a factor of two can be achieved at the cost of 10 % efficiency.


H. Sakulin


(GeV/c)Generated p

0 20 40 60 80 100

Eff

icie

nc

y

0

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T

Figure 6.18: Preliminary results for the efficiency for muons fromW → µν decays and for muonsfrom minimum bias interactions as a function of generatedpµT after applying an isolation cut at level–1.High efficiency is achieved for isolated muons fromW decays. Rejection of non-isolated muons fromminimum bias interactions is powerful at high muonpT but cannot be applied to muons of lowpT sincethe deposited energy of the respective low–ET jets in the calorimeters is below the quiet threshold. Quietthreshold ofEQuietT ≥ 5 GeV/c, isolation window of2× 2 calorimeter regions. ORCA 5 simulation.

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0 20 40 60 80 100

Eff

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Figure 6.19: Preliminary results for the efficiency of the MIP confirmation for muons fromW → µνdecays and from minimum bias interactions as a function of generatedpT for candidates reconstructedwith pGMT

T ≥ 25 GeV/c. The confirmation can be used to suppress candidates with poorpT assign-ment: if a highpT is assigned to a muon of low generatedpT then the projection may point to a wrongcalorimeter region and the muon candidate cannot be confirmed. MIP threshold ofEMIP

T ≥ 1 GeV/c.ORCA 5 simulation.



6.8 Conversion of Parameters

In parallel to the matching and rank assignment, the parameters of the candidates are con-verted to the output scale. The pseudorapidity coordinateη is converted to the GMT outputscale (see Table6.11) using a look-up-table. Optionally, theφ coordinate is projected to thevertex since in topological triggers conditions, which can be applied in the Global Trigger, thedirection of the muon at the vertex is of interest. The projection is realized using a LUT to lookup a∆φ and an adder/subtracter. The LUT defines a 6-bit∆φ from 5 bits ofpT and 4 bits ofη.The contents of the look–up–table are calculated in analogy with the previous section.

6.9 Muon Merger Unit

The pair logic finds pairs of complementary measurements that belong to the same physicalmuon. For each pair, a Muon Merger Unit combines the parameterspT , charge,η, φ, MIP,ISO and sort–rank of the two measurements in order to forward a single muon candidate withimproved parameters to the Global Trigger. Improving the assignment is most important forthepT measurement, because it determines the trigger’s capability to filter interesting high-pTmuons out of a large background of low-pT muons. There are four Muon Merger Units in theBarrel Logic FPGA and four in the Endcap Logic FPGA.

Multiple merging methods exist for each parameter. Table6.8 gives an overview over themerging methods available and the default method currently used in simulations for each of theparameters. For all parameters it is possible to pre-define the system that delivers the parameter.The parameter of the complementary system is then inhibited. This can be useful when there isa known problem with the parameter in one of the systems or when one of the systems alwaysdelivers a more accurate measurement. Furthermore, for all parameters it is possible to decidethe system that delivers the parameter based on a merge–rank as described in Subsection6.9.1or based on the minimumpT measurement as described in Subsection6.9.2. The latter twomethods can be combined as explained in Subsection6.9.3. Finally, for the parametersη,charge,pT and the MIP and ISO bits, additional special merging methods exist as described inSubsections6.9.4, 6.9.5, 6.9.6and6.9.7.

The charge measurement should generally be taken from the system that was selected todeliver thepT . If the optional projection of theφ coordinate to the vertex (see Section6.8) isused, then also theφ coordinate should generally be selected from the system that was selectedto deliver thepT , since the projection depends on thepT measurement.

6.9.1 Merging Based on a Merge–Rank

Similar to the sort–rank explained in Section6.5, a merge–rank can be defined for eachmuon candidate. It indicates how well the parameters are measured, most importantly thepT .Generally, this rank will depend onη and the quality of the candidate, but to some extent alsoa dependence onη andφ can be taken into account in order to reduce merge ranks for certainproblematic detector regions. Additionally, also a dependence onpT and quality is foreseen.

Since the quality codes of muons use up to 3 bits, merge–ranks of 5 bits should give enoughflexibility. Figure 6.20 shows the logic that assigns the merge rank to each candidate. Inthe hardware, it is combined with the Rank Assignment Unit responsible for assigning sortranks (see Section6.5). If merging based on merge–ranks is selected for all parameters, then


H. Sakulin

6.9 Muon Merger Unit 91

Table 6.8: Available merging methods for the parameters of the muon candidates and current defaultmethod (DEF). See text. (A programmable offset is added to the sort–ranks before merging in order toindicate that the candidate was detected by two complementary systems.)

parameter always always higher combined minpT smart smart mix smart

DT/CSC RPC rank higher rank η charge pT MIP/ISO

φ x x x DEF - - - -

η x x x x DEF - - -

charge x x x DEF - x - -

pT x x x DEF - - x -

MIP bit x x x x - - - DEF: OR

ISO bit x x x x - - - DEF: AND

sort–rank x x x DEF - - - -

the Muon Merging Unit operates in winner/looser mode described in earlier designs of theGMT [18]. Alternatively, this method could be used only forpT , φ (and charge) while specialmethods are used for the other parameters. A default programming of the merge–rank assign-ment was determined based on thepT resolution of the candidates of different qualities at agiven pseudorapidityη: the category of candidates with the lowest RMS error on thepT mea-surement as shown in Figure5.19gets assigned the highest merge rank. The upper curve inFigure6.22shows the resulting trigger rates if thepT measurements are merged on the basis ofmerge ranks. The upper histogram in Figure6.23shows the efficiency for triggering on muonsfrom W → µν decays with apT threshold of 14 GeV/c as a function of pseudorapidity whenthe rank-based merging method is used for thepT . The turn–on curves, shown in Figure6.24a,reach high plateau efficiency and show only a very small decrease of the plateau at higher triggerthresholds.

6.9.2 Merging Based on MinimumpT Measurement

In some cases thepT assignment of both matched candidates is very poor with a tendency totoo highpT measurements. This situation can occur especially in the overlap regions and end-caps. In these cases, instead of choosing the parameters from the candidate with higher mergerank, the parameters can be chosen from the candidate with lowerpT . For thepT assignmentthis simply means that the lowerpT is forwarded. A large reduction in trigger rates is possibleusing this method at the cost of some efficiency.

The lower curve in Figure6.22shows the resulting trigger rates if the minimumpT is chosenfor all matched candidates. The rate can be reduced by a factor of 1.5 with respect to the rateachieved by the merging based on merge ranks. The lower histogram in Figure6.23shows theefficiency for triggering muons fromW → µν decays with apT threshold of 14 GeV/c as afunction of pseudorapidity for this scenario of merging. The efficiency loss due to taking theminimum pT is tolerable, except in narrow regions of pseudorapidity around|η| = 0.2 and|η| = 0.5, and to some extent in the overlap region. Figure6.24b shows the turn–on curvesusing the minimumpT merging method. The method causes a further decrease of plateauefficiencies at higherpT thresholds with respect to the decrease in the regional triggers discussedin Chapter5, Section5.4.7.3.



6.9.3 Combined Merging Based on a Merge–Rank and the MinimumpTMeasurement

In order to benefit from the rate reduction of the minimum–pT merging method and to avoidthe resulting efficency losses, a Merge Method Selection Logic has been devised that allowsto combine rank based and minimum–pT merging as shown in Figure6.21. Two extra flagsfrom theη-quality LUTs of the merge rank assignment logic are used to decide whether to usethe minimumpT or the higher rank as a criterion for merging. In case of equal merge ranks aprogrammable default system can be used. It is possible to disable measurements of one of theregional triggers in a specific detector region by setting the merge rank to zero. In this case themeasurement of the other system is used.

Merge Rank

assignment

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take DT

se

lect

me

th

od

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5pT RPC

merge by min pT

DT

RPC

Figure 6.20: Compacted look–up–tables tocompute the merge rank.

Figure 6.21: Merge Method Selection Logic.Shown for the barrel case. See text.

The Merge Method Selection Logic has been optimized with the objective of optimal ratereduction at a tolerable efficency loss: by default the minimum–pT method is used for all typesof matched candidates except the following, where the efficiency losses would be too large:• RPC quality code 0 matched with DT quality codes 1, 4, 6, 7 in the entire barrel region.• RPC quality code 0 matched with DT quality codes 2, 3 in the barrel for|η| < 0.9.• RPC quality code 3 matched with CSC quality code 2 in the overlap region for|η| < 1.2.• RPC quality code 3 matched with CSC quality code 3 in the entire endcap region.

As shown in Figures6.22and6.23, the combination of the two merging methods results inalmost as powerful a rate reduction as the minimum–pT method while keeping the efficiency al-most as high as with merging based on merge ranks. The plateau reached in the turn–on curvesis almost as high as with the merging based on merge ranks and there is only a small decreaseof the plateau efficiency at higher trigger thresholds remaining in the overlap region (see Fig-ure6.24c). The optimized combined merging method is used as a default merging method forthepT measurement, the charge measurement andφ measurement.

6.9.4 Smart Merging ofη Measurements

Theη-coordinates already have to agree within a small window in order to form a matchedpair of measurements and hence the choice of merging method does not have a large impact


H. Sakulin



1 10 102

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gg

er

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z)

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10

102

103

104

105

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GMT optimized merging (default)

mergingT

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DT/CSC standalone

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generated rate

Figure 6.22: Trigger rates as a function of trigger threshold at low luminosity (L = 2× 1033 cm−2s−1)for three types of GMT merging (see text). The default settings for the “smart” exclusion of unconfirmedlow–quality candidates from the single muon trigger as described in6.6are used in all cases. Obtainedusing the minimum bias dataset described in Chapter8, Section8.4. Updated ORCA 6.2.3 simulation.

|µ

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Efficiency /

%

70

75

80

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90

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mergingTGMT minimum p

Figure 6.23: Efficiency for triggering on muons fromW → µν decays as a function of pseudorapiditywith a pT threshold of 14 GeV/c for three types of GMT merging (see text). The default settings forthe “smart” exclusion of unconfirmed low–quality candidates from the single muon trigger as describedin 6.6are used in all cases. Obtained using theW sample described in Chapter8, Section8.3. UpdatedORCA 6.2.3 simulation.



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Figure 6.24: GMT turn–on curves in the barrel, overlap and endcap regions for three types of merg-ing (see text). The default settings for the “smart” exclusion of unconfirmed low–quality candidatesfrom the single muon trigger as described in6.6 are used in all cases. Obtained using the single muonsample described in Chapter8, Section8.2. Updated ORCA 6.2.3 simulation.


H. Sakulin


on the outputη resolution. In the barrel the assignment ofη can be improved by taking intoaccount the fine/coarse bit of theη measurement of the DT Track Finder; this is more accuratethan that of the RPC Trigger when theη-Track Finder is used (fine method). If for some rea-son (see Chapter5, Section5.4.2.2) the coarseη assignment method has to be used, then themeasurement is less accurate than that of the RPC System (see Figure5.24). The “smart”ηmerging method therefore takes the DT measurement if the fine-bit is set and otherwise takesthe RPC measurement. This method is used by default in the barrel. Figure5.25shows that theCSC System always gives a finer resolution forη. In the endcaps the “smart”η merging methodtherefore defaults to always taking the CSC measurement.

6.9.5 Smart Merging of Charge Assignments

Depending on the pseudorapidity region and the muonpT the regional trigger systems havedifferent probabilities for wrong charge assignment (see Chapter5, Section5.4.7.6). Generally,high pT tracks are straighter and charge assignment becomes more difficult. In most cases theregional trigger systems can detect if they are not able to assign a charge and can indicate thiscase via thecharge-validbit. The “smart” charge merging method takes into account the charge-valid bits: if only one of the complementary systems indicates a valid charge assignment, itsassignment is forwarded; if both systems indicate a valid charge, the assignment of a pre-definedsystem, by default the DT or CSC System, is taken. If both systems indicate an invalid chargeassignment, then the charge at the output is set to be invalid.

6.9.6 Mixing of pT Measurements

Besides the basic merging methods, thepT measurement can also be obtained by “mixing”thepT measurements of the two systems. To make the “mixing” fully flexible, this method isimplemented by a LUT that takes the twopTs measured by the two systems as input and has anew “mixed”pT as output. The output can be any function of the twopT measurements such asfor example the average of the two measurements.

6.9.7 Smart Merging of MIP and Isolation Bits

The muon candidates found by the regional trigger systems are projected to the calorime-ters/vertex in order to assign MIP/Isolation bits as explained in Section6.7. In the Muon MergerUnit these bits are merged using either one of the basic methods or an additional “smart”method: the output MIP/Isolation bit can be the logical OR or the logical AND of the respectivebits of the two candidates to be merged. By default for the MIP bits the logical OR is used whilefor the Isolation bits the logical AND is used.

6.9.8 Merging of Sort Ranks

The sort–rank of a muon candidate that has been reported by two systems is increased withrespect to the sort–ranks of candidates seen by only one system by adding a constant to therank. If a large constant is added, then confirmed candidates are always ranked higher than allunconfirmed candidates. If a lower constant is added, high–pT unconfirmed muons can havesimilar or even higher ranks than low–pT confirmed muons. The merging method only decideswhich of the two ranks is used as a base for adding the constant.



6.9.9 Optional Suppression of Very–Low–Quality Candidates

As discussed before, it can happen that both candidates of a matched pair are of very lowquality, i. e. have a very poorpT resolution. In order to achieve a very effective rate reduction,such matched candidates can optionally be excluded from default trigger algorithms in certainregions of pseudorapidity like for example the overlap region. In the hardware this functionalityis implemented with a look-up-table that has the pseudorapidity of the matched pair and the twoquality codes of the candidates as input and two Very–Low–Quality bits as output. The Very–Low–Quality bits are used in the same way as for the exclusion of unconfirmed candidates.

Simulation Studies have shown that an effective rate reduction could be achieved in theoverlap region using this functionality. However the efficiency loss would be of the order ofseveral per cent. The method is therefore not used by default.

6.10 Sorter

The sorter sorts the output muon candidates by rank in order to find the best four candidatesin the detector which are then forwarded to the Global Trigger. The sorting procedure is imple-mented in two stages as illustrated in Figure6.1: in a first stage, the candidates from the barreland the candidates from the endcaps are sorted in separate sorters.

The inputs to these sorters are the merged or unconfirmed DT/CSC candidates from theMuon Merger Units and the unconfirmed RPC candidates. The sorter has additional cancel-outinputs for each candidate: for the RPC candidates they are used to cancel candidates that arepart of matched pairs. Furthermore the Overlap Cancel–Out Units use the cancel-out inputs tocancel DT/CSC and also RPC candidates.

The best four candidates found in the barrel and the best four found in the endcaps are thensent to a second sorter stage which finds the best four over-all candidates.

6.11 Summary of the GMT Output

The output of the GMT are the four best muon candidates in the whole detector. Table6.9shows the parameters that are sent to the Global Trigger for each muon candidate. As the GlobalTrigger resides in the same crate, the data are sent on direct parallel links via the backplane.

Table 6.9: Output of the Global Muon Trigger sent to the Global Trigger.

Parameter scale & range bits comment

pT common scale 5 see Table5.7

φ 0..143, 2.5o bins 8 defined at muon station 2

or optionally at vertex

η non-linear scale 6 5 bits + 1 bit pseudo-sign see Table6.11

Quality 0..7 3 see Table6.10

MIP confirmed=1 1 calorimeter confirmation

ISO isolated=1 1 calorimetric isolation

Sync/Charge coded 2 muon charge or sync. bits, see Table6.12


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6.11 Summary of the GMT Output 97

Table 6.10: Default Programming of the output quality scale of the Global Muon Trigger sent to theGlobal Trigger.

Code description

7 halo trigger from CSC

6 matched,pT taken from DT/CSC

5 matched,pT taken from RPC

4 unmatched DT/CSC

3 unmatched RPC

2 candidate to be excluded from di-muon trigger (likely to be ghost)

1 candidate to be excluded from single-muon trigger (very poorpT measurement)

0 candidate to be excluded from single- and di–muon trigger (likely to be ghost/fake)

Table 6.11: Default Programming of the GMT output pseudorapidity scale. There is a bin-boundary atη = 0. The most-significant bit is a pseudo-sign determining if the candidate is in the positive (0) ornegative endcap (1).

Bit code 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

|ηmax| 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60

|ηcenter| 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.05 1.15 1.25 1.35 1.45 1.55

Bit code 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

|ηmax| 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40

|ηcenter| 1.65 1.725 1.775 1.825 1.875 1.925 1.975 2.025 2.075 2.125 2.175 2.225 2.275 2.325 2.375

Table 6.12:Coding of charge and synchronization bits at the output of the Global Muon Trigger sent tothe Global Trigger.

Code description

00 positive charge

01 negative charge

10 charge assignment not valid

11 synchronization word


Chapter 7

Global Muon Trigger HardwareImplementation

100 7. Global Muon Trigger Hardware Implementation

The Global Muon Trigger logically belongs to the L1 Muon Trigger System. Physically itwill be located in the same VME crate as the Global Trigger. It consists of several input boardsthat receive and synchronize data and one main logic board that performs the all functionsdiscussed in the previous chapter. This chapter briefly describes the main features of the designof the logic board.

7.1 Choice of Technology

Field Programmable Gate Arrays (FPGAs) were chosen as a technology for the implemen-tation of the Global Muon Trigger since radiation hardness is not an issue and device counts arevery small. Modern FPGAs offer up to several millions of configurable logic gates, of the orderof 1000 input/output pins and internal memory blocks. Due to the available expertise at the In-stitute for High Energy Physics (HEPHY), it was decided to base the design on the Virtex II [38]series of FPGAs produced by Xilinx [39]. The largest device in the series with a packaging thatcan currently be handled by the electronics group at HEPHY is the Virtex XC2V3000 which isbecoming available at the time of writing. With 3 million system gates it offers 14000 freelyconfigurable logic slices, each containing two small 4 bit→ 1 bit look–up–tables that can beused to implement any logic function. Additionally, 96 configurable memory blocks of 18 kbitare available which can be used to implement larger look–up–tables. With the proposed pack-aging, 484 user input/output pins will be available for trigger and control data. The logic designof the Global Muon Trigger has been based on this chip model and was elaborated using thementioned constraints.

7.2 GMT System Overview

Originally [18] it was planned to implement the GMT on two separate VME boards, oneprocessing the barrel muon candidates and one processing the candidates in the endcaps. Largeexternal memory blocks were planned for the assignment of sort ranks and for the projectionof muon candidates from the muon system to the calorimeters and vertex. As explained inChapter6, Sections6.5 and 6.7, the rank tables and projection logic have been compactedusing two stages of smaller look–up–tables so that it became possible to fit them inside theFPGAs. With this compacted design and with a special wide front-panel to receive all 16 muoncandidates from the regional triggers on parallel links, it has been possible to fit all the GlobalMuon Trigger functions on a single VME board. Apart from reducing the latency, this hasthe advantage that cancel–out links between the two processing chains become possible andduplicated muon candidates in the overlap region can be canceled out as explained in Chapter6,Section6.4.

With the new single–board solution, the entire Global Muon Trigger consists of four VMEboards, the GMT Logic Board and three Pipeline Synchronizing Boards (PSBs) [18]. All boardsare located in the Global Trigger Crate as shown in Figure7.1. The three PSB boards receivethe 252 MIP and 252 Quiet bits from the Global Calorimeter Trigger and synchronize them toeach other and to the muon data. The synchronized bits are sent on 80 MHz point–to–pointlinks to the GMT Logic Board via the backplane.


H. Sakulin

7.2 GMT System Overview 101

8��

C, 4 DT, 4 CSC muon

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Technical

signals

RUN

Control

VME

L1A, CMD

32 cables to 32 TTCvi

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PSB

12

Figure 7.1: Schematic view of the Global Muon Trigger in the Global Trigger Crate.



Front panel

VME

VME

LVDS receivers

FINAL

GMT

SORTER

4 m uons2 6 x 4 bits

VME

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1 8 0 pins

14 4 p ins

52 pins

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4 µµµµ

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4 µµµµ

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4 µµµµ

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Forward Logic FPGA

Barrel Logic FPGA

GMT-IN

FPGA

4 µµµµ

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FPGA

4 µµµµ

��

Figure 7.2: Schematic view of the Global Muon Trigger Logic Board.

7.3 GMT Logic Board

Figure7.2shows a schematic view of the GMT Logic Board. The muon candidate data fromthe regional triggers are received on 40 MHz parallel Low Voltage Differential Signal (LVDS)links using Shielded Twisted Pair (STP) cables. One cable is used per candidate, transferringthe data discussed in Chapter5, Section5.4.8. In order to fit the 16 connectors on the frontpanel, a special input board occupying four VME slots will be mounted parallel to the frontpanel and connected to the main board via edge connectors. LVDS receivers convert the signalsto low voltage TTL level. Nine large Virtex XC2V3000 FPGAs contain the logic functionsdefined in Chapter6: four GMT Input FPGAs, two GMT Logic FPGAs, two GMT MIP andISO Assignment FPGAs and the GMT Final Sorter FPGA. Table7.1 gives an overview overneeded user input/output pins and memory resources for each chip.

The muon candidate data are synchronized to each other and the LHC clock using a syn-chronization logic located in theGMT Input FPGAs: all input bits are first sampled four timesper bunch crossing at 160 MHz. The phase sampled furthest from the switching time of theinput word is selected and sent to the following delay pipeline which can delay the input databy up to 16 bunch crossings. All delays can be programmed via VME. The GMT Input FPGAsfurther contain monitoring ring buffers with a depth of 1k which save the input data and can beread out later, when a bunch crossing was triggered or a separate read–out request was issued.Each GMT Input FPGA will handle four muon candidates and send the synchronized muon can-didate data to the corresponding GMT MIP and ISO Assignment FPGA and the correspondingGMT Logic FPGA(s) on point–to–point links.

Two GMT Logic FPGAsreceive synchronized muon candidate data and perform most ofthe logical functions. The GMT Barrel Logic FPGA receives barrel–RPC and DT data as well


H. Sakulin

7.3 GMT Logic Board 103

as part of the CSC data (φ and reducedη only) while the GMT Forward Logic FPGA receivesforward–RPC and CSC data as well as part of the DT data. Each of the GMT Logic FPGAscontains a Matching Unit, eight Rank Assignment Units, eight Parameter Conversion Units, twoOverlap Region Cancel–Out Units, four Muon Merger Units and one Sorter which perform thelogical functions discussed in Chapter6. Additional cancel–out links between the two GMTLogic FPGAs are used for the overlap cancel–out units as indicated in the figure. The GMTLogic FPGAs further receive eight MIP and eight ISO bits from the respective GMT MIP andISO Assignment FPGAs and attach them to the muon candidates. The best four candidatesfound in a GMT Logic FPGA are sent to the GMT Final Sorter FPGA together with a sort–rankthat is used in the final sorting.

Two GMT MIP and ISO Assignment FPGAsproject the barrel and forward muons from themuon system to the calorimeters and vertex as discussed in Chapter6, Section6.7. Apart fromthe muon candidate data for 8 Muons, they receive the MIP and ISO bits for their correspondingdetector region from the PSB boards via the backplane using 80 MHz parallel point–to–pointlinks. The outputs of the GMT MIP and ISO Assignment FPGAs are one MIP and one ISO bitper muon candidate which are sent to the respective GMT Logic FPGAs.

TheGMT Final Sorter FPGAreceives the four best muon candidates from the GMT Bar-rel and Forward Logic FPGAs and performs the final sorting stage based on the sort ranks itreceives for each candidate. The best four overall candidates are sent directly to the GlobalTrigger on point–to–point links via the backplane using 80 MHz parallel signals. Furthermore,the GMT Sorter FPGA contains monitoring ring buffers with a depth of 1k which save the out-put data and can be read out later, when a bunch crossing was triggered or a separate read–outrequest was issued.

Table 7.1: Bit counts and used chip memory resources of the nine Virtex XC2V3000 FPGAs on theGlobal Muon Trigger Logic Board (ROP = Read Out Processor).

Chip inputs / outputs SelectRAM

in out VME ROP total memory blocks

max. resources in XC2V3000, 676 pin 484 96

GMT Input FPGAs, RPC 128 192 44 24 388 16

GMT Input FPGAs, DT/CSC 128 248 44 24 444 16

GMT Logic FPGAs 264 156 44 - 464 92

GMT MIP and ISO Assignment FPGA, barrel 340 16 44 - 400 80

GMT MIP and ISO Assignment FPGA, forward 376 16 44 - 436 96

GMT Final Sorter FPGA 272 52 44 24 392 32

Apart from the nine Virtex XC2V3000 FPGAs, the Global Muon Trigger also containsseveral smaller chips for control and read–out. AVME Interfaceallows to read and write allregisters and look–up–tables in all FPGAs on the board. ARead–Out Processor (ROP)readsout data from the monitoring ring buffers for three consecutive bunch crossings when a crossingwas accepted by the Level–1 Trigger. In order to deal with L1 accept signals occurring innarrow sequence, data are first shifted from the ring buffers to de-randomizing buffers and thentransferred to the Global Trigger Front–end (GTFE) card on low–bandwidth Channel Links.The Timing and Control Board concentrates the data from all boards in the crate and sendsthem to the data acquisition system. A JTAG (Joint Test Action Group) chain is connected toeach of the FPGAs and allows to configure the chips and to perform Boundary Scans (readingand writing of each of the inputs/outputs) for testing.



7.4 Latency

In order to keep the latency as small as possible the GMT receives muon candidates as par-allel data, uses a fast synchronization circuit, does calculations in parallel and sends the outputmuons as parallel data via the backplane to the Global Trigger. The minimum latency along thecritical path for the processing of muon data will be 10 bunch crossings. For MIP/Quiet bitswhich arrive at the GMT, earlier, the minimum latency will be 16 bx.


H. Sakulin

Chapter 8

Trigger Simulation

106 8. Trigger Simulation

Detailed simulations of the entire CMS detector and its trigger system are necessary in orderto understand the performance of the trigger and to optimize the individual components andalgorithms. This chapter deals with the software and techniques used for simulation as well asthe signal and background samples that were produced as a benchmark of the performance of thetrigger system. The correct treatment of muons coming from pile–up events in the simulationof di–muon trigger rates has been one of the main topics of this thesis.

8.1 Simulation Software and Parameters

Figure8.1gives and overview over the simulation software currently used and being devel-oped in the CMS collaboration. PYTHIA [40] and other particle generators are used to simu-late proton–proton interactions and the resulting short–lived particles. CMSIM [41], a programwritten in FORTRAN based on GEANT 3.21 [42], then traces the long–lived decay productsthrough the detector material taking into account interactions with the detector material, furtherdecays of these particles, and the magnetic field. The output of CMSIM arehits in sensitivedetector elements i. e. the positions and angles of passage of particles and information aboutthe energy deposited in the detector material. The response of the detectors to these hits and thesuperimposed hits of other interactions occurring in the same and neighboring bunch crossingsis then digitized in the object–oriented detector simulation software ORCA [43]. ORCA is alsoused to simulate the entire processing chains of the L1 Trigger and high–level triggers: units ofhardware such as boards and chips are modeled by C++ objects that perform bitwise identicaloperations to the corresponding hardware components. The output of the ORCA simulationis stored in ntuples or ROOT trees which can then be analyzed with the analysis programsPAW [44] or ROOT [45].

The generation of signal samples for efficiency studies and minimum bias samples for thestudy of trigger rates are covered in Sections8.3and8.4, respectively.

At the CMSIM detector simulation step, energy loss, multiple scattering, bremsstrahlung,Compton scattering and pair–production processes were activated. Energy cutoffs in the last10 cm of iron layers before the muon chambers were lowered with respect to the default settingsin order to have a realistic simulation of delta–rays and shower processes in the chambers [46].Hadronic interactions at energies as low as 1 MeV were included in the simulation.

The simulation of the muon chambers (see Chapter4, Section4.4) in ORCA takes into ac-count the residual magnetic field and uses parameterizations for drift velocities obtained fromdedicated simulation studies or from test–beam data. The simulation of analog–to–digital con-verters and discriminators includes parameterizations of electronic noise. In the RPC System

GEANT 3.21

CMSIM 125 (FORTRAN)

ZEBRA.fz

HEPEVT ntuples

Objectivitydatabase

HBOOKntuple

ROOT

1

2

3

4

5

1

2

3

4

5

C++ analysis macro

DIGI

ORCA 6 (C++)

Trg. Pr. Reg.Trg.

RPC

DT

CSC

PACT

DTTF

CSCTF

GMT L1GT

CALO CALO

High Level Trigger

Reconstruction

GCT

ROOTfile

PYTHIA6.158

Figure 8.1: Simulation and analysis software used for trigger studies.


H. Sakulin

8.2 Samples of Single Muons 107

a cluster size of 1.5 strips and a chamber efficiency of 95 % were assumed. The simulation ofintrinsic chamber noise, to which the RPC System is very sensitive, was not included in thestudies since to RPC Trigger is currently being re–designed to improve rejection of this type ofnoise.

Muon detectors are also sensitive to background from thermal neutrons as described inChapter5, Section5.4.6. A considerable impact on the trigger rates is however only expectedin the RPC Trigger which is currently being upgraded to improve rejection of this type ofbackground. Parameterizations for this long–time pile–up exist but but were not enabled due toexcessive CPU time spent on digitizing a large number of random hits.

The simulation of the GMT electronics in ORCA was used extensively to study differentscenarios of GMT algorithms. During the course of the project it was extended and updatedaccording to the evolution of the hardware design. The results in Chapter9 are based onORCA 6.2.3 with several updates that will be included as a default in later releases of ORCA:• wider matching windows as described in Chapter6, Section6.3.• new cancel–out units as described in Chapter6, Section6.4.• optimized combined merging ofpT measurements based on minimumpT and merge rank

as described in Chapter6, Section6.9.3.• only very–low quality muons that are likely to be ghosts or noise disabled in the di–muon

trigger as described in Chapter6, Section6.6.• projection of theφ measurement from the muon system to the vertex as described in

Chapter6, Section6.8.• charge assignment taken from same candidate aspT as described in Chapter6, Sec-

tion 6.9.

All plots in this thesis were obtained using the ROOT framework with analysis code writtenin C++.

8.2 Samples of Single Muons

In order to study the performance of the trigger algorithms independent of a particular signal,two general single-muon samples have been generated. They contain muons that originatefrom the nominal interaction point and cover a range of transverse momenta that ranges fromthe lowest that can reach the muon system up to very high at which tracks essentially “look”straight to the L1 muon triggers. In the first sample momenta are distributed uniformly while thesecond sample contains muons peaked at low momenta. Both samples include equal amounts ofpositively and negatively charged muons and cover the entire acceptance region:0 < φ ≤ 2π,−2.4 < η < 2.4.

105 events with uniformly distributed transverse momentum ranging from 2.5 GeV/c up to100 GeV/c were generated in the first single muon sample. It was used for studies of efficiency,ghosting probability,pT resolution, and charge assignment.

2 × 105 events with apT distribution proportional to1/pT were generated in the secondsample. The lower threshold of muon transverse momentum has been set low enough to includeall muons that can possibly cause a trigger and depends on pseudorapidity (see Table8.3). Thesame threshold as for the minimum bias “pt1” sample described in Section8.4 was applied.This second single muon sample was used for studies of the trigger behavior at lowpT and inorder to compute the projection look–up–tables to extrapolate muons from the muon system tothe vertex (see Chapter6, Sections6.7and6.8).



8.3 Signal Samples

In order to demonstrate the trigger efficiencies for real processes from among the physicsgoals, a number of signal samples have been generated [46] using PYTHIA 6.158 with pa-rameters listed in Table8.1. TheW , Z/γ∗, tt and Higgs samples contain high–pT muons andare efficiently triggered by a single–muon trigger. The samples ofB0

S decays were generatedaccording to a dedicated procedure [47]. They result in low–pT muons and were used as abenchmark of the di–muon trigger which operates at lower thresholds (see Chapter9).

TheW andZ/γ∗ samples are also considered in the simulation of trigger rates (see Sec-tion 8.4), while the other signals with much smaller cross-sections only give negligible contri-butions to the trigger rates.

Table 8.1: Signal samples produced for efficiency studies.σgen is the cross-section of the generatedprocess,σsel, the cross–section of events that fall into the kinematic acceptance,Nsel the number ofselected events in the sample, andIint the integrated luminosity.tLHC is the running time of the sampleat high LHC luminosityL = 1034 cm−2s−1 (1 LHC–year = 100 fb−1). In the filteredZ sample thefollowing invariant mass cut was used to select realZ bosons:86 GeV/c2 < minv < 96 GeV/c2.

signal kinematic range σgen σsel Nsel Iint tLHC

inclusiveZ/γ∗ pµT ≥ 3 GeV/c, |ηµ| < 2.5 1.00µb 22.0 nb50000 2262 nb−1 3.8 min

Z → 2µ (filtered) pµT ≥ 3 GeV/c, |ηµ| < 2.5 1.00µb 0.625 nb 1414 2262 nb−1 3.8 min

inclusiveW pµT ≥ 3 GeV/c, |ηµ| < 2.5 0.185µb 16.2 nb50000 3162 nb−1 5.2 min

W → µν (filtered) pµT ≥ 3 GeV/c, |ηµ| < 2.1 0.185µb 10.5 nb33043 3162 nb−1 5.2 min

tt→ µ+X pµT ≥ 3 GeV/c, |ηµ| < 2.5 0.624 nb 0.270 nb20000 0.0741 fb−1 2.1 h

tt→W→µν +X (filtered) pµT ≥ 3 GeV/c, |ηµ| < 2.1 0.624 nb 0.105 nb 7759 0.0741 fb−1 2.1 h

H(120)→WW → 2µ2ν pµT ≥ 3 GeV/c, |ηµ| < 2.5 36.3 fb 26.8 fb 10000 373 fb−1 3.7 yr

H(160)→WW → 2µ2ν ” 182 fb 143 fb 10000 69.8 fb−1 0.7 yr

H(200)→WW → 2µ2ν ” 104 fb 83.1 fb 10000 120 fb−1 1.2 yr

H(130)→ ZZ∗ → 4µ ” 0.90 fb 0.53 fb 100001.87× 104 fb−1 187 yr

H(150)→ ZZ∗ → 4µ ” 1.69 fb 1.06 fb 10000 9473 fb−1 95 yr

H(200)→ ZZ → 4µ ” 3.45 fb 2.31 fb 10000 4331 fb−1 43 yr

pµT > 2 GeV/c, |ηµ| < 2.4B0s → J/ψ→µ+µ−φ→K+K− pKT > 0.5 GeV/c, |ηK | < 2.4

1.25 nb0.0963 nb11500 0.119 fb−1 3.3 h

B0s → µ+µ− pµT ≥ 2.5 GeV/c, |ηµ| < 2.5 396 fb 95 fb 10000 105 fb−1 1 yr

8.4 Monte–Carlo Generation for the Simulation of TriggerRates

For trigger rate studies, samples of Monte-Carlo generated events are necessary that includeall processes that can occur in inelastic interactions at LHC. Since no specific processes areselected in the generation of these events, such events are called “minimum bias” events. Muonspectra in minimum bias events are dropping rapidly with increasingpT and therefore very largesamples of completely unbiased events would be required in order to obtain enough statisticsof high–pT muons to be able to estimate trigger rates at highpT thresholds with reasonable


H. Sakulin

8.4 Monte–Carlo Generation for the Simulation of Trigger Rates 109

accuracy. An optimized procedure to generate minimum bias events in bins of muon-pT istherefore used as described in Section8.4.1. The resulting generated rates are presented inSection8.4.2. Section8.4.3discusses the treatment of pile–up events that occur in the samebunch crossing as the signal event or in neighboring bunch crossings. An analytic method totake into account trigger rates caused by muons in pile–up events is presented in Section8.4.4.Section8.4.5describes an alternative method to construct crossings from multiple minimumbias events that contain a muon and were generated in bins of muon–pT . Technical issues ofthis method are discussed in Section8.4.7. The resulting rates of generated crossings with atleast two muons are presented in Section8.4.8.

8.4.1 Production of Minimum Bias Events

Muons in minimum bias events come from two main sources:prompt muons from decaysof b- andc-quarks or heavy objects likeW orZ bosons andnon-promptmuons from pion/kaondecays. Minimum bias events were produced using PYTHIA 6.158 with parameters describedin [46]. Muon spectra in minimum bias events are dropping rapidly with increasingpT . Verylarge samples of completely unbiased events would therefore be required in order to obtainenough statistics of high–pT muons. In order to save disk space and computing time, the gener-ation of minimum bias events for muon trigger rates has been split into three bins of muon-pTas shown in Table8.2. The statistics of high-pT muons have been increased by generating moreintegrated luminosity for bins of higher muon-pT . The lowerpT threshold for muons in the firstbin depends on the detector and on pseudorapidity: it has been chosen low enough to includeall potentially triggering muons (see Table8.3). This is important since the rates of low–pTmuons are high (several MHz) and the trigger, especially at level–1, shows a certain probabilityto assign a highpT measurement to a muon of very lowpT . Among other causes, non–promptmuons from pion/kaon decays and multiple scattering are responsible for this “feed–through”effect in the trigger.

Table 8.2: Minimum bias samples produced for trigger rate studies. CMS 2002 Monte–Carlo production.For the generation cutpcutT (η) in the “pt1” sample, see Table8.3. pT,cut is the minimum acceptedtransverse momentum of the underlying hard process at parton level.σj,gen is the generated cross sectionfor the sample,σj the cross section for the kinematic acceptance range (after skipping pions/kaons thatinteracted hadronically with the detector in the CMSIM step).Nev is the number or events that fall intothe accepted kinematic range ( also after CMSIM) andw the average weight of these events.s is the lossof statistical significance due to weight fluctuations as given by Equation8.2. The equivalent integratedluminosityIeqint is given by Equation8.1. rj is the factor by which the equivalent integrated luminositywas increased for higherpT bins with respect to the first bin as given by Equation8.3.

j Name pT -range / GeV/c pT,cut σj,gen σj Nev Iint w s Ieqint rj

( GeV/c ) ( mb ) ( mb ) ( nb−1 ) ( nb−1 )

1 pt1 pcutT (η) ≤ pT < 4 0 55.22 0.685 146× 103 0.0246 0.116 1.13 0.187 1

2 pt4 4 ≤ pT < 10 0 55.22 0.0251 248× 103 0.991 0.100 1.01 9.78 52.4

3 pt10 pT ≥ 10 10 2.66 0.000706 87× 103 11.4 0.093 1.11 111 596

A cut on minimum accepted transverse momentum of the underlying hard process at partonlevel, pT , was used in the “pt10” sample in order to speed up event generation. The resulting



Table 8.3: Minimum generatedpT or p of muons that can possible cause a trigger as a function of pseu-dorapidity (pcutT (η)). Used for the generation of the “pt1” sample. CMS 2002 Monte–Carlo production.

Pseudorapidity range Minimum pT or p

0.0 ≤ |η| < 1.2 pT ≥ 3.0 GeV/c

1.2 ≤ |η| < 1.7 pT ≥ 1.8 GeV/c

1.7 ≤ |η| p ≥ 3.5 GeV/c

increase in the light flavor component of the “‘pt10” sample has been accounted for with anormalization factor, which is applied only to the light flavor component of the sample.

A weighting technique has been used to speed up the generation of events [46]. Withoutweighting, the full integrated luminosity of unbiased events would have to be generated, ac-cepting only a small fraction of events that contain muons falling into the kinematic region ofthe respective bin. Using the weighting technique, possible parents of muons are forced to decayinto muons inside the kinematic region of the corresponding bin and the probability for such adecay to happen is assigned as an event weight. Only a small nominal integrated luminosityIinthas to be generated but the sample actually corresponds to a much larger equivalent integratedluminosityIeqint, given by

Ieqint =Iintws

, (8.1)

wherew is the average event weight in the sample ands is a factor that accounts for the lossof statistical significance due to fluctuating weights with respect to an unweighted sample. It isgiven by

s =1Nev

∑(w2)

( 1Nev

∑w)2

=w2

w2 , (8.2)

whereNev is the number of events in the sample andw are the event weights. In a weightedsample, a factors more events are needed to obtain the same error on trigger rates as in the caseof unweighted events.

The fluctuation of weights in the minimum bias samples has been reduced by two additionalsteps: events with small weights were down–scaled [46] and big weights ofb- and c-quarkprocesses were reduced by producing 10 times the integrated luminosity and scaling the weightsby a factor of 0.1. This procedure results in weighted samples with fairly constant weights ands ≈ 1.

A factor rj can be defined for each sample indicating the increase in equivalent integratedluminosity with respect to the first sample:

rj =Ieq,(j)int

Ieq,(1)int

. (8.3)

To ensure that the bins are non-overlapping, events with muons outside the bin’s kinematicrange have been skipped in the analysis. Production of heavy objects was not included in thethree minimum bias samples. TheW andZ samples discussed in Section8.3 were thereforeseparately added in the analysis of trigger rates. The cross–sections for the production of otherheavy objects are so small that their contribution to the trigger rates can be neglected (seeFigure2.1).


H. Sakulin


(GeV/c)µTp

0 10 20 30 40 50 60 70 80

(nb/

GeV

)µ T

/dp

σd

10-4

10-3

10-2

10-1

1

10

102

103

104

105

106

> 1 GeVµT > 0 GeV , pTpMB :



> 3 GeVµT+X : pµ→W

> 3 GeVµT+X : pµ→*γZ/

> 3 GeVµT+X : pµ→tt

Figure 8.2: Differential cross section with respect topµT of the three minimum bias samples and theW ,Z andtt samples. Limited to|η| < 2.1.

Decays of long–lived pions and kaons are normally treated in CMSIM. In order to includethese decays in the above event weighting procedure, these decays have been simulated inPYTHIA instead. A decay vertex is chosen in PYTHIA along the pion/kaon trajectory ac-cording to the expected exponential decay length distribution. Since PYTHIA does not includematerial effects, an additional step is necessary at CMSIM level: pions/kaons are simulatedagain in CMSIM and if they interact with the material before reaching the decay vertex chosenby PYTHIA, the respective event is skipped.

It has to be noted that the above method of binned production does not include triggers dueto punch–through or neutron background in beam crossings that do not contain a muon that canreach the muon system. Separate studies have shown the first effect to have negligible impacton the trigger, while the second effect is expected to have an impact only on the Level–1 RPCTrigger which is currently being upgraded to improve rejection of this type of background.

8.4.2 Generated Rates

Figure8.2shows the differential cross–sections with respect topµT of muons from the threesamples of minimum bias events and theW , Z andtt samples. The resulting integrated ratesof single muons as a function ofpµT threshold are shown in Figure8.3 for the high luminosityscenario (L = 1034 cm−2s−1). The muons are restricted to the reduced trigger acceptance of|η| < 2.1. The contributions according to muon parents are shown. The single muon rates aredominated by non–prompt muons from decays of pions and kaons up to about 8 GeV/c. Aboveand up to about 25 GeV/c, prompt muons fromb andc quark decays dominate the rates. Muonsfrom decays ofW andZ only become important at higher transverse momenta.



threshold (GeV/c)µTp

0 10 20 30 40 50 60 70 80

Rat

e (H

z)

10-2

10-1

1

10

102

103

104

105

106

total±π/± K

L0 K

c bτ

± W*γ/0 Z

Figure 8.3: Integrated muon rates at generator level per muon parent for the three minimum bias samples,and theW andZ samples. High luminosityL = 1034 cm−2s−1 (1 nb

∧= 10 Hz). Limited to|η| < 2.1.

8.4.3 Treatment of Pile–Up

As discussed in Chapter2, Section2.3, at the LHC the total inelastic cross-section is ex-pected to beσT = 55.22 mb. The LHC will operate at a bunch crossing rate of 40 MHz. Only79.5 % of the bunch crossings will be usable, resulting in an effective bunch crossing rate of

Reffbx = 32 MHz. (8.4)

The average numberµ of interactions (in the following also called events) per bunch cross-ing is given by

µ =RHz

Reffbx

=σTLReffbx

. (8.5)

µ = 17.3 events per beam crossing in the high luminosity scenario (L = 1034 cm−2s−1) andµ = 3.5 events per beam crossing in the low luminosity scenario (L = 2× 1033 cm−2s−1).

In order to simulate a realistic trigger response under these conditions, pile–up events haveto be added to the signal and minimum–bias events. Due to the time structure of 25 ns betweentwo bunches, some of the sub-detectors integrate over pile–up events produced before and afterthe signal crossing. The number of bunches to be taken into account is determined by theslowest sub-detector, in the case of CMS the calorimeters (which are used in studies of muonisolation). In order to simulate their response correctly, a window of 9 bunch crossings has to beopened [48], including five crossings preceding the signal crossing and 3 crossings following it.The same window is also opened in the digitization of the CSC System, since the CSC Triggercan be affected by out–of–time pile–up. Due to the good timing resolution and bunch–crossing


H. Sakulin


identification capabilities of the DT and RPC Triggers, the effect of out–of–time pile–up isestimated to be small and only in–time pile–up was digitized for these detectors.

An average of9× 17.3 = 156 pile–up events therefore have to be piled up in each crossingat high luminosity. An additional sample of106 completely unbiased events was generated to beused for this purpose. Due to limitations of resources, the pile–up events have to be “recycled”,so that each pile–up event is used many times in the digitization of the minimum bias samples.However, since events in the minimum bias samples are forced to contain muons (see Sec-tion 8.4.1), adding unbiased events that may contain a muon would cause an artificial increasein di–muon rate. Moreover, the di–muon rates would be biased due to multiple occurrence offew triggering pile–up events. Muons in the pile–up sample therefore were filtered (using thecutspT > 1 GeV/c in |η| < 2.0 andp > 3 GeV/c in 2.0 ≤ |η| < 2.5) and their contribution tothe di–muon rate was taken into account, separately, using one of the two methods discussed inthe following [49]:• The trigger response can be simulated, for single minimum bias events containing muons

and the effect of piling up multiple events of this kind in a beam crossing can be takeninto account, analytically. This method neglects interference effects of particles of multi-ple events but otherwise gives exact results. The muon detectors are highly granular andthe resulting occupancy of chambers is small. To a first order approximation, the muontrigger objects created by muons from multiple events in a beam crossing can thereforebe considered independent. Section8.4.4discusses how this method can be applied toobtain single muon trigger rates and di-muon trigger rates with symmetric and asymmet-ric trigger thresholds. The method was used to obtain (small) corrections to the di–muontrigger rates in the low luminosity scenario.• Alternatively, bunch crossings can be constructed by superimposing multiple minimum

bias events that contain muons as they will occur at the LHC and simulating the trig-ger response for these beam crossings. This approach implicitly includes all interferenceeffects of particles from multiple events in the trigger. It can also be used to study trig-ger rates for complicated trigger conditions such as topological multi-object triggers orhigh–level trigger conditions based on the positions of vertices or reconstructed invariantmasses. A method was developed to construct bunch crossings by piling up weightedevents generated in bins of muonpT (see Section8.4.1). It is presented in Section8.4.5.

8.4.4 Analytic Method to Treat Pile–Up with Muons

8.4.4.1 Obtaining Trigger Probabilities from the Minimum Bias Samples

In order to obtain trigger rates analytically, the probability that a certain trigger condition isfulfilled by a random event is of interest. This trigger probability can be obtained from samplesof minimum bias events. The simplest case is a sample of completely unbiased events withintegrated luminosityIint. Such a sample contains a total number ofNT = σT × Iint events,whereσT = 55.22 mb is the total inelastic cross-section at LHC. The trigger probabilityptrigcan be obtained by counting the number of eventsNtrig that fulfill the trigger condition ofinterest:

ptrig =Ntrig

NT

=Ntrig

σT × Iint. (8.6)

If the production is binned inN bins of muon–pT as explained in Section8.4.1and if eventweighting is used, then the probabilityp(j)

trig, that a random event comes from binj and



fulfills the trigger condition is given by

p(j)trig =

triggered events∑i

w(j)i

σT × I(j)int

, (8.7)

wherew(j)i are the event weights in samplej andI(j)

int is the (nominal) integrated luminosity ofsamplej. The total trigger probabilityptrig is the sum of the contributions from the samplesj

ptrig =N∑j=1

p(j)trig. (8.8)

8.4.4.2 Single Muon Trigger Rates

First the probabilityptrig,1 that a random single event triggers a single muon trigger con-dition with a certainpT -threshold has to be evaluated. This is done as described in the previ-ous section using the condition that the event contains one or more muon trigger objects withptrigT ≥ pthresholdT . The probability that in a collection ofn events at least one fulfills the triggercondition is then given by by1− (1− ptrig,1)n. The probability for a crossing to have exactlynevents is given by the Poissonian distributionP (n;µ) = e−µ µ

n

n!whereµ is the mean number of

events per crossing. The overall fractionF of crossings that fulfill the trigger condition is thengiven by [50]

F =∞∑n=0

e−µµn

n![1− (1− ptrig,1)n] = 1− e−ptrig,1µ = ptrig,1µ+O((ptrig,1µ)2). (8.9)

The trigger rate is then given by

Rtrig,1 = Reffbx × F. (8.10)

Since the typical trigger rates of interest are much smaller than the total rate of inelasticevents hitting the detector, the trigger probabilities usually are very small, so thatptrig,1µ� 1.In this case the probability that a crossing fulfills the trigger condition becomesF ≈ ptrig,1µ.This approximation is commonly used in analysis code. It should be noted that in this casethe trigger rate is proportional to the trigger probability per eventptrig,1. If multiple samplescontribute to the trigger rate this allows to calculate the trigger rates separately for each sampleand to later add them to obtain the total trigger rate, which is common practice in analysis code.

8.4.4.3 Di-Muon Trigger Rates with Symmetric Thresholds

For di-muon trigger rates two contributions have to be considered: firstly, the crossings thatare triggered by two muons (or a muon and a ghost) coming from a single event and secondly,the crossings that are triggered by two muons from different events inside the crossing.

The first contribution is obtained in analogy to the single muon trigger rate in Sec-tion 8.4.4.2. Instead of measuring the probability to trigger a single muon trigger condition, theprobabilityptrig,2 that a random event fulfills a di-muon trigger condition withpT,1,2 ≥ pthresholdT

has to be evaluated. The fractionF2 of crossings that contain one or more events that trigger the


H. Sakulin


di-muon condition can then be obtained in analogy to Equation8.9. It includes all crossings inwhich two muon trigger objects from one event fulfill the trigger condition, whether it was tworeal muons or only one muon and a ghost:

F2 =∞∑n=0

e−µµn

n![1− (1− ptrig,2)n] = 1− e−ptrig,2µ = ptrig,2µ+O((ptrig,2µ)2). (8.11)

In order to compute the second contribution, the probabilityptrig,≡1 that in one event exactlyone muon trigger object has apT greater or equal to the (symmetric) trigger threshold has to beobtained as described in Section8.4.4.1. Events in which more than one muon trigger object isabove the threshold have to be rejected since these are already counted in the first contribution.The fraction of crossingsF2,mix in which at least two events have exactly one muon triggerobject withptrigT ≥ pthresholdT can be obtained in analogy to the single muon trigger case:

F2,mix =∞∑n=0

e−µµn

n![1− (1− ptrig,≡1)n − nptrig,≡1(1− ptrig,≡1)n−1] =

= 1− e−ptrig,≡1µ − ptrig,≡1µe−ptrig,≡1µ =

p2trig,≡1µ

2

2+O(p3

trig,≡1µ3). (8.12)

The trigger rate is then easily obtained by summing the two independent fractionsF2 andF2,mix of bunch crossings that fulfill the trigger condition and multiplying by the bunch crossingrate:

Rtrig,2 = Reffbx × (F2 + F2,mix). (8.13)

The contributionF2,mix from two muons from different events in the same bunch crossingis roughly proportional to the square of the average number of events per bunch crossingµ, i.e.it grows with the square of the LHC luminosity.

In order to calculate the combined rate from a single and a di-muon trigger condition, it isinteresting to know the rate of di-muon triggers which are only triggered by a di-muon triggercondition and not at the same time by the single muon trigger condition with a higher thresholdpSMUT . To obtain this “exclusive” di-muon trigger rate, events that contain a muon trigger object

with a ptrigT ≥ pSMUT have to be excluded when evaluating the trigger probabilities for both

contributions to the di-muon trigger rates. The rest of the procedure remains the same as above.

8.4.4.4 Di-Muon Trigger Rates with Asymmetric Thresholds

As in the case of symmetric thresholds, two contributions to the trigger rates have to be con-sidered. The contribution from two muon trigger objects coming from one event is calculatedas before with the only difference that now an asymmetric trigger condition has to be applied tothe trigger objects. The trigger probability per bunch crossingF2 is obtained as for the case ofsymmetric trigger thresholds using Equation8.11.

The second contribution of two muons from different events in the same bunch crossing isa little more complicated to obtain than before: there are two classes of events that do not bythemselves trigger a di-muon trigger condition but can conspire to fulfill the trigger condition ifthey appear in the same bunch crossing. The first class (A) contains exactly one muon candidateabove the higher trigger threshold but none between the lower and the higher thresholds. There



can be any number of muon candidates below the lower trigger threshold. The probabilitypAfor a random event to fall into this class can be determined according to Section8.4.4.1. Thesecond class (B) of events contains one or more muon candidates with apT between the twothresholds but none with apT above the higher threshold. Again the event may have any numberof muon candidates below the lower threshold. Its probabilitypB is also determined accordingto Section8.4.4.1.

The probability that in a collection ofn events the di-muon trigger condition is fulfilled by acombination of events from class A and/or B is given by1− (1− pA)n−npA(1− pA− pB)n−1.In other words, there are two configurations that do not trigger the di-muon trigger condition: aconfiguration with no event of class A in the bunch crossing and a configuration with exactly oneevent of class A but all the other events neither from class A nor from class B. The probabilityper bunch crossingF2,mix is then given by

F2,mix =∞∑n=0

e−µµn

n![1− (1− pA)n − npA(1− pA − pB)n−1] =

= 1− e−pAµ − pAµe−(pA+pB)µ =p2Aµ

2

2+ pApBµ

2 +O(p3µ3). (8.14)

The overall di-muon trigger rates are again given by Equation8.13. “Exclusive” di-muontrigger rates can be obtained as for the case of symmetric thresholds: events that also triggera single muon trigger have to be excluded when the trigger probabilitiesptrig,2 and pA areevaluated. The definition ofpB remains the same if a single muon trigger threshold higher thanthe di-muon trigger thresholds is assumed.

8.4.5 Piling up Single Events with Muons to Form Bunch Crossings

Constructing a sample of bunch crossings by overlaying multiple events as they will occur atLHC and simulating the trigger response on a bunch crossing basis is the most straightforwardway to obtain trigger rates in the presence of pile-up. It implicitly includes all interferenceeffects in the trigger between close particles from different events in the same bunch crossingand it can be used to obtain trigger rates for any kind of multi-object trigger condition includingtopological conditions.

Since muon spectra in minimum bias are dropping rapidly with increasingpT , constructingthese crossings from completely unbiased events would require a huge number (O(108 . . . 109))of events to be generated in order to get enough statistics at higher trigger thresholds. Anenormous reduction in the required computing time and disk space can be achieved if singleevents are produced in bins of muon–pT as explained in Section8.4.1 and then piled up toform crossings. However, this makes the procedure for piling up events more complicated, asdiscussed in the following.

If a binned production is used, a crossing no longer is made up fromn random events.Instead, it belongs to a configuration~k = (k1, k2, . . . , kj, . . .) with k1 events from sample 1,k2

events from sample 2 and so forth. The crossing then containsk =∑

j kj events with at leastone muon in the final state. Additionally, an average ofµ events without muons that can reachthe detector are superimposed onto each crossing as explained in Section8.4.6.

The procedure to generate an optimized sample of beam crossings from the samples ofsingle events binned in muon–pT includes the following main steps:


H. Sakulin


• Crossings of configurations~k are produced according to the probabilities of the configu-rations in a sample of completely unbiased crossings by overlaying random events fromthe samplesj.• The event weights are taken into account by defining a crossing weight proportional to

the product of event weights.• The number of crossings that contain muons from higherpT bins is increased.• The number of crossings in configurations that suffer from loss of statistical significance

due to fluctuating weights is increased to compensate for the loss of significance.• High order configurations are skipped on the basis of their contribution to the trigger

rates.

The probabilityP~k that a random unbiased crossing with an average ofµ events is of type~kis given by the product of the Poissonian probabilities to get exactlykj events from samplesjin the crossing:

P~k =N∏j=1

P (kj; p(j)genµ) =

N∏j=1

e−p(j)genµ

(p(j)genµ)kj

kj!. (8.15)

p(j)gen is the probability that a random generated event falls into the kinematic range of samplej.

It is given by

p(j)gen =

σjσT

=

all events in kinematic region∑i

w(j)i

σT × I(j)int

, (8.16)

whereσj is the cross–section of events with muons in the kinematic region of samplej as givenin Table8.2. The samplesj correspond to non-overlapping bins in muon–pT by definition. Ifevents in a sample contain muons with apT outside the sample’s nominal range they have to beexcluded from the summation.

In order to produce a crossing of configuration~k, kj random events are chosen from each ofthe samplesj and overlaid. Care has to be taken that each event in the samplesj is only usedonce. In order to take into account the event weights of the events in the samplesj, a bunch

crossing weightw(~k)bx,i is defined proportional to the product of the weights of the contributing

events:

w(~k)bx,i =

w(~k)prod,bx,i

w(~k)prod,bx

with w(~k)prod,bx,i =

all events in crossing∏wevent. (8.17)

The crossing weight is normalized to the average product of event weights in crossings of type~k which can be pre-determined.

A valid sample of crossings could be built by choosing configurations according toP~k andfollowing the procedure outlined above. Two more steps are however introduced to improve thestatistical performance of the generated sample.

As explained in Section8.4.1, the production was binned in bins of muon–pT in order toincrease statistics for bins with higher muon–pT . The equivalent integrated luminosity of binsjwas increased by a factorrj with respect to the equivalent integrated luminosity of the first bin.The factorsrj have been optimized in order to study trigger rates at higher thresholds both atlevel–1 and at higher trigger levels. In order to increase statistics at higherpT thresholds in the



same way also for multi-muon triggers the statistics for crossings of type~k can be increased bya factorr~k given by:

r~k =N∏j=1

rkjj . (8.18)

The fluctuation of crossing weights in the subset of crossings with configuration~k increaseswith the number of eventsk in the crossing. As discussed in Section8.4.1the weight fluctua-tions cause a loss of statistical significance with respect to an unweighted sample. In analogyto Section8.4.1, a factors~k quantifies this loss of significance:

s~k =1Nev

∑w2bx,i

( 1Nev

∑wbx,i)2

=w2bx,i

wbx,i2 . (8.19)

In order to compensate for this loss of statistical significance, it is proposed to increase theproduction of crossings of type~k by a the factors~k.

The numberN (~k)bx of crossings of type~k to be produced for an integrated luminosityIint is

then given by

N(~k)bx = IintσT

1

µP~ks~kr~k. (8.20)

The event weights have to be scaled in order to take into account the two factors used toincrease statistics. The new event weights are then given by

w′(~k)bx,i =

w(~k)bx,i

s~kr~k. (8.21)

The trigger rates are easily obtained by summing the weights of the bunch crossings thatpass a certain trigger condition. Any trigger condition including topological trigger conditionscan be applied.

Rtrig = Reffbx

triggered crossings∑i

w′(~k)bx,i

Iint × σT × 1µ

. (8.22)

Theoretically, all possible configurations~k would have to be included in the sample of cross-ings. For all practical purposes, only configurations that give a certain minimum contributionto the trigger rates are of interest. Neglecting the interference of muons from different eventsin the same crossing in the formation of trigger objects, the contribution of crossings of type~kto the trigger rate can be estimated using simple combinatorics. The contribution of crossing oftype~k to the single muon trigger rate is

R(~k)trig,SMU = Reff

bx P~k

(1−

N∏j=1

(1− f (j)trig)

kj

), (8.23)

wheref (j)trig is the probability that an event in binj causes a trigger. It is given by

f(j)trig = p

(j)trig/p

(j)gen, (8.24)


H. Sakulin


with p(j)trig from Equation8.7andp(j)

gen from Equation8.16. The contribution of crossings of type~k to the part of the di–muon trigger rate that is caused by two muons from the same event canalso be obtained from Equation8.23, using the di-muon trigger as a condition.

The contribution of crossings of type~k to the part of the di–muon trigger rate (symmetricthresholds) that is caused by two muons from different events in the same crossing, is given by

R(~k)trig,DMUmix = Reff

bx P~k

[1−

(1 +

N∑j=1

kjf(j)trig

1− f (j)trig

)

)N∏j=1

(1− f (j)trig)

kj

]. (8.25)

Table8.4 lists the contributions of various configurations~k of bunch crossings to a singlemuon trigger at level–1 with a threshold of 20 GeV/c and to the two parts of the trigger rate ofa symmetric di-muon trigger (also at level–1) with a threshold of 4 GeV/c. Only configurationsthat contribute at least 0.1 Hz to any of the rates are listed. Based on the contributions to thetrigger rates the configurations marked with “Y” were included in the sample of crossings. Ingeneral all crossings that contribute at least 1 Hz to any of the trigger rates were included.

However, since the integrated luminosities of the available samples were optimized mainlyfor the study of trigger rates at higher trigger levels, the statistical performance at level–1 isnot optimal. Available statistics in the first sample (“pt1”) are limited since this sample onlygives small contributions at higher trigger levels due to betterpT resolution and higher expectedtrigger thresholds. The expected numbers of triggered events are thus very small in crossingscontaining multiple events form this sample resulting in rather large statistical errors on theexpected trigger rate contributions at level–1. Crossings with four or more events from the“pt1” sample were therefore not included in the sample of crossings.

8.4.6 Adding Pile-Up Without Muons

After overlaying a number of events with at least one muon that can reach the muon system,additional events without muons are piled up to form full bunch crossings. The average numberof events that has to be piled up depends on the average multiplicity in bunch crossings of theconfiguration under consideration. The average multiplicity in bunch crossings that contain arare type of event was investigated in [50].

In a similar way the average multiplicity in bunch crossings of a certain configuration~k canbe determined:

First, the probability to have a bunch crossing made up ofn events out of which exactlykpass the generator cut is considered. It is given by

Pn and exactlyk with a muon = P (n;µ)Cn,kpkgen(1− pgen)n−k =

= e−µµn

n!

n!

k!(n− k)!pkgen(1− pgen)n−k =

=(µpgen)k

k!e−µpgenP (n− k;µ(1− pgen)), (8.26)

wherepgen is the probability that a random generated event contains a muon that can possiblycause a trigger.



Table 8.4: Configurations~k and their estimated contributions to the Level–1 trigger rates at typicalthresholds (all trigger rates for|η| < 2.1). High luminosityL = 1034 cm−2s−1. Only configurations thatcontribute at least 0.1 Hz to any of the trigger rates are shown. Configurations that have been includedin the generation of the sample of crossings are marked with “Y”. Numbers of events are based on anintegrated luminosity ofIint = 0.107 nb−1.k1, k2, k3: number of events from the “pt1”, “pt4” and “pt10” samples in the crossing.

P~k: probability to get the configuration~k in an unbiased sample.

r~k: factor to increase the statistics of high-pT muons.

s~k: loss of statistical significance due to fluctuations of crossing weights.

w(~k)bx,prod: average product of event weights.

w′: average weight in the mixed sample.

N(~k)bx : number of crossings to be produced for an integrated luminosity ofIint = 0.107 nb−1.

RSMU : contribution to a single muon trigger with a threshold of 20 GeV/c

according to Equation8.23.

RmixDMU : contribution to the part of the di-muon trigger rate with symmetric threshold of 4 GeV/c,

that is caused by two muons from different events, according to Equation8.25.

RDMU : contribution to the part of the di-muon trigger rate with symmetric threshold of 4 GeV/c,

that is caused by two muons from the same event according to Equation8.23.

nSMU , nmixDMU , nDMU : expected numbers of triggered crossings assuming constant crossing weight

corresponding toRSMU ,RmixDMU andRDMU .

Nmix: events actually generated.

k1 k2 k3 P~k r~k s~k w(~k)bx,prod w′ N

(~k)bx nSMU RSMU nmixDMU RmixDMU nDMU RDMU incl Nmix

(Hz) (Hz) (Hz)

1 1.76E-011.00E+001.14 1.16E-018.79E-01 68478 9.8 802.2 0.0 0.0 5.1 419.2 Y 68477

1 6.27E-035.24E+011.01 1.00E-011.89E-02113604 1562.6 2752.7 0.0 0.0 655.3 1154.3 Y 113604

1 1.76E-045.96E+021.11 9.28E-021.52E-03 39703 10777.0 0.0 0.0 1160.5 1160.5 Y 39603

2 1.94E-021.00E+001.30 1.34E-027.69E-01 8650 2.5 177.3 9.6 688.8 1.3 92.6 Y 8573

1 1 1.39E-035.24E+011.15 1.16E-021.66E-02 28528 396.4 614.6 711.3 1102. 166.7 258.4 Y 28435

1 1 3.88E-055.96E+021.23 1.08E-021.37E-03 9739 2644.5 336.7 270.3 34.4 285.4 36.3 Y 9929

2 2.47E-052.74E+031.02 1.01E-023.57E-04 23710 647.8 21.6 13263.8 441.3 272.7 9.1 Y 23456

1 1 1.39E-063.12E+041.12 9.30E-032.86E-05 16608 4674.6 12.5 10342.1 27.5 578.5 1.5 Y 16463

2 1.94E-083.56E+051.19 8.61E-032.36E-06 2825 1325.3 0.3 1957.9 0.4 162.7 0.0 Y 2828

3 1.43E-031.00E+001.47 1.56E-036.81E-01 720 0.3 19.6 2.3 148.8 0.2 10.2 Y 694

2 1 1.53E-045.24E+011.30 1.35E-031.47E-02 3558 50.0 68.6 175.5 241.0 21.1 28.9 Y 3732

2 1 4.29E-065.96E+021.40 1.25E-031.20E-03 1228 333.6 37.2 67.3 7.5 36.1 4.0 Y 1221

1 2 5.46E-062.74E+031.17 1.16E-033.13E-04 5977 164.1 4.8 3418.7 99.7 69.2 2.0 Y 6035

1 1 1 3.06E-073.12E+041.25 1.08E-032.57E-05 4087 1150.7 2.8 2590.6 6.2 142.6 0.3 Y 4083

1 2 4.29E-093.56E+051.36 9.96E-042.07E-06 710 333.1 0.1 498.6 0.1 40.9 0.0

3 6.50E-081.44E+051.03 1.01E-036.75E-06 3294 134.1 0.1 2771.7 1.7 56.7 0.0 Y 3264

2 1 5.46E-091.64E+061.13 9.35E-055.40E-07 3463 1008.9 0.1 3024.3 0.2 139.9 0.0

1 2 1.53E-101.86E+071.23 8.63E-044.36E-08 1203 573.5 0.0 1085.2 0.0 75.9 0.0

3 1.43E-122.12E+081.30 7.99E-043.63E-09 135 82.9 0.0 125.1 0.0 11.5 0.0

4 7.90E-051.00E+001.67 1.80E-045.99E-01 45 0.0 1.4 0.3 16.1 0.0 0.8

3 1 1.13E-055.24E+011.49 1.56E-041.28E-02 302 4.3 5.1 22.1 26.3 1.8 2.2 Y 287

3 1 3.16E-075.96E+021.53 1.44E-041.10E-03 98 26.8 2.7 8.0 0.8 2.9 0.3 Y 118

2 2 6.04E-072.74E+031.32 1.35E-042.76E-04 748 20.7 0.5 437.2 11.3 8.7 0.2 Y 732

2 1 1 3.38E-083.12E+041.44 1.25E-042.22E-05 522 147.0 0.3 336.5 0.7 18.3 0.0 Y 566

2 2 4.74E-103.56E+051.65 1.16E-041.71E-06 95 44.7 0.0 67.7 0.0 5.5 0.0

1 3 1.44E-081.44E+051.17 1.17E-045.94E-06 827 33.8 0.0 700.2 0.4 14.3 0.0

5 3.49E-061.00E+001.90 2.10E-055.26E-01 2 0.0 0.1 0.0 1.2 0.0 0.0

4 1 6.23E-075.24E+011.73 1.81E-051.10E-02 19 0.3 0.3 1.9 1.9 0.1 0.1

4 1 1.75E-085.96E+021.71 1.67E-059.80E-04 6 1.7 0.2 0.7 0.1 0.2 0.0

3 2 4.45E-082.74E+031.50 1.57E-052.43E-04 63 1.7 0.0 37.3 0.8 0.7 0.0


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pgen is given by the sum of the probabilitiesp(j)gen for the samplesj from Equation8.16:

pgen =N∑j=1

p(j)gen. (8.27)

.The mean multiplicityn in bunch crossings with exactly k events that pass the generator cut

is then given by

n =

∞∑n=k

nPn and exactlyk with a muon∞∑n=k

Pn and exactlyk with a muon

=∞∑n=k

nP (n− k;µ(1− pgen)) =

=∞∑n=0

(n+ k)P (n;µ(1− pgen)) = k + µ(1− pgen). (8.28)

Since the crossing already containsk events with muons, the average number of additionalevents without muons to be piled up isnpile−up = µ(1−pgen). The distribution of the number ofpile-up events is Poissonian. It is an interesting result that the number of additional events thathave to be piled up is independent of the configuration of the crossing. Table8.5 summarizesthe mean multiplicities in bunch crossings of various configurations for high and low LHCluminosity and the number of events that have to be piled up to these crossings.

Table 8.5: Mean multiplicities in bunch crossings of various configurations and number of events thathave to be piled up (pgen = 0.0132, CMS 2002 Monte–Carlo production).

high luminosityL = 1034 cm−2s−1 low luminosityL = 2× 1033 cm−2s−1

configuration mean average # of events mean average # of events

of crossing multiplicity w/o muon to pile up multiplicity w/o muon to pile up

any 17.3(≡ µ) - 3.5(≡ µ) -

exactly 1 event with muons 18.1 17.1 4.5 3.5

exactly 2 events with muons 19.1 17.1 5.5 3.5



8.4.7 Technical Issues in the Mixing of Bunch Crossings

Figure8.4 shows a schematic view of the steps of the simulation of trigger rates. Previ-ously [51] it has only been possible to overlay events at the level of HEPEVT ntuples (theoutput of PYTHIA). The events with muons are overlaid and then treated like a single event inthe further processing steps. Pile–up without muons is added at the level of ORCA digitiza-tion with a constant average number of pile–up events according to a Poissonian distribution,which poses no problems since the number of additional pile–up events is independent of thenumber of events with muons in the crossing (see Section8.4.6). For each configuration~k one



would need to create a sample withN (~k)bx events according to Equation8.20, and bunch cross-

ing weightsw′(~k)bx according to Equation8.21. This approach however requires development of

new FORTRAN code and the handling of a large number of sub–samples, and it suffers fromsome other technical limitations like the maximum number of particles that can be stored in theHEPEVT ntuples which are the input to CMSIM.

Figure 8.4: Schematic view of the steps in the CMS Monte–Carlo production, where mixing is per-formed at the level of HEPEVT ntuples as done in previous productions. The “oohit” step convertsdetector hits from the output format of CMSIM (“fz files”) to an object–oriented database, while the“digi” step simulates detector response. The trigger is simulated in the “trig” step.

A different approach was therefore investigated: the number of samples that have to behandled can be reduced by mixing one big sample containing all the configurations~k in ran-dom order. Instead of handling different samples, only parts of the same sample have to behandled. The processing is further simplified if the events are overlaid in the proper place inthe digitization step of ORCA as suggested in [50]. A new Pile–Up Generator class has beendeveloped to perform this task. Figure8.5 illustrates the steps using this simplified procedure.The samples of single events are processed through CMSIM and up to the hit–formatting stepof ORCA. Bunch crossings are built from these events and from the additional pile–up eventswithout muons at the digitization step. This way of processing has several advantages. Firstly,with just one processing through CMSIM the single–event samples can serve a double purpose.They can be used for obtaining rates via the analytic method described in Section8.4.4and theycan be used at the same time to construct bunch crossings. Secondly, only new C++ code hadto be developed and no new FORTRAN code. Thirdly, events that are skipped in CMSIM, be-cause the parent of the muon (π orK) interacted hadronically before decaying into a muon, areautomatically excluded from the mixing. Finally, some technical problems such as exceedingthe maximum number of particles in the HEPEVT ntuples can be avoided. In the following,this new approach is detailed.

As a first step, the weights of the input samplesj have to be analyzed and the mixing ofcrossings has to be simulated for each crossing type~k in order to determine the average bunch


H. Sakulin


sample of

crossings

(digis)

��

Pile-Up generator

Figure 8.5: Schematic view of the steps in the Monte–Carlo production, where a new approach formixing at the level of digitization in ORCA is used. The “oohit” step converts detector hits from theoutput format of CMSIM (“fz files”) to an object–oriented database, while the “digi” step simulatesdetector response. The trigger is simulated in the “trig” step.

crossing weightsw(~k)prod,bx and the loss of statistical significance due to weight fluctuationss~k.

The fraction of crossingsP~k of type~k and the factorsr~k have to be determined.

After this analysis, and after deciding what configurations~k to include in the sample, thecrossings can be mixed. In order to be able to run ORCA digitization jobs in parallel, thecomposition of crossings is determined in this step only and written to a file which is later usedas a steering file for the ORCA jobs. For each bunch crossing the event numbers (actually,object IDs are used) of the events to be piled up and the resulting crossing weights are saved inthe file. For each crossing the following steps are performed:

• A configuration~k for the bunch crossing is randomly chosen according to the frequencyF~k to have such a crossing in the final sample

F~k =P~kr~ks~k∑

selected~kP~kr~ks~k

. (8.29)

• According to~k, kj random events are chosen from the samplesj and their numbers (orobject IDs) are written to the steering file. The events are marked as used to preventusing them again in other crossings. The bunch crossing weight is calculated accordingto Equation8.21and saved in the file.

As a third step the ORCA digitization is run including an new “Pile–Up Generator” Classthat reads in pile–up events from the samplesj according to the steering file prepared in theprevious step. The new “Pile–Up Generator” step has been made completely transparent, so thatit was possible to use the modified ORCA jobs in the standard CMS production environment.

It has to be noted, that the sub–samples corresponding to simple configurations that haveexactly one muon of a certain bin in the crossing (k = 1) are identical to the digitization of therespective single–event input samples. These subsamples constitute about2/3 of the sample



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Figure 8.6: Integrated rates of di-muons at generator level for the sample of crossings mixed fromminimum bias samples binned in muon–pT (see Section8.4.5), and for theW andZ samples. Limitedto |ηµ| < 2.1. High luminosity (L = 1034 cm−2s−1).

of crossings. A considerable saving of resources was achieved by using parts of the single–event input samples, that have already been digitized for use in analytic calculations of triggerrates, directly as a part of the sample of crossings (of course the weights have to be adjustedaccording to Equation8.21). Only the configurations with more than one event with muons percrossing (k ≥ 2) were then mixed as described above using events from the input samples thathave not been used directly.

8.4.8 Generated Di-Muon Rates

Figure8.6 shows the integrated rates of di-muons at generator level as a function of (sym-metric) pT threshold for high luminosity (L = 1034 cm−2s−1) using the sample of crossingsexplained above. Contributions of di-muons from the same event and di-muons from two dif-ferent events in the same beam crossing are shown, separately. The contribution of two muonsfrom different minimum bias interactions in the same crossing becomes important at lowpT anddominates the total di–muon rate below 4 GeV/c. Above a threshold of 13 GeV/c the dominantcontribution to the di–muon rate comes from decays ofZ bosons.


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Chapter 9

Global Muon Trigger Performance

126 9. Global Muon Trigger Performance

This chapter gives a summary of the simulated performance of the CMS L1 Muon Triggerafter combining the results of the regional muon triggers with the Global Muon Trigger. TheGlobal Muon Trigger has been simulated using the default settings as described in Chapter6applying the simulation procedures described in Chapter8. The algorithmic performance of theGMT is demonstrated for samples of generated single muons. The rates of single and di-muontriggers from minimum–bias interactions at high and low LHC luminosity are analyzed and theefficiencies for selected signals are shown. A reduced coverage of the trigger up to|η| < 2.1has been assumed in all plots that do not depend explicitly on pseudorapidity.

9.1 GMT Algorithmic Efficiency and Ghosting

Figure9.1 shows the efficiency to find single muons of flatpT distribution as a functionof pseudorapidity for the GMT and the regional muon triggers. GMT candidates that are sup-pressed in the single–muon trigger are excluded from the GMT efficiency as described in Chap-ter 6, Section6.6. No pT threshold is applied. The efficiency of the GMT is generally above97 % except in several particular regions of gaps in the geometrical coverage of chambers be-tween the wheels in the barrel, in the overlap region and between rings of chambers in theendcap. After combination of the regional triggers by the GMT the efficiency is generallyhigher than the efficiency of each of the regional triggers except in some very small regionswhere candidates that are not confirmed by the complementary trigger had to be excluded fromthe single muon trigger (see Chapter6, Section6.6). The efficiency for triggering on muonsfromW → µν decays as a function of pseudorapidity with apT threshold of 14 GeV/c appliedhas been shown in Chapter6, Figure6.23.

The efficiency of the GMT and regional muon triggers as a function ofφ are shown inFigures9.2 and9.3 for the barrel and endcap regions, respectively. The GMT improves theover–all efficiency and recovers efficiency in the regions of geometrical gaps between muonstations inφ.

Figures9.4and9.5show the efficiency of the GMT and the regional triggers as a function ofgenerated transverse momentum for the barrel and endcap region, respectively. Above 5 GeV/ca plateau of high efficiency is reached. The GMT increases efficiency with respect to the re-gional triggers. In the endcap, below 5 GeV/c the efficiency of the GMT lies between the onesof the CSC and RPC Triggers since very–low–quality RPC triggers that are not confirmed byCSC triggers had to be suppressed from the single muon trigger (see Chapter6, Section6.6).

Figure9.6shows the probability for ghosting (i. e. to find two muons in a sample of singlemuons of flatpT distribution) as a function of pseudorapidity for the GMT and the regionalmuon triggers. GMT candidates that are suppressed in the di–muon trigger are excluded fromthe GMT ghosting probability. The GMT introduces only negligible additional ghosting dueto failure to match candidates of the regional triggers. Ghosts in the overlap region are almostcompletely canceled out by the Cancel–Out–Units (see Chapter6, Section6.4). The suppressionof very–low quality candidates that are not confirmed by the complementary regional triggerreduces ghosting with respect to the CSC Trigger in the region of1.1 < |η| < 1.25 and withrespect to the RPC Trigger in the region of1.6 < |η| < 2.1.


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9.1 GMT Algorithmic Efficiency and Ghosting 127

(units)genη0 0.5 1 1.5 2 2.5

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Figure 9.1: Efficiency of the GMT and regional muon triggers as a function of pseudorapidityη forthe sample of single muons with flatpT distribution described in Chapter8, Section8.2. No pT thresh-old applied. GMT candidates that are suppressed in the single–muon trigger are excluded. UpdatedORCA 6.2.3 simulation.

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Figure 9.2: Efficiency of the GMT and the DT and RPC Triggers in the barrel region as a function ofφ.Obtained using the single muon sample described in Chapter8, Section8.2. No pT threshold applied.GMT candidates that are suppressed in the single–muon trigger are excluded. Updated ORCA 6.2.3simulation.



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Figure 9.3: Efficiency of the GMT and the CSC and RPC Triggers in the endcap region as a function ofφ. Obtained using the single muon sample described in Chapter8, Section8.2. NopT threshold applied.GMT candidates that are suppressed in the single–muon trigger are excluded. Updated ORCA 6.2.3simulation.

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%),

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Figure 9.4: Efficiency of GMT and the DT and RPC Triggers in the barrel region as a function of (gen-erated) muonpT . Obtained using the single muon sample described in Chapter8, Section8.2. No pTthreshold applied. GMT candidates that are suppressed in the single–muon trigger are excluded. UpdatedORCA 6.2.3 simulation.


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9.1 GMT Algorithmic Efficiency and Ghosting 129

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Figure 9.5: Efficiency of the GMT and the CSC and RPC Triggers in the endcap region as a functionof (generated) muonpT . Obtained using the single muon sample described in Chapter8, Section8.2.No pT threshold applied. GMT candidates that are suppressed in the single–muon trigger are excluded.Updated ORCA 6.2.3 simulation.

genη0 0.5 1 1.5 2 2.5

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Figure 9.6: Ghosting probability as a function of pseudorapidity in the GMT and regional muon triggers.No pT threshold is applied. Candidates that are suppressed in a di–muon trigger are excluded (seeSection9.4). Obtained using the single muon sample described in Chapter8, Section8.2. UpdatedORCA 6.2.3 simulation.



genT ) * pgen

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1.2≤| ηGMT overlap 0.8 < |Chi2 / ndf = 383.7 / 33

9.318 ±Constant = 842.3

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genT ) * pgen

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19.19 ±Constant = 2958

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2.1≤| ηGMT endcap 1.2 < |Chi2 / ndf = 2253 / 33

19.19 ±Constant = 2958

0.001308 ±Mean = -0.2084

0.001024 ±Sigma = 0.2319

Figure 9.7: 1/pT resolution of the Global Muon Trigger for the barrel, overlap and endcap regions. GMTcandidates that are suppressed in a single muon trigger are excluded. The solid lines represent adaptedGaussian distributions. Obtained using the single muon sample described in Chapter8, Section8.2.Updated ORCA 6.2.3 simulation.

9.2 Transverse Momentum Resolution and Turn–On Curves

Figure 9.7 shows the1/pT resolution at the output of the Global Muon Trigger for thebarrel, overlap and endcap regions using the sample of single muons with flatpT distributionas reference. GMT candidates that are suppressed in a single muon trigger are excluded. Thedistributions are not centered at zero due to the 90 % efficiency definition of thepT scale atlevel–1 (see Section5.4.7.3). The non-Gaussian tails are caused by the coarsepT resolution ofthe regional triggers in several problematic regions of the detector as shown in Figure5.20. Inthe barrel, a1/pT resolution of 15 % can be achieved. In the endcaps, where bending is smaller,a 1/pT resolution of 23 % is achieved. In the overlap region, where the magnetic field is highlyinhomogeneous and bending is even smaller, the achievable1/pT resolution is 27 %.

The resulting turn–on curves of the Global Muon Trigger have been shown in Figure6.24cfor the barrel, overlap and endcap regions. By definition of the level–1pT scale, the turn–oncurves reach 90 % of the plateau efficiency for muons with apT equal to the applied triggerthreshold. A high plateau efficiency of greater than 95 % in the barrel and endcaps and around95 % in the overlap region is reached. The plateau efficiency at higherpT thresholds decreasesby a few percent due to a number of effects in several regions of pseudorapidity at the levelof the regional triggers as discussed in Chapter5, Section5.4.7.3. In the default merging ofpT measurements care has been taken not to use the minimumpT method in these problem-atic regions since this method would further decrease the plateau efficiencies (see Chapter6,Section6.9.3).


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9.3 Single Muon Trigger Rates 131

9.3 Single Muon Trigger Rates

Figure9.8shows the single muon trigger rates of the GMT and the regional muon triggersas a function of appliedpT–threshold at low LHC luminosity for the barrel, overlap and end-cap regions. The GMT achieves a rate reduction with respect to the the standalone rates ofthe regional muon triggers by excluding very-low-quality muons that are not confirmed by thecomplementary system (see Chapter6, Section6.6) and by optimally combining thepT mea-surements (see Chapter6, Section6.9.3). A good control of the trigger rates is possible over twoto three orders of magnitude by varying thepT threshold. Trigger rates at level–1 are about anorder of magnitude higher than the generated rates due to the feed–through effect as explainedbelow. The higher trigger rates are generated in the overlap region due to the poorpT resolutionin this region.

Figures9.9 and 9.10 show the single muon trigger rates as a function of appliedpT–threshold for the full detector (|η| < 2.1) at low and high LHC luminosity, respectively. Thetrigger rates roughly scale linearly with the luminosity. Good control of the trigger rates ispossible over 2.5 orders of magnitude.

Figures9.11and9.12show the differential rates of generated muons that contribute to thesingle muon trigger rates at typicalpT thresholds of 14 GeV/c and 25 GeV/c for the low and highLHC luminosity scenarios, respectively. Due to the feed–through effect of the level–1 triggersand due to the high rate of background of low–pT muons, the trigger rates at rather high triggerthresholds are completely dominated by muons of very lowpT . Due to the limited resolutionof the level–1 trigger, non–prompt lowpT muons fromπ/K decays in the calorimeters may berecognized as straight (high–pT ) tracks coming from the vertex. Prompt muons fromb andcquark decays may be assigned much higher transverse momentum due to multiple scattering.This background of low–pT muons can only be suppressed effectively at higher trigger levelswhich work with higher–resolution data.

The single muon trigger rate at a threshold of 14 GeV/c as a function of pseudorapidity hasbeen shown in Figure6.10 for the low LHC luminosity scenario (rates from low-quality un-matched muons have to be deducted as given by Table6.7). As discussed before, the highestrates come from the overlap region. The forward region of2.1 < |η| < 2.4 would also con-tribute rather high trigger rates if coverage of the CSC trigger should in the future be restoredup to|η| < 2.4.

9.4 Di–Muon Trigger Rates

Figures9.13and9.14show the di-muon trigger rate at the output of the GMT as a functionof symmetricpT threshold for low and high LHC luminosity, respectively. GMT candidates thatare suppressed in the di–muon trigger as described in Chapter6, Section6.6 are not includedin the rates . Contributions from two muons from the same interaction, from two muons fromdifferent interactions in the same bunch crossings, from ghosts and from one muon plus a faketrigger are shown. At both luminosities the di-muon trigger rate is dominated by triggers fromtwo real muons from minimum bias events (orW andZ decays). At low luminosity the con-tribution from di-muons originating from the same interaction dominates over the entire rangeof thresholds. The contribution from triggers caused by two muons from different interactionsin the same crossing is only of the order of 20 % at low thresholds. At high luminosity thecontribution from triggers caused by two muons from different interactions in the same cross-




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Figure 9.8: Single-muon trigger rates of the Global Muon Trigger and regional triggers as a function oftrigger threshold at low luminosity (L = 2 × 1033 cm−2s−1) in the barrel, overlap region and endcap.Obtained using the minimum bias sample described in Chapter8, Section8.4. Updated ORCA 6.2.3simulation.


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Figure 9.9: Single-muon trigger rates of theGlobal Muon Trigger and regional triggers asa function of trigger threshold at low luminos-ity (L = 2 × 1033 cm−2s−1). Obtained usingthe minimum bias sample described in Chapter8,Section8.4. |η| < 2.1. Updated ORCA 6.2.3simulation.

Figure 9.10: Single-muon trigger rates of theGlobal Muon Trigger and regional triggers asa function of trigger threshold at high luminos-ity (L = 1034 cm−2s−1). Obtained using theminimum bias mix sample described in Chap-ter 8, Section 8.4.5. |η| < 2.1. UpdatedORCA 6.2.3 simulation.


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9.4 Di–Muon Trigger Rates 133

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Figure 9.11: Contributions of generated muonsaccording to muon parents to the single-muontrigger rates at apT threshold of 14 GeV/c. Lowluminosity (L = 2 × 1033 cm−2s−1). Obtainedusing the minimum bias sample described inChapter8, Section8.4. |η| < 2.1. UpdatedORCA 6.2.3 simulation.

Figure 9.12: Contributions of generated muonsaccording to muon parents to the single-muontrigger rates at apT threshold of 25 GeV/c. Highluminosity (L = 1034 cm−2s−1). Obtained usingthe minimum bias sample described in Chapter8,Section8.4. |η| < 2.1. Updated ORCA 6.2.3simulation.

ing becomes much more important: it dominates the di-muon trigger rate up to a threshold of∼ 5 GeV/c. While the di-muon trigger rate from di-muons originating from the same interactionscales approximately linearly with luminosity, the contribution from two muons from differentevents in the same crossing scales approximately with the square of the luminosity. The contri-bution from ghosts is well under control at both luminosities: it lies between 10 and 20 % of thetotal rate, but it decreases less rapidly at higherpT thresholds than the contribution of triggersfrom two real muons. The contribution from a trigger caused by a real muon and a fake trigger,for example from chamber noise or punch through, in the same crossing is negligible at bothluminosities.

The definition of the classes of di–muon triggers in Figures9.13and9.14was chosen asfollows: for each GMT candidate, other candidates close in space were retrieved and all thecandidates were sorted bypT . The number of generated muonsnclose with positions in station 2of the muon system close to the one of the GMT candidate(s) was determined. If no generatedmuon was found for a GMT candidate, the candidate was classified as a fake trigger. Otherwise,if more GMT candidates than generated muons were found, thenclose GMT candidates withthe highest transverse momenta are considered as caused by the generated muon(s) and theremaining candidates with lower transverse momenta were classified as ghosts.

The inclusive di–muon trigger rates at the output of the GMT as a function of thepT thresh-olds applied to the highest-pT and second–highest–pT muons are shown in Figures9.15and9.16for low and high LHC luminosity. Depending on thepT spectra of the muons, for certain sig-nals an asymmetric di–muon trigger can be more efficient than a symmetric one operating at thesame trigger rate. However, for the signal samples used to study the di-muon trigger efficiencyin Section9.6, the possible efficiency gain has been found to be negligible. Only symmetricdi–muon thresholds are therefore considered in the following.



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Figure 9.13: Inclusive di-muon trigger rates at the output of the GMT as a function of a symmetricpT threshold. Low luminosity (L = 2 × 1033 cm−2s−1). Obtained using the minimum bias samplesdescribed in Chapter8, Section8.4, and the analytic calculation of the di-muon trigger rate as describedin Section8.4.4. Updated ORCA 6.2.3 simulation.

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Figure 9.14: Inclusive di-muon trigger rates at the output of the GMT as a function of a symmetricpT threshold. High luminosity (L = 1034 cm−2s−1). Obtained using the minimum bias mix sampledescribed in Chapter8, Section8.4.5. Updated ORCA 6.2.3 simulation.


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9.5 Combined Single–Muon and Di–Muon Trigger Rates 135

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Figure 9.15: Inclusive di-muon trigger rates atthe output of the GMT as a function of thepTthresholds applied to the highestpT and second–highestpT muon. Low luminosityL = 2 ×1033 cm−2s−1. Obtained using the minimumbias sample described in Chapter8, Section8.4and the analytic calculation of the di-muon trig-ger rate as described in Section8.4.4. UpdatedORCA 6.2.3 simulation.

Figure 9.16: Inclusive di-muon trigger ratesat the output of the GMT as a function of thepT thresholds applied to the highestpT andsecond–highestpT muon. High luminosityL =1034 cm−2s−1. Trigger rates in kHz. Obtainedusing the minimum bias mix sample described inChapter8, Section8.4.5. Updated ORCA 6.2.3simulation.

9.5 Combined Single–Muon and Di–Muon Trigger Rates

In order to separately study the main streams of L1 triggers, a preliminary splitting of avail-able data acquisition bandwidth (maximum level–1 trigger rate) among the main L1 triggerstreams has been agreed upon between the Physics Reconstruction and Selection (PRS) groupsin CMS. It is indicated in Table9.1for low and high LHC luminosity assuming a reduced DAQbandwidth of 50 kHz for the initial operation at low luminosity. A safety factor of 3 is appliedto take into account uncertainties of cross-sections at LHC energies. Of course, this bandwidthsplitting is only a starting point and will evolve over time as more complex trigger conditionsusing multiple trigger objects are studied. According to this preliminary bandwidth splitting abandwidth of approximately 4 kHz (8 kHz) will be available to the combined single muon anddi–muon triggers at low (high) LHC luminosity.

Figures9.17and9.18show contours of equal trigger rate for a combined single muon triggerand di–muon trigger with symmetric thresholds at low and high LHC luminosity. Assumingthe preliminary bandwidth splitting, the single muon and di–muon trigger thresholds can bechosen anywhere along the contours of 4 kHz and 8 kHz, for low and high LHC luminosity,respectively. Choosing apT threshold different from the available thresholds in the current L1pT scale (see Table5.7) would however require to re–program thepT scale which is currentlynot straightforward in the simulation. ProposedpT thresholds in the following are thereforechosen according to the current L1pT scale.



Table 9.1: Preliminary allocations of DAQ bandwidth (maximum level–1 trigger rate) at low and highLHC luminosity.

bandwidth L = 2× 1033 cm−2s−1 L = 1034 cm−2s−1

Available to DAQ 50 kHz 100 kHz

after safety factor of 3 and

≈ 1 kHz for MB trigger16 kHz 32 kHz

BW for µ and 2µ triggers 4 kHz 8 kHzBW for e/γ and2(e/γ) triggers 4 kHz 8 kHz

BW for τ and2τ triggers 4 kHz 8 kHz

BW for jet,ET , EmissT and combined triggers 4 kHz 8 kHz

At low LHC luminosity the single muon trigger could be set to 14 GeV/c and the di-muontrigger as low as 1.5 GeV/c. At high LHC luminosity two operating points are compatible withthe current L1pT scale: 25 GeV/c for the single muon trigger and 4 GeV/c for the di-muontrigger or 20 GeV/c for the single muon trigger and 5 GeV/c for the di-muon trigger (the latterwould slightly exceed 8 kHz). Corresponding efficiencies for various signals of interest at theseworking points are listed in Table9.2.

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Figure 9.18: Contours of equal trigger ratein the plane ofpT thresholds for level-1 singleand di-muon triggers. High luminosityL =1034 cm−2s−1. Trigger rates in kHz. Obtainedusing the minimum bias mix sample described inChapter8, Section8.4.5. Updated ORCA 6.2.3simulation.


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9.6 Trigger Efficiency for Selected Signals 137

9.6 Trigger Efficiency for Selected Signals

Trigger efficiencies have been studied for a number of channels among the physics goalsas listed in Chapter8, Table8.1. All efficiencies have been normalized to the selected kine-matic ranges indicated in the table. Since reduced trigger acceptance up to|η| < 2.1 has beenassumed, muons from theW → µν andtt → W→µν + X channels have been required to bewithin |η| < 2.1. As for the other channels, in which multi–muon decays occur, muons havebeen required to have|η| < 2.4 or 2.5 as listed in the table. This results in slightly lower effi-ciencies quoted but higher yields due to the larger selected cross–sections. Such normalizationis certainly justified for channels with high–pT muons which are expected to be accepted by thehigh level triggers, even if not all the muons can be reconstructed. In case of theB channelswith two soft muons, however, the events can only be kept by the higher trigger levels if bothmuons can be reconstructed. It is currently not clear whether the higher level triggers will beable to reconstruct muons in the region of2.1 ≤ |η| < 2.4, where no level–1 muon candidatesexist as a seed for reconstruction.

Efficiencies of the single muon trigger and inclusive di–muon trigger are discussed in thefollowing. Table9.2gives a summary of trigger efficiencies and expected yields at level–1 fora combined single muon and di–muon trigger at possible working points for low and high LHCluminosity as discussed in Section9.5

Figure9.19shows the efficiency to trigger onW → µν, Z → 2µ andtt → W→µν + Xas a function of muonpT threshold, for the single muon trigger and for an inclusive di–muontrigger with symmetric thresholds. The efficiencies are shown for the low LHC luminosityscenario (L = 2 × 1033 cm−2s−1), but the results are almost identical at high LHC luminosity.All three signals can be triggered efficiently with a single–muon trigger at typicalpT thresholds.Z → 2µ decays can also be triggered with high (∼ 70 %) efficiency by an inclusive di–muontrigger; this can be important if for any reason the single muon trigger has to be run with higherthresholds than foreseen. The efficiency for triggeringtt→ W→µν +X lies between 20 % and30 % at prospective di–muon trigger thresholds. As indicated in Table9.2, large statistics canbe collected for all three channels even at low LHC luminosity so that precision measurementsare already possible at the beginning.

Figure9.20shows the efficiency to trigger onH → WW → 2µ2ν events at Higgs massesof 120, 160 and 200 GeV/c2 as a function of muonpT threshold, for the single muon triggerand for an inclusive di–muon trigger with symmetric thresholds. All three cases are triggeredwith high efficiency (> 90 %) by a single muon trigger of typical thresholds. They can also betriggered with> 80 % efficiency by an inclusive di–muon trigger at expected di–muon triggerthresholds. The highest yield is expected at a Higgs mass of 160 GeV/c2 since the branchingratio of this channel is highest at this mass (see Chapter3, Figure3.2(b)).

The efficiency to trigger onH → ZZ(∗) → 4µ events at Higgs masses of 130, 150 and200 GeV/c2 as a function of muonpT threshold is shown in Figure9.21 for the single muontrigger and for an inclusive di–muon trigger with symmetric thresholds. Due to the high numberof muons, the efficiencies for both triggers are close to 100 % at typical trigger thresholds.Yields are however small (see Table9.2) due to the low branching ratio into this channel asshown in Chapter3, Figure3.2(b).

Efficiencies to trigger on the decaysB0s → J/ψ→µ+µ−φ→K+K− and on the rare decayB0

s →µ+µ− as a function of muonpT threshold are shown in Figure9.22for a single muon triggerand a di–muon trigger with symmetric thresholds. At typical trigger thresholds, both channelsare triggered predominantly by the di–muon trigger with an efficiency between 15 and 25 %.



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Figure 9.20: Efficiencies to trigger onH → WW → 2µ2ν decays with Higgs masses of 120, 160and 200 GeV/c2 as a function of muonpT threshold, (a) for the single muon trigger and (b) for aninclusive di–muon trigger with symmetric thresholds. Reduced trigger acceptance up to|η| < 2.1.Low luminosity (L = 2 × 1033 cm−2s−1). Obtained using the signal samples described in Chapter8,Section8.3. Updated ORCA 6.2.3 simulation.


H. Sakulin

9.6 Trigger Efficiency for Selected Signals 139


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Figure 9.21: Efficiencies to trigger onH → ZZ(∗) → 4µ decays with Higgs masses of 130, 150and 200 GeV/c2 as a function of muonpT threshold, (a) for the single muon trigger and (b) for aninclusive di–muon trigger with symmetric thresholds. Reduced trigger acceptance up to|η| < 2.1.Low luminosity (L = 2 × 1033 cm−2s−1). Obtained using the signal samples described in Chapter8,Section8.3. Updated ORCA 6.2.3 simulation.

Between 5 and 10 % efficiency is achieved by the single muon trigger at typical thresholds,events triggered exclusively by the single muon trigger are however only useful, if the secondmuon can later be recovered at higher trigger levels. In theB0

s → J/ψ→µ+µ−φ→K+K− channela rather high threshold of 0.5 GeV/c was applied to the transverse momenta of the kaons inorder to ensure their reconstruction at higher trigger levels, which will be necessary in orderto trigger this channel. Reconstruction of this channel at the higher trigger levels will onlybe possible at low LHC luminosity due to the pile–up. The rare decay ofB0

s → µ+µ− has avery small branching ratio and only very small yields are therefore expected. It is therefore ofinterest to continue the study of this channel at high luminosity [10]. Di–muon trigger efficiencyin this channel decreases rapidly at higherpT thresholds. Since muons in this channel areclose inφ andη and of opposite charge, efficiency can be increased by running an additionaltopological di–muon trigger algorithm in the Global Trigger. Thresholds could be lowered inthe topological trigger algorithm requiring only a fraction of the additional bandwidth of triggerrate with respect to a di–muon trigger without topological conditions at the same threshold.




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s → µ+µ− asa function of muonpT threshold, (a) for the single muon trigger and (b) for an inclusive di–muontrigger with symmetric thresholds. Reduced trigger acceptance up to|η| < 2.1. Low luminos-ity (L = 2 × 1033 cm−2s−1). Obtained using the signal samples described in Chapter8, Section8.3.Updated ORCA 6.2.3 simulation.

Table 9.2: Signal efficiencies and yields at Level–1 for several L1 working points of a combined singlemuon and di-muon trigger. Reduced trigger acceptance up to|η| < 2.1. Obtained using the signalsamples described in Chapter8, Section8.3. Updated ORCA 6.2.3 simulation.

LHC luminosity L = 2× 1033 cm−2s−1 L = 1034 cm−2s−1

working point µ: 14 GeV/c; µµ: 1.5 GeV/c µ: 25 GeV/c; µµ: 4 GeV/c µ: 20 GeV/c; µµ: 5 GeV/c

Efficiency / % ev/year Efficiency / % ev/year Efficiency / % ev/year

signal in 10 fb−1 in 100 fb−1 in 100 fb−1

Z → 2µ 96.7 6.0× 106 94.8 5.9× 107 95.7 6.0× 107

W → µ+X 91.0 9.5× 107 76.9 8.0× 108 84.4 8.8× 108

tt→W→µν +X 95.6 1.0× 106 87.7 9.2× 106 91.6 9.6× 106

H(120)→WW → 2µ2ν 95.7 256 91.4 2.4× 103 93.1 2.5× 103

H(160)→WW → 2µ2ν 97.1 1.4× 103 95.1 1.4× 104 96.2 1.4× 104

H(200)→WW → 2µ2ν 97.7 813 96.2 8.0× 103 97.0 8.1× 103

H(130)→ ZZ∗ → 4µ 99.9 5.3 99.7 53 99.7 53

H(150)→ ZZ∗ → 4µ 99.9 11 99.8 105 99.9 105

H(200)→ ZZ → 4µ 99.9 23 99.9 231 99.9 231

B0s → J/ψ→µ+µ−φ→K+K− 28.1 2.7× 105 - - - -

B0s → µ+µ− 28.5 246 20.7 1.8× 103 16.6 1.4× 103


H. Sakulin

Chapter 10

Conclusions

142 10. Conclusions

The research project presented in this thesis dealt with the design and the simulation ofthe First Level Global Muon Trigger for the CMS experiment at CERN. The CMS experimentincludes three muon sub–systems based on different types of muon chambers: Drift Tubesin the barrel, Cathode Strip Chambers in the endcaps and additional layers of Resistive PlateChambers both in the barrel and in the endcaps. All three muon sub–systems participate inthe First Level Trigger. Regional muon triggers independently find muon candidates basedon hits or track segments found in each of the sub–systems. It is the task of the Global MuonTrigger to combine these muon candidates and to find the best four muon candidates in the entiredetector. By making use of the complementarity of the muon systems it increases efficiency andsubstantially improves background rejection. It further correlates muon candidates with regionsin the calorimeter in order to achieve confirmation by the calorimeter and to apply isolationcriteria.

The algorithms of the Global Muon Trigger have been elaborated and optimized accordingto the expected performance of the regional muon triggers based on detailed simulations of theentire detector and the trigger system. The functionality of the Global Muon Trigger has beenimproved and extended with respect to original ideas in many ways and the extensions havebeen incorporated in the simulation software used by the Muon Physics Group. Muon triggerrates have been studied using Monte–Carlo generated samples of minimum–bias interactionsprovided by the Muon Physics and Production Groups and a contribution has been made bydeveloping a method to obtain multi–muon trigger rates in the presence of pile–up by overlayingmultiple weighted minimum bias events that contain muons. In addition to studying di–muontrigger rates at level–1 the method has in the following also been used by the Muon PhysicsGroup to investigate di–muon trigger rates at higher trigger levels.

It has been found, that a reduction of single muon trigger rates by a factor of two to three at aminimal cost of efficiency can be achieved at the Global Muon Trigger by selectively excludinglow–quality muon candidates that have only been reported in one regional trigger in certainregions of pseudorapidity. Such low–quality candidates (i. e. candidates that were reconstructedwith a small number of hits or segments) may have only a very coarse transverse momentumassignment or may be likely to be ghosts or fake candidates in certain detector regions. A largereduction can also be achieved in di–muon trigger rates by excluding unconfirmed low–qualitycandidates that are likely to be ghosts or fake candidates.

A method has been developed to improve the transverse momentum resolution of muoncandidates that are reported by two regional triggers. Depending on the pseudorapidity and thequalities of the two measurements either the measurement with better resolution can be selectedor alternatively, for certain qualities of measurements and in certain regions, the smaller of thetwo pT–measurements can be assigned. Optimal combination of the two options can furtherreduce the trigger rates by a factor of 1.5 at a minimal cost in efficiency.

In the overlap regions between barrel and endcaps, muon candidates can be duplicated be-tween the DT and CSC regional triggers resulting in a high rate of fake di–muon triggers unlesscounter–measures are taken. Simulations have shown that solutions at the level of the regionaltriggers cannot achieve the necessary reduction in duplication and hence additional measuresare necessary at the Global Muon Trigger. Requiring DT/CSC candidates to be confirmedby an RPC candidate in the Global Muon Trigger can remove the duplication but makes theDT/CSC trigger dependent on the RPC trigger and limits the efficiency to that of the RPCSystem. Cancel–out units therefore have been devised to cancel out the duplicated candidatesin the Global Muon Trigger independent of the RPC Trigger, allowing to achieve a ghostingprobability below 0.1 % without loss in efficiency.


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143

Applying the described methods, the Global Muon Trigger can reduce over–all single muontrigger rates at typicalpT thresholds by a factor of four to five with respect to the standalonetrigger rates of the regional triggers. Most of the rate reduction is achieved in the endcap andoverlap regions where standalone trigger rates in the CSC and RPC triggers are extremely highdue to limited bending of muon tracks. Di–muon trigger rates at typical thresholds are wellunder control with a tolerable contribution from ghosts around 10 to 20 %. The Global MuonTrigger increases trigger efficiency with respect to the standalone efficiency of the regionaltriggers, especially in regions of gaps in the geometrical acceptance of the muon system.

Single muon and di–muon trigger thresholds have been studied for low and high LHC lu-minosities (L = 2× 1033 cm−2s−1 andL = 1034 cm−2s−1, respectively) taking into account theexpected available data acquisition bandwidth for muon triggers and a safety factor of three inthe trigger rates due to uncertainties of cross–sections at LHC energies. Single muon triggerthresholds as low as 14 GeV/c at low luminosity and between 20 and 25 GeV/c at high lumi-nosity will be possible. Under the same assumptions, (symmetric) di–muon trigger thresholdsas low as 1.5 GeV/c (or even lower as corresponding to the lowest transverse momenta that canreach the muon system) at low luminosity and between 4 and 5 GeV/c at high luminosity will befeasible. At these trigger thresholds, the trigger will be fully efficient for the discovery channelH → ZZ(∗) → 4µ, even with reduced acceptance of the CSC trigger up to|η| < 2.1. Forthe channelH → WW → 2µ2ν trigger efficiencies between 92 % and 98 % can be obtaineddepending on the Higgs mass and the luminosity scenario. Due to the low di–muon triggerthresholds at low LHC luminosity the trigger will be fully efficient for di–muons (for examplefromB meson decays) if they have enough transverse momentum to reach the muon system. Athigh luminosity the efficiency will however be lower. In the case of the rare decayBo

s → µ+µ−,which is of interest also at high luminosity, the efficency decreases by 30 to 40 % in comparisonwith the low luminosity scenario, some of which might be recovered by a topological di–muontrigger.

In summary, despite the limitedpT resolution in the endcap regions, after combination ofthe regional triggers by the Global Muon Trigger, single and di–muon trigger thresholds inaccordance with the available data acquisition bandwidth can be set sufficiently low so thatexcellent efficiency is obtained for channels among the physics goals to be triggered by muontriggers. The algorithms of the Global Muon Trigger have been optimized according to thecurrently expected performance of the regional triggers. They are however fully configurable inorder to adapt them to future needs and changes of performance.

In parallel to the development of the algorithms, the logic design of the main Global MuonTrigger electronics board has been elaborated based on the technology of Field ProgrammableGate Arrays (FPGAs). The design has been compacted with respect to original plans by split-ting large look–up–tables into cascaded smaller ones so that they could be moved from externalmemory blocks to internal ones in the FPGAs thus allowing the entire GMT logic to be imple-mented on one VME board. The new solution speeds up the processing and allows cancel–outto be performed in the overlap region as described above. FPGA models have been selectedand the algorithms have been partitioned into nine large and several small FPGAs according torequired memory resources and available input/output pins.

The implementation of the FPGAs and of the electronics board are planned for 2003 and2004. Since the logic design has been developed in close collaboration with the electronicsgroup at HEPHY, no major problems are expected.


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Acknowledgements

This project was undertaken at CERN as a member of the CMS collaboration and the CMSTrigger group of the Institute for High Energy Physics (HEPHY) of the Austrian Academy ofSciences. I would like to thank all my colleagues at HEPHY for many interesting discussions,help and explanations. I am thankful to Dr. Claudia Wulz, the leader of the CMS Trigger groupof HEPHY, for the independence she allowed me in the project. Prof. Dr. Manfred Markytanhas been my supervisor at the Technical University of Vienna. I would like to thank him for hisconstant support and encouragement and for carefully proof–reading my thesis.

I am indebted to Dr. Massimiliano Fierro for introducing me to CMS in general and totrigger simulation and analysis of simulated data in particular. I am grateful for his constantcollaboration in the simulation of the Global Muon Trigger and for always taking the time forinteresting discussions. I am thankful to DI Anton Taurok for introducing me to the design ofprogrammable electronics and for a very fruitful collaboration in the design of the Global MuonTrigger hardware. In the CMS L1 Trigger community I would like to thank Prof. Dr. WesleySmith and Prof. Dr. Darin Acosta for many productive discussions about the hardware design.

During my work on Monte–Carlo simulations in the framework of the Muon Physics Recon-struction and Selection Group I had the pleasure to work with many gifted people: I would espe-cially like to thank Dr. Nicola Amapane, Dr. Giacomo Bruno, Dr. Stefano Lacaprara, Dr. SilivaArcelli, Dr. Alessandra Fanfani and Dr. Norbert Neumeister for their collaboration over thecourse of the thesis. I further would like to thank the members of the CMS Production team,who processed millions of events used in the studies, and Dr. Vincenzo Innocente for his helpin implementing a new method for the treatment of pile–up in ORCA. Dr. Andrei Starodumovand Dr. Nikita Stepanov have to be thanked for the production ofB physics samples used forbenchmarks.

The major part of this project was financed by the Austrian Government through the CERNAustrian Doctoral Student Program. I am grateful to Prof. Dr. Christian Fabjan, who coordinatesthe program at CERN, and to Dr. Sergio Cittolin, who was my CERN supervisor. Additionalfunding for the remaining part of the project was provided by the Austrian Academy of Sci-ences. I am grateful to Prof. Dr. Walter Majerotto and Dr. Claudia Wulz for their support inobtaining this funding.

On a personal side I would like to thank all my friends who shared the good and bad timesduring my work on this thesis with me. I would like to thank my parents for their constantsupport and Karina for her love.

Curriculum Vitae

152 Curriculum Vitae

Personal Information

Name Hannes SakulinDate of birth 9.12.1972Place of birth Graz, AustriaNationality AustrianAddress 37, rue de Geneve

F-01170 Gex, FranceE-mail [email protected]

Education

07.1999-12.2002 Technical University of Vienna: doctoral student. PhD thesis “De-sign and Simulation of the First Level Global Muon Trigger for theCMS Experiment at CERN”, research work carried out at the Eu-ropean Particle Physics LaboratoryCERN, Geneva, Switzerland,in collaboration with theInstitute for High Energy Physics of theAustrian Academy of Sciences, Vienna, Austria.

05.1998-07.1998 WIFI Steiermark, Graz, Austria: course in business administra-tion (Unternehmerakademie).

07.1998 Austrian Chamber of Commerce (WirtschaftskammerOsterreich):degree in business administration (Unternehmerprufung) — withhigh distinction.

1991-1998 Technical University of Graz, Austria: studies of TechnicalPhysics (Diplomstudium Technische Physik). Diploma thesis“Measurement of Strain with Electronic Speckle Pattern Interfer-ometry”, accomplished as a Masters by Research thesis atRoyalMelbourne Institute of Technology, Melbourne, Australia, July1996 – July 1997.

05.1998 Diplomingenieur degree in Technical Physics with high distinction1983-1991 High School BG/BRG Lichtenfelsgasse, Graz, Austria06.1991 Final exam — with high distinction


H. Sakulin

Curriculum Vitae 153

Worksince 08.2002 Institute for High Energy Physics of the Austrian Academy of Sci-

ences: conducting Monte–Carlo simulation studies of the perfor-mance of the First Level Muon Trigger for the Compact MuonSolenoid Experiment at CERN, designing the Global Muon Trig-ger logic and electronics. Work carried out at the European ParticlePhysics LaboratoryCERN, Geneva, Switzerland.

1988-1999,part time

Electric Power Systems Consulting, Graz, Austria: developed com-plete on-line and off-line software for a measurement system forflicker (voltage fluctuations) in electric power grids for the inter-national market; installed measurement systems and trained cus-tomers.

10.1998-03.1999 EPRI-PEAC Corporation, Knoxville, Tennessee, USA (ElectricPower Research Institute, Power Electronics Application Center):developed models for the spread of transients in electric powergrids; developed a test protocol and a test bench for flicker–meters; tested flicker–meters of various manufacturers for theNorth-American market; held flicker training for electric utilityemployees.

08.1995-09.1995 Institute for High Energy Physics of the Austrian Academy of Sci-ences: developed software for asynchronous data acquisition inthe test beam for the Compact Muon Solenoid Experiment (C,UNIX); work carried out at the European Particle Physics Labo-ratoryCERN, Geneva, Switzerland.


Lebenslauf

156 Lebenslauf

Personliche Daten

Name Hannes SakulinGeburtsdatum 9.12.1972Geburtsort GrazNationalitat OsterreicherAnschrift 37, rue de Geneve

F-01170 Gex, FrankreichE-mail [email protected]

Ausbildung

07.1999-12.2002 Technische Universitat Wien: Doktoratsstudium der TechnischenNaturwissenschaften. Dissertationsthema “Design and Simulationof the First Level Global Muon Trigger for the CMS Experiment atCERN”, Arbeiten durchgefuhrt amCERN, Genf in Zusammenar-beit mit demInstitut fur Hochenergiephysik derOsterreichischenAkademie der Wissenschaften, Wien.

05.1998-07.1998 WIFI Steiermark: Unternehmerakademie.07.1998 WirtschaftskammerOsterreich: Unternehmerprufung — mit

Auszeichnung bestanden1991-1998 Technische Universitat Graz: Diplomstudium Technische Physik.

Diplomarbeit “Measurement of Strain with Electronic Speckle Pat-tern Interferometry”, durchgefuhrt im Rahmen eines einjahrigenAuslandsaufenthaltes als Masters Thesis amRoyal Melbourne In-stitute of Technologyin Melbourne, Australien.

05.1998 Zweite Diplomprufung — mit Auszeichnung bestanden1983-1991 BG/BRG Lichtenfelsgasse, Graz06.1991 Matura — mit ausgezeichnetem Erfolg


H. Sakulin

Lebenslauf 157

Beruflicher Werdegang

seit 08.2002 Institut fur Hochenergiephysik derOsterreichischen Akademie derWissenschaften: Wissenschaftlicher Mitarbeiter. Design und Si-mulation des Globalen Muon Triggers fur das Compact MuonSolenoid Experiment am CERN, Arbeiten durchgefuhrt amCERN,Genf.

1988-1999,freier Mitarbeiter

Elektrische Anlagen Consulting, Graz: Entwicklung der komplet-ten Software (C) eines Meßsystems zur Analyse von Flicker inelektrischen Versorgungsnetzen fur den internationalen Markt. An-passung an kundenspezifische Problemstellungen, Installation undEinschulung.

10.1998-03.1999 EPRI-PEAC Corporation, Knoxville, Tennessee, USA (ElectricPower Research Institute, Power Electronics Application Cen-ter): Entwicklung von Modellen zur Ausbreitung von Transien-ten in elektrischen Versorgungsnetzen, Entwicklung eines Testpro-tokolls und Teststandes fur Flickermeter und Durchfuhrung einesPerformance-Tests von Flickermetern verschiedener Hersteller furden nordamerikanischen Markt. Flicker-Training fur Mitarbeitervon US-Elektrizitatsversorgungsunternehmen.

08.1995-09.1995 Institut fur Hochenergiephysik derOsterreichischen Akademieder Wissenschaften: Erstellung von Software fur die asynchroneDatenerfassung beim Testbeam fur das Compact Muon SolenoidExperiment (C, UNIX), Arbeiten durchgefuhrt amCERN, Genf.


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