"Science, Faculty of"@en . "Physics and Astronomy, Department of"@en . "DSpace"@en . "UBCV"@en . "Cormier, Felix"@en . "2017-01-21T04:05:39"@en . "2016"@en . "Master of Science - MSc"@en . "University of British Columbia"@en . "This document provides a thorough overview of an emulation method for new generation ATLAS Inner Detector design and optimization. The new ATLAS Inner Detector, named ITk, will track charged particles from proton-proton collision at record speed and flux, requiring a a thorough optimisation of its silicon sensors to perform within specifications inside these challenging dense environments consisting of very high momentum particles, collimated particles. The TIDETester emulation presented here is a fast simulation able to quickly simulate the effects of varying ITk geometries and analyse the track performance in order to inform layout decisions. A variety of Inner Detector layouts are studied, and results are obtained showing an improvement in dense environment tracking performance up to 10% when changing long strips to smaller pixels, and a small performance improvement up to 6% when using thinner pixel elements, from 150 \u00CE\u00BCm to 25 \u00CE\u00BCm. Changes in strip length between 23.82 and 47.64 \u00CE\u00BCm were found to have no effect on dense environment tracking performance, while the two proposed pixel sizes of 50 \u00C3\u0097 50 and 25 \u00C3\u0097 100 \u00CE\u00BCm were found to be equivalent in performance. Negligible performance improvement were found by moving the last three pixel layers as much as 10 mm from the interaction point, while moving strip layers back as much as 100 mm was found to have a modest improvement in performance, up to 10%."@en . "https://circle.library.ubc.ca/rest/handle/2429/60267?expand=metadata"@en . "Simulating the Next Generation of the ATLAS Inner Detector:Tracking in Dense EnvironmentsbyFelix CormierA THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Physics)The University of British Columbia(Vancouver)December 2016c\u00C2\u00A9 Felix Cormier, 2016AbstractThis document provides a thorough overview of an emulation method for new generation ATLASInner Detector design and optimization. The new ATLAS Inner Detector, named ITk, will trackcharged particles from proton-proton collision at record speed and flux, requiring a a thoroughoptimisation of its silicon sensors to perform within specifications inside these challenging denseenvironments consisting of very high momentum particles, collimated particles. The TIDETesteremulation presented here is a fast simulation able to quickly simulate the effects of varying ITkgeometries and analyse the track performance in order to inform layout decisions. A variety ofInner Detector layouts are studied, and results are obtained showing an improvement in dense envi-ronment tracking performance up to 10% when changing long strips to smaller pixels, and a smallperformance improvement up to 6% when using thinner pixel elements, from 150 \u00C2\u00B5m to 25 \u00C2\u00B5m.Changes in strip length between 23.82 and 47.64 \u00C2\u00B5m were found to have no effect on dense en-vironment tracking performance, while the two proposed pixel sizes of 50\u00C3\u0097 50 and 25\u00C3\u0097 100 \u00C2\u00B5mwere found to be equivalent in performance. Negligible performance improvement were found bymoving the last three pixel layers as much as 10 mm from the interaction point, while moving striplayers back as much as 100 mm was found to have a modest improvement in performance, up to10%.iiPrefaceThis dissertation is based on the experimental and simulation base of the ATLAS collaboration,which is an international scientific collaboration. This dissertation is wholly original not takendirectly from previously published articles.The design of the whole ATLAS detector detailed in Chapter 4 and the tracking methods inChapter 5 as well as the simulation infrastructure, from particle generation to detector simulationdetailed in Chapter 2 and Section 4.5 respectively are a necessary explanation of work done by theATLAS collaboration in order to motivate and understand the original worked detailed in the restof this work.The methods detailed in Chapter 6 for detector emulation as well as the validation of emu-lation tools as well as event analysis and conclusions in Chapter 7 were my own work, and areunpublished.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.1 Fundamental Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.2 Fundamental Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Simulating Events in Particle Physics . . . . . . . . . . . . . . . . . . . . . . . . 52.2.1 Parton Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.1 Current LHC Accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.1.1 Principles of Synchrotron Accelerators . . . . . . . . . . . . . . . . . . . 73.1.2 LHC Injection System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.1.3 LHC Accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 High-Luminosity LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12iv4 ATLAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.1 Detector Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.2 ATLAS Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.2.1 Electromagnetic Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . 194.2.2 Hadronic Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.2.3 Muon Spectrometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.3 Current Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.3.1 Silicon Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.4 ITk Upgrade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.5 Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.1 ATLAS Track Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.1.1 Pattern Recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.2 Tracking in Dense Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . 566 Emulation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626.1 Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626.2 Samples Used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636.3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.3.1 Energy Deposit Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.3.2 Re-clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 736.3.3 Truth Matching and ITk TIDE Neural Network . . . . . . . . . . . . . . . 796.4 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 816.4.1 Shared Hits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 816.4.2 Pion Tracks Accepted . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867.1 Layout Studies Using Single Tau . . . . . . . . . . . . . . . . . . . . . . . . . . . 867.1.1 Letter of Intent Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 877.1.2 CMOS Pixels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 887.1.3 Strip Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 907.1.4 Converting Strips to Pixels . . . . . . . . . . . . . . . . . . . . . . . . . . 917.1.5 Pixel Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 927.1.6 Pixel Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 947.1.7 Strip Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 978 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101vA Supporting Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106A.1 Diffusion Width Angle Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . 106viList of TablesTable 4.1 Design specification for Step 1 ITk pixel elements. The radius is the distancefrom the beam pipe of each layer, the R and Z-dimensions are the size of theindividual deteector elements, and the thickness is the thickness of active silicon. 40Table 4.2 Design specification for Step 1 ITk strip elements. The radius is the distancefrom the beam pipe of each layer, the R and Z-dimensions are the size of theindividual deteector elements, and the thickness is the thickness of active silicon. 40Table 6.1 The Run 2 TIDE Neural Network confusion matrix. Each row shows the numberof truth charged particles going through a cluster, while each column shows thefraction of the time the NN determined that particular cluster was from 1, 2 or 3particles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81viiList of FiguresFigure 2.1 All the fundamental particles included in the Standard model. Not shown arethe anti-particles described in text. [1] . . . . . . . . . . . . . . . . . . . . . . 4Figure 3.1 The concept of phase stability in a synchrotron accelerator. A bunch is charac-terized by the the synchronous particle (black dot) and the surrounding parti-cles (grey circle) - as these go through cavities with a time-varying RF voltage,particles in the bunch leading in time will obtain a negative voltage and thoselagging in time a positive voltage compared to the synchronous particle, keep-ing the whole bunch in time. The length between RF waveforms is called abucket. [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Figure 3.2 Left: Labelled forces due to quadrupole magnets. In this example, the quadrupolesin the beam are set up such that the beam is focused on the x-direction. Right:Cumulative effect of magnetic lensing in the x (top) and y (bottom) directionsleads to a cumulative focusing of the beam. [2] . . . . . . . . . . . . . . . . 9Figure 3.3 The LHC injection system. In normal proton-proton mode, the protons are firstaccelerated in the LINAC2, then in succesive sunchrotrons Booster, PS, SPSand finally to the LHC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Figure 3.4 The two beams in the LHC, going in opposite directions - red (clockwise) andblue (counter-clockwise). The arc and straight sections, as well as the interac-tion points are all labelled. There is also a beam dump to cease operations andbeam cleaning spots along the LHC. . . . . . . . . . . . . . . . . . . . . . . 11Figure 3.5 The magnetic field in a twin-bore beam pipe. The concept means there is op-posite magnetic fields in each pipe, both in the center left/right of the diagram,such that protons bunches can travel in opposite directions. . . . . . . . . . . 12Figure 3.6 Left: The difference between nominal, or luminosity during LHC runs; level-ling at HL-LHC and no levelling at HL-LHC. Both HL-LHC amounts of in-tegrated luminosity over the 15 hours will be the same, and about five timeshigher than LHC, but with levelling the pileuo will be constant. Right: Show-ing the average luminosity in solid lines and instantaneous luminosity withdashed lines for levelling and no levelling at the HL-LHC. [3] . . . . . . . . . 13viiiFigure 3.7 Left: A tt\u00C2\u00AF event from an ATLAS proton-proton collision during Run 2, witha number of pileup events about 20. Right: A simulated tt\u00C2\u00AF event from anATLAS proton-proton collision during the HL-LHC Run, with a number ofpileup events of 200. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Figure 4.1 A fully labelled cut-away view of the ATLAS detector. . . . . . . . . . . . . . 16Figure 4.2 A sketch of the role each part of ATLAS plays in particle identification andmeasurement. From the interaction point: the inner tracker detects chargedparticles and estimates their trajectory; the electromagnetic calorimeter mea-sures the energy of electrons and photons; the hadronic calorimeter measuresthe energies of the numerous hadrons produced - in this example protons andneutrons; finally the muon spectrometer acts as an extension of the inner trackerfor precise muon measurements far from the dense environment close to the in-teraction point. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Figure 4.3 Data flow for ATLAS trigger during Run 2. The level 1 trigger receives dataat about 40 MHz which is the bunch crossing rate, filtering it down to 100 kHzas input to the High Level Trigger (HLT). The HLT then only keeps 1 kHz forstorage int he CERN data networks. [4] . . . . . . . . . . . . . . . . . . . . . 18Figure 4.4 A 3D representation of the ATLAS calorimeters, including the barrel LiquidArgon EM calorimeter, the barrel Tile Hadronic calorimeter, the Liquid Argonendcaps for both EM and Hadronic calorimetry and finally the forward LiquidArgon Calorimeter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Figure 4.5 Diagram showing the chain reaction of an EM shower inside material. Eachlabelled t = n interval is a radiation length for an electron inside the material. . 20Figure 4.6 Diagram showing details of the ATLAS LAr EM calorimeter. The accordionshape can be seen, as well as the segmentation in the \u00E2\u0088\u0086\u00CE\u00B7 and \u00E2\u0088\u0086\u00CF\u0086 directions. [5] 21Figure 4.7 The proportion of each particle produced in a hadronic shower from an incident100 GeV proton in lead. [6] . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Figure 4.8 The segmentation of the hadronic calorimeter, showing the tiles that make-upthis part of the detector. [7] . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Figure 4.9 A 3D view of the muon spectrometers in ATLAS, showing where each of the 4different detectors are placed in the barrel and endcaps. . . . . . . . . . . . . 24Figure 4.10 Left: Operation of MDT, with a wire in a gas-filled tube, and muon tracksionization drifting to the wire. Right: Schematic of the CSC, with cathodestrips and anoe wires as readout. [8] . . . . . . . . . . . . . . . . . . . . . . 25Figure 4.11 Cross section of an RPC chamber. The strips and polysterene plates are shown.[8] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 4.12 Left: Location of the TGCs on the end-caps of ATLAS. Right: Schematic viewof the chamber, with the gap between graphite layers smaller than the spacebetween wires, meant to give fast timing information for triggering purposes. [8] 26ixFigure 4.13 3D view of the ATLAS Inner Detector, showing the barrel and end-cap regions.The pixels, strips and TRT can all be seen. . . . . . . . . . . . . . . . . . . . 27Figure 4.14 Schematic of the entire ATLAS Inner Detector for Run 1 (valid until 2012).Pixels, SCT and TRT are all shown, with a zoom into the pixel layers. Theradial distance of each from the beam pipe is shown, as well as the \u00CE\u00B7 range ofthe barrel and end-cap parts of each detector. [9] . . . . . . . . . . . . . . . . 28Figure 4.15 a 3D diagram of the ATLAS Inner detector, valid up to Run 1 (2012). Variousbarrel and end-cap features are shown. [9] . . . . . . . . . . . . . . . . . . . 28Figure 4.16 An R-\u00CF\u0086 view of the IBL in ATLAS Run 2. The beam pipe goes in/out of thepage. The local r is thus along the stave plane shown here, and the local z inand out of the page on the pixels shown. [10] . . . . . . . . . . . . . . . . . 29Figure 4.17 Left: An n-doped piece of silicon is attached to a p-doped piece of silicon. Thediffusion of electrons and holes create a depletion region. Right: The depletionregion is formed when diffusion and electric field due to charges reaches anequilibrium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Figure 4.18 An idealized view of charge drift and diffusion in a silicon detector. The driftcauses charge carriers to follow the electric field to the sensors, while the dif-fusion causes the charge carriers to spread out in the direction parallel to thedrift. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Figure 4.19 Diagram showing that a Lorentz angle is equivalent to a rotation of the detec-tor element equal to that angle. The particle traversing the detector element isshown as an arrow, while the signal on the top sensors is shown as grey distri-butions. [11] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Figure 4.20 A cross-section of the silicon inside ATLAS\u00E2\u0080\u0099s pixel detector (not to scale). Then-bulk in grey is shown between the n+ of the pixels and the p+ on the otherside of the silicon. Guard-rings and p-sprays are two other prominent featuresshown here which help protect against material buildup and radiation damage.The sensors are bump bonded through the bum pad to the front-end electronics.[12] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Figure 4.21 A blown-up view of the various pixel electronics for hybrid pixel modules. Thepixel sensors are connected to front end electronic chips, and on the other sidea printed circuit to route signal and power, with above it a module control chipand finally connections to electrical services. [13] . . . . . . . . . . . . . . . 33Figure 4.22 An R-\u00CF\u0086 view of the IBL in ATLAS Run 2. The beam pipe goes in/out of thepage. The local r is thus along the stave plane shown here, and the local z inand out of the page on the pixels shown. [14] . . . . . . . . . . . . . . . . . 34Figure 4.23 Two SCT sensors glued together with a stereo angle of \u00C2\u00B120 mrad, also con-nected to the services through the Hybrid assembly shown here. [14] . . . . . 35xFigure 4.24 The obsolete LoI-VF (Very Forward) layout showing the ITk with pseudo-rapidity coverage up to |\u00CE\u00B7 | = 4.0. The red are pixels, while blue are strips.The x and y axes are both in units of meter. [15] . . . . . . . . . . . . . . . . 38Figure 4.25 T The Extended 4.0 Layout concept for Step 1 ITk. 5 pixel layers in the centralregion are perpendicular to the beam pipe, with endcaps extending to a pseudo-rapidity of 4.0. The strips have a similar format. . . . . . . . . . . . . . . . . 39Figure 4.26 The Fully Inclined 4.0 Layout concept for Step 1 ITk. The 5 pixel layers inthe barrel region have inclined sensors at pseudo-rapidity above 1, leading tosmaller cluster sizes there. The rest of the layout is similar to the Extended 4.0. 39Figure 4.27 The data flow for the ATLAS data infrastructure. The top left shows the parti-cle generators, which first create the particles, and finally the top reight showsthe end-goal, raw data for reconstruction. Simulation goes through Hits, whichis where particles deposit energy, to digitization, which simulates detector re-sponse, to be eventually turned into Raw Data Objects (RDO). The bottomATLAS detector diagrams shows where ATLAS data starts, output through theelectronics into RDO for further reconstruction - this is where data and simula-tion converge. [16] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Figure 5.1 In examples (a), (b) and (d), the points x are connected through CCA. In exam-ple (c), the two x\u00E2\u0080\u0099s are not connected. [17] . . . . . . . . . . . . . . . . . . . 43Figure 5.2 Example of space points on different layers leading to an estimate of the tracktrajectory [18] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Figure 5.3 Diagram of simplified patter recognition in the Run 2 ATLAS Inner Detector.Space Points are seen in yellow, and rejected seeds frin global pattern recogni-tion output are shown with circles. The green circled track candidate as well asthe blue dashed line are rejected since they do not fit with the nominal interac-tion point. Red tracks show fully fitted track candidates, while the dashed circleshows a seed which shares space points with another accepted track candiddate,shown as a black line. [19] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Figure 5.4 The perigee parameters in the x-y plane (left) and in the r-z plane (right). [20] 46Figure 5.5 Example of the large number of seeds created, in Run 1 with only 3 pixel layersand 4 strips, and low number of pile-up. [21] . . . . . . . . . . . . . . . . . . 46Figure 5.6 Illustration of the inhomogeneous magnetic field in ATLAS for Run 1. The topimage is for the an r- screenshot of the field for the whole detector. Bottom leftshows how the magnetic field changes for both radius and andlge \u00CF\u0086 , the fieldhere is at z=0. Bottom right is a zoomed in diagram of the magnetic field in theinner detector. [22] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48Figure 5.7 Example of navigation of a track through the full inner detector geometry setup.The track parameters are calculated and fitted at each surface using the propa-gator method of choice. [22] . . . . . . . . . . . . . . . . . . . . . . . . . . 49xiFigure 5.8 The equation of motion is evaluated at four point k along the trajectory for afourth-order Runge-Kutta propagator. The position r and tangent vector to thetrack T are calculated at the initial step point, the two steps midway throughand the final step point. [23] . . . . . . . . . . . . . . . . . . . . . . . . . . 50Figure 5.9 Multiple scattering example for a 5 GeV muon through a silicon detector, show-ing projected scattering angle \u00CE\u00B8 pro j . The left shows Monte Carlo simulationsof 25000 muon events using Geant4, compared to two models, Highland andGaussian mixture model. On the right is an illustration of multiple scatteringand the effect on the particles\u00E2\u0080\u0099 direction. [22] . . . . . . . . . . . . . . . . . 51Figure 5.10 Material in each layer is modelled as surfaces with a certain thickness eachtrack goes through as seen on left, with exact material descriptions containedin databases for the extraplation and reconstruction. On the right is shown theagreement of tracking material with the full simulation. [22] . . . . . . . . . 52Figure 5.11 Diagram showing the propagation of track parameters through the detector lay-ers. At each layer, the propagated position and covariance matrix make up thewhite circles, with the track parameters and their covariance matrix make upthe cylinder predicting the extrapolation to the next layer. [22] . . . . . . . . 53Figure 5.12 Simulation of charged particle in jets, showing the average separation betweenthe two closest charged particles in both the transverse and longitudinal direc-tion, in the first pixel layer (R= 50.5 mm) as a function of transverse momentumof jets. The horizontal lines shown illustrate the size of a 50\u00C3\u0097 400 \u00C2\u00B5m pixel.[24] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Figure 5.13 Left figure is a pictorial representation of multiple tracks deposing energy andforming one cluster. Right figure - (a) shows the perspective from the siliconthickness where 1 particle deposits energy and (b) where multiple particles do.[24] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Figure 5.14 A working point plot for the Run 1 NN clustering. Determined through MonteCarlo, the cuts chosen split 71% of clusters from 2 particles correctly, while7.5% if clusters from 1 particle are incorrectly split. [24] . . . . . . . . . . . 58Figure 5.15 The average number of pixel clusters per track is shown for (a) \u00CF\u0081 sample and(b) \u00CF\u0084 sample. Baseline shows track reconstruction without track splitting in theAmbiguity Solver, while Ideal shows a truth-based reconstruction showing themaximum algorithmic efficiency. The \u00CF\u0081 has a two-prong decay while the \u00CF\u0084 hasa three-prong decay. This plot shows how the two-particle splitting of the TIDENN has a much better identification rate than the three-particle splitting. [25] . 59Figure 5.16 Ideal, or truth-based reconstruction efficiency for reconstructing all chargeddecay products of (a) \u00CF\u0081 and (b) \u00CF\u0084 is shown shown. The dependence on themaximum number of shared SCT clusters is clearly outlined. [25] . . . . . . 60xiiFigure 5.17 Algorithmic Reconstruction efficiency for single-\u00CF\u0084 to 3 charged pion events,defined as reconstruction efficiency when all clusters are not shared by morethan 2 particles in the truth record. [25] . . . . . . . . . . . . . . . . . . . . . 60Figure 5.18 Track Reconstruction efficiency for 3 TeV Z\u00E2\u0080\u0099 events where all tracks consideredhave a production vertex before the first layer. [25] . . . . . . . . . . . . . . 61Figure 6.1 Pictorial representation of particle decays. In this case, a particle labelled \u00CF\u0081decays into two charged particles. In (a), this decay is seen in the \u00CF\u0081 rest frame -the decay products are back to back due to conservation of momentum. In (b),we boost to the lab frame of a \u00CF\u0081 with low momentum - the two decay productsare well separated. In (c), we boost to the lab frame of a high momentum \u00CF\u0081 -the two decay products are emitted close together and have little separation -they are highly collimated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Figure 6.2 A 2D projection onto the x-y axis of a track is shown going through a layer ofsilicon. with one inner cylinder used find the track\u00E2\u0080\u0099s coordinates at the inneredge, and the outer cylinder to find the track\u00E2\u0080\u0099s coordinates at the outer edge.The incidence angle is accounted for, but no multiple scattering effects are con-sidered for the cylinder\u00E2\u0080\u0099s radius for extrapolation. Diagram is not to scale. . . 65Figure 6.3 From TIDE section - a projection onto the local r axis - the energy deposit widthfor one particle on that axis is shown on (a), and for a cluster of two particleson (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Figure 6.4 A 3D representation of a detector element, showing the local r and local z axison the detector element as well as the global (x,y,z) coordinate system. . . . . 66Figure 6.5 Left:A charged particle going through silicon projected onto the local r axisof the detector element. The first approximation to the energy deposit widthis the space in r between where the track exits the silicon and the point whereelectrons, travelling at the Lorentz angle, reach the edge of the silicon. Right:Energy deposit width projected onto the local z axis, in this case the electrons atthe drift edge travel straight up to the edge of the silicon, following the electricfield. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Figure 6.6 Left: A 3D representation of a track depositing energy (red) in a cluster ofdetector elements. The local r and z axes are shown along the edges of theelements. Right: At first the center coordinates of each track are found, thenthe distance in r (\u00E2\u0088\u009A\u00E2\u0088\u0086x2+\u00E2\u0088\u0086y2) is found between each, as well as the distance inz ( \u00E2\u0088\u0086z ). The maximum of each is the width of the cluster in r and z respectively. 67xiiiFigure 6.7 Cluster width in the r-dimension, as a function of incidence angle, for the vari-ous pixel layers (0-4). The fully simulated width is shown as red points whereasthe emulation, without correciton, is shown as a blue line. The lower plot showsthe ratio of emulated over simulated width. The black line in the ratio plot isa polynomial fit to the difference, which will be the correction applied to theemulation in order to properly emulate the width. . . . . . . . . . . . . . . . . 69Figure 6.8 Cluster width in the r-dimension, as a function of incidence angle, for the var-ious strip layers. Due to each strip layer being a combination of two strip de-tectors, there are eight corrections instead of four. Layers 5-8 denote the stripdetector closest to the interaction point for strip layer 0-3 respectively. Thefully simulated width is shown as red points whereas the emulation, withoutcorreciton, is shown as a blue line. The lower plot shows the ratio of emulatedover simulated width. The black line in the ratio plot is a polynomial fit to thedifference, which will be the correction applied to the emulation in order toproperly emulate the width. . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Figure 6.9 Cluster width in the r-dimension, as a function of incidence angle, for the var-ious strip layers. Due to each strip layer being a combination of two strip de-tectors, there are eight corrections instead of four. Layers 9-12 denote the stripdetector further from the interaction point for strip layer 0-3 respectively. Thefully simulated width is shown as red points whereas the emulation, withoutcorreciton, is shown as a blue line. The lower plot shows the ratio of emulatedover simulated width. The black line in the ratio plot is a polynomial fit to thedifference, which will be the correction applied to the emulation in order toproperly emulate the width. . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Figure 6.10 Cluster width in the z-dimension, as a function of incidence angle, for the vari-ous pixel layers (0-4). The fully simulated width is shown as red points whereasthe emulation, without correciton, is shown as a blue line. The lower plot showsthe ratio of emulated over simulated width. The black line in the ratio plot isa polynomial fit to the difference, which will be the correction applied to theemulation in order to properly emulate the width. . . . . . . . . . . . . . . . . 72xivFigure 6.11 Two tracks are shown going through 3 pixel layers. Their emulated energydeposit is shown in red, whereas the true simulated deposit is shown in green.In Layer (1), the energy deposit of the reference track overlaps in both local rand local z with another track, so this cluster will be shared - this matches theclustering from the baseline simulation. In Layer (2), there is overlap in thelocal z, but not in r - however, the distance in r is small, less than 1 detectorelement - the simulated cluster is thus also shared between the two tracks. InLayer (3), there is overlap in local r only as well, but the distance is muchgreater than in (2) - there is one simulated cluster per track in this case. Tore-cluster each energy deposit, the distance in r and z below which two tracksshare one cluster must be determined. . . . . . . . . . . . . . . . . . . . . . . 74Figure 6.12 Left: The previously shown energy deposit width diagram in local r, with theadded diffusion at the Lorentz angle. Right: Previously shown energy depositwidth diagram in local z, with the added diffusion at the incidence angle of 0. . 75Figure 6.13 The relevant geometry for calculating contributions for both edges of diffusionis shown, as projected onto the local r axis of the silicon. The same calculationcan be done for any positive or negative Lorentz Angle, and positive or negativeincidence angle. In the z direction, \u00CE\u00B8L is simply 0. . . . . . . . . . . . . . . . 76Figure 6.14 Depiction of the scan to find ideal cut values for clustering. Left: In the base-line simulation, the two tracks share a cluster on this particular layer. Afterfinding the energy deposit width, a scan in both r and z local axes is started,going from 0 (the energy deposit width) until 1 pixel width away from the en-ergy deposit width, where a deposit from another track is. Thus, if the cut valuewas 1 pixel width in both axes, emulation would consider this a shared cluster- in which case, the simulated cluster would have two tracks and the emulatedcluster would have two tracks; leading to a simulated over emulated ratio of 1.Right: Same scan, but in this case simulation has the two tracks having differ-ent, singular clusters. The cut value would need to be two detector elements inr and z for emulation to consider this a shared cluster. . . . . . . . . . . . . . 78Figure 6.15 The scan, as described in Figure 6.14, is done for all 5 pixel layers. A ratio onthe y-axis of 1 means that emulation has the same number of shared clusters asthe baseline simulation of the layout. On the x-axis is the scanned distance, inboth local r and z, below which two energy deposits from two tracks would beconsidered a single shared cluster. . . . . . . . . . . . . . . . . . . . . . . . . 78xvFigure 6.16 The scan, as described in Figure 6.14, is done for all 4 strip layers - due to thefact that each strip consists of two detectors, this means 8 total detector layersmust be scanned over. A ratio on the y-axis of 1 means that emulation has thesame number of shared clusters as the baseline simulation of the layout. On thex-axis is the scanned distance, in both local r and z, below which two energydeposits from two tracks would be considered a single shared cluster. . . . . . 79Figure 6.17 Comparing the fraction of shared clusters on each layer for the simulation ver-sus the emulation of TIDETester. The y-axis is the fraction of shared clusterswhile the x-axis is the radius of each layer from the beam pipe - thus each datapoint is the fraction of shared clusters at a specific layer. The black points arefull simulation for all tracking detectors, while red only has pixel detector em-ulated, green has only strip detector emulated, and blue data points have bothpixel and strip detectors emulated using TIDETester. The bottom insert showsthe ratio of shared clusters for TIDETester over the nominal (black) layout. . . 82Figure 6.18 Comparing the fraction of shared clusters on each pixel layer predicted byTIDETester depending on distance. The y-axis is the fraction of shared clusterswhile the x-axis is the radius of each layer from the beam pipe. In this test alllayers are moved away from the beam pipe to compare to the next layer - blackdata points are the first pixel layer, red the second, green the third, blue thefourth and brown the fifth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Figure 6.19 Comparing the fraction of shared clusters on each strip layer predicted byTIDETester depending on distance. The y-axis is the fraction of shared clusterswhile the x-axis is the radius of each layer from the beam pipe. In this testall layers are moved towards the beam pipe to compare to the previous layer- black data points are the first strip layer, red the second, green the third andblue the fourth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Figure 6.20 Comparing the track reconstruction efficiency for the simulation versus the em-ulation of TIDETester. The y-axis is the fraction of events where all threecharged pions from the \u00CF\u0084 were reconstructed as tracks, while the x-axis is thetruth transverse momentum of the \u00CF\u0084 lepton. The black points are full simulationfor all tracking detectors, while red only has pixel detector emulated, green hasonly strip detector emulated, and blue data points have both pixel and strip de-tectors emulated using TIDETester. The bottom insert shows the ratio of sharedclusters for TIDETester over the nominal (black) layout. . . . . . . . . . . . . 85xviFigure 7.1 LOI Layout ITk simulation. Testing the change of strip layers into pixels. They-axis shows the average efficiency to reconstruct the three charged pions fromthe tau lepton decay, as a function of the truth tau transverse momentum on thex-axis. The bottom insert shows the ratio of efficiency over the nominal (black)efficiency. Black point are baseline layout, red point have the first strip layerchanged into a pixel (50\u00C3\u0097 150 mum), green points have first two strip layerschanged to pixels, blue points have first three strip layers changed to pixels. . . 87Figure 7.2 STEP 1 ITk Layout - Baseline. The y-axis shows the average efficiency toreconstruct the three charged pions from the tau lepton decay, as a function ofthe truth tau transverse momentum on the x-axis. The baseline layout is shownin black, while the outermost (red) and two outermost (green) pixel layers areemulate with CMOS sensors. The bottom insert shows the ratio of efficiencyover the nominal (black) efficiency. . . . . . . . . . . . . . . . . . . . . . . . 88Figure 7.3 STEP 1 ITk Layout - the truth TIDE Neural Network splitting has been turnedoff for all pixel layers. The y-axis shows the average efficiency to reconstructthe three charged pions from the tau lepton decay, as a function of the truthtau transverse momentum on the x-axis. The baseline layout is shown in black,while the outermost (red) and two outermost (green) pixel layers are emulatewith CMOS sensors. The bottom insert shows the ratio of efficiency over thenominal (black) efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89Figure 7.4 STEP 1 ITk Layout - Baseline. The y-axis shows the average efficiency toreconstruct the three charged pions from the tau lepton decay, as a function ofthe truth tau transverse momentum on the x-axis. The baseline layout is shownin black, with the same baseline with TIDE NN turned off in last two pixellayers in red, with NN turned off and CMOS in last pixel layer in green, andfinally NN turned off and CMOS in last two pixel layers in blue. The bottominsert shows the ratio of efficiency over the nominal (black) efficiency. . . . . . 90Figure 7.5 STEP 1 ITk Layout - Baseline. The y-axis shows the average efficiency toreconstruct the three charged pions from the tau lepton decay, as a functionof the truth tau transverse momentum on the x-axis. The baseline geometryis in black, while largest strip lengths (47.64 mm) in all layers is in red, andshortest strip length (23.82 mm) in green. The bottom insert shows the ratio ofefficiency over the nominal (black) efficiency. . . . . . . . . . . . . . . . . . . 91xviiFigure 7.6 STEP 1 ITk Layout - Baseline. The y-axis shows the average efficiency toreconstruct the three charged pions from the tau lepton decay, as a function ofthe truth tau transverse momentum on the x-axis. The baseline geometry is inblack, while the first strip layer is changed to a 50\u00C3\u0097 400 \u00C2\u00B5m pixel in the reddata, and the first two strip layers are changed to a 50\u00C3\u0097 400 \u00C2\u00B5m pixel in thegreen data. The bottom insert shows the ratio of efficiency over the nominal(black) efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Figure 7.7 STEP 1 ITk Layout - Baseline. The y-axis shows the average efficiency toreconstruct the three charged pions from the tau lepton decay, as a function ofthe truth tau transverse momentum on the x-axis. The baseline geometry isin black, while in red are pixel dimensions 25\u00C3\u0097 100 \u00C2\u00B5m, and in green pixeldimensions 100\u00C3\u0097 25\u00C2\u00B5m. The bottom insert shows the ratio of efficiency overthe nominal (black) efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . 93Figure 7.8 STEP 1 ITk Layout - Baseline. This plot is binned in \u00CE\u00B7 to show the discrep-ancy in behaviour between the two tested pixel sizes. The baseline geometryis in black, while in red are pixel dimensions 25\u00C3\u0097100 \u00C2\u00B5m, and in green pixeldimensions 100\u00C3\u0097 25\u00C2\u00B5m. The bottom insert shows the ratio of efficiency overthe nominal (black) efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . 94Figure 7.9 STEP 1 ITk Layout - Baseline. The y-axis shows the average efficiency toreconstruct the three charged pions from the tau lepton decay, as a function ofthe truth tau transverse momentum on the x-axis. The baseline geometry is inblack, while data points in red move each pixel layer 20mm radially from thebeam pipe, in green 40mm, blue 60mm and brown 80mm. The bottom insertshows the ratio of efficiency over the nominal (black) efficiency. . . . . . . . . 95Figure 7.10 STEP 1 ITk Layout - Baseline. The y-axis shows the average efficiency toreconstruct the three charged pions from the tau lepton decay, as a function ofthe truth tau transverse momentum on the x-axis. The baseline geometry isin black, while data points in red move the first two pixel layers 5mm awayradially from the beam pipe, in green 10mm away, blue 5mm towards the beampipe and brown 10mm towards the beam pipe. The bottom insert shows theratio of efficiency over the nominal (black) efficiency. . . . . . . . . . . . . . . 96Figure 7.11 STEP 1 ITk Layout - Baseline. The y-axis shows the average efficiency toreconstruct the three charged pions from the tau lepton decay, as a functionof the truth tau transverse momentum on the x-axis. The baseline geometryis in black, while data points in red move the last three pixel layers 10mmradially towards from the beam pipe, in green 10mm away, blue 20mm andbrown 30mm away. The bottom insert shows the ratio of efficiency over thenominal (black) efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97xviiiFigure 7.12 STEP 1 ITk Layout - Baseline. The y-axis shows the average efficiency toreconstruct the three charged pions from the tau lepton decay, as a function ofthe truth tau transverse momentum on the x-axis. The baseline geometry is inblack, while data points in red move the first three strips layers 50mm radiallyaway from the beam pipe, in green 100mm away, blue 50mm towards the beampipe and brown 100mm towards. The bottom insert shows the ratio of efficiencyover the nominal (black) efficiency. . . . . . . . . . . . . . . . . . . . . . . . 98Figure A.1 Diagram with necessary labels to carry out the derivation of angle of electrondiffusion in silicon. The track, in red, traverses at the Lorentz Angle, leaving ameasurable energy deposit width l. Thickness t is known, as well as the Lorentzangle. Triangle lengths a and b are unknown but will be used in the derivation;\u00CE\u00B8D is the wanted variable. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106Figure A.2 Result of solving the equations of this section with mathematica. . . . . . . . 107xixList of AcronymsCERN Conseil Europe\u00C2\u00B4en pour la Recherche Nucle\u00C2\u00B4aire , translates to European Organisation forNuclear Research, main body coordinating research at the Large Hadron ColliderLHC Large Hadron Collider , the accelerator complex used to accelerate and contain particlesfor particle physics researchATLAS A Toroidal LHC ApparatuS , one of the detectors placed in the Large Hadron Collidermain ring to reconstruct particle collisions for particle physics researchCMS Compact Muon Solneoid , one of the detectors placed in the Large Hadron Collider mainring to reconstruct particle collisions for particle physics researchHL-LHC High Luminosity Large Hadron Collider , the planned upgraded Large Hadron Collidercomplex to deliver about an order of magnitude more data than the current outputITK Inner Tracker , the name of the planned charged particle tracker to be inserted intoATLAS in 2024QED Quantum Electro Dynamics , a field theory governing the interactions between chargedparticles mediated by the photonQCD Quantum Chromo Dynamics , a field theory governing the interactions between coloredparticles mediated by the gluonsEM Electro-Magnetic , one of the four fundamental forces of nature, mediated by photons andinvolving the interaction between charged particlesRF Radio Frequency , any electromagnetic wave emitted in the frequency range of radio,about 3 kHz to 300 GHzID Inner Detector , the part of ATLAS closest to interaction point, tracking detectors thatmeasure charged particles\u00E2\u0080\u0099 trajectory as they go through the detectorTRT Transition Radiation Tracker , the outer part of the ATLAS Inner Detector; set up suchthat electrons going through produce Cherenkov radiation so they are identified correctlyxxIBL Insertable B-layer , a new layer of pixel detectors added for ATLAS Run 2, closest to theinteraction point, whose main purpose is tracking of particles involving b-quarksLOI Letter of Intent , a 2012 technical document outlining initial plans for a new ATLAS InnerDetector to be inserted in 2024CCA Connected Component Analysis , an algorithm made to assemble nearby pixel or striphits together in order to determine what detector elements charged particles have gonethrough in the ATLAS Inner DetectorTIDE Tracking in Dense Environments , an algorithm developed to aid in track reconstructionwhen the track separation is on the order of the size of individual detector elements(pixels,strips)NN Neural Network , in this work, a reference to the Neural Network developed in ATLASfor improving reconstruction in dense track environmentsRDO Raw Data Object , a data format in ATLAS which encodes voltages and timings from thedetector, and needs to be further analysed for performance and physics useCMOS Complementary metal-oxide-semiconductor , an integrated circuit technology - in ATLASCMOS sensors refer to detector elements where many components can be joined togetherto save space and materialxxiGlossaryATHENA is a complex computer program uniting the ATLAS simulation, reconstruction and anal-ysis code base. It comprises hundreds of thousands of lines of code, mostly in Python andC..barn , equal to 10\u00E2\u0088\u009224 cm2, is a measure of a particle event\u00E2\u0080\u0099s cross section, or the probability thatan event occurs. A femtobarn, commonly used in particle physics is thus 10\u00E2\u0088\u009215 barns.barrel is the part of the ATLAS Inner Detector with detector elements parallel to the beam pipe,and at low pseudorapidity. However, it also sometimes contains inclined sensors..boosted is a term for an object with high Lorentz factor, meaning its speed is close to the speed oflight causing special relativistic effects. A high mass object typically decays to many boostedparticles, leading to densely grouped showers producing dense environments in a particledetector.bunches are a packet of about 1034 protons for LHC collider; in typical operation there are thou-sands of bunches travelling in opposite directions at the LHC and colliding at the variousdetector experiments - due to low cross-section these high numbers result in at most hun-dreds of proton interactions per bunch collision.collimation is when groups of particles have trajectories very close together, typically with a sep-aration on the order of a detector elements\u00E2\u0080\u0099 size. This leads to difficulties in resolving theindividual collimated objects.cross-section a property that relates to the likelihood of scattering occurring for a particle, has unitsof area, and differs for each unique particle..dE/dx refers to the energy loss of a particles as they go through the ATLAS detector, usually as aresult of interaction with detector material.displaced vertices happen when a particle decays a measurable distance inside the detector fromthe bunch collision - this creates a vertex not from proton collisions displaced from wheremost particles in an event came from.xxiievent is the result of two bunches of protons colliding, and encompasses the aftermath of whathappens after this one particular collision.fluence is the energy received per surface per unit area.integrated luminosity is the total delivered luminosity over time to a detector, which can also bethought of as the total delivered data, usually stated in units of inverse femtobarn.interaction point is the position where the two bunches of protons are made to collide at the centerof the ATLAS detector.inverse femtobarn is a unit of measurement of the total number of collisions events per femtobarn,encoding information about both the cross-section of the collision and the total amount ofdelivered data.jets are the result of the showering of particles when a quark is momentarily not confined in astable state, seen in particle detectors as a cone of particles..luminosity is a measurement of the total number of collisions that are expected to be produced ina detector per second and per cm2.minimum bias refers to an unbiased selection of proton-proton collisions; since most collisions areglancing blows a minimum bias distribution includes a majority of low-momentum productsof proton-proton collisions, a good model for pileup.missing transverse energy is a calculation done using conservation of momentum; since all theproton momentum is initially in the longitudinal plane, all proton collision products shouldhave a total vectorial transverse momentum add up to zero. If it does not, it indicates oneor more particles in the event not seen in the detector, with total energy equal to the missingtransverse energy.pileup is the result of many protons colliding during the same event - usually only one interactionwill be of interest, and the others are a hindrance to reconstruction - these others are what isknown as pileup. In-time pileup.primary vertices are where the particles with the highest total momentum in an event originate -usually the product of two protons colliding, and the interaction of interest in the event.pseudorapidity or \u00CE\u00B7 , describes a function the angle relative to the beam axis of a particle detector,\u00CE\u00B7 = \u00E2\u0088\u0092 ln[tan(\u00CE\u00B82 )], used primarily since the particles produced are constant as a function ofpseudorapidity, and differences in pseudorapidity are Lorentz invariant under boosts alongthe beam axis..xxiiiRun 1 is the ATLAS data-taking period from 2011 to 2012, containing collisions at center of massenergy of 7 and 8 TeV.Run 2 is the ATLAS data-taking period from 2015 to 2018, containing collisions at center of massenergy of 13 and (tentatively) 14 TeV.secondary vertices is where the particles which do not have the highest total momentum in anevent originate - usually the product of two protons colliding, but generating particles notcommonly useful for research.services are a general name for material inside the Inner Detector which does not constitute activesensing - these include coolant pipes, data wires and other such connections.time over threshold refers to the time a specific readout channel in a detector element is abovea certain voltage threshold - dependent on how much energy a particle deposited in thatelement.tracks are an object constructed in the ATLAS Inner Detector, connecting energy deposits in activedetector elements meant to approximate a charged particles\u00E2\u0080\u0099 trajectory from interaction to itsexit from the detector, decay or absorption in material.transverse plane is the plane perpendicular to the beam axis, which is also called the longitudinalaxis.vertex is a position from which particles in an event originate; typically there are primary, sec-ondary and displaced vertices.xxivAcknowledgmentsJe voudrais remercier mes parents, Nancy et Luc, sans qui rien de tout cela n\u00E2\u0080\u0099aurait e\u00C2\u00B4te\u00C2\u00B4 possible.Also thanks to Claudine and Simone - you guys have some catching up to do.I would also like to thank Anadi Canepa, who was the catalyst behind me taking on this project.Very special thanks also to Alison Lister, who was behind me the whole time with lifesaving adviceand words of encouragement. I would also like to acknowledge the entire UBC ATLAS groupfor their tremendous aid, both technical through our many meetings but most of all for being atremendous community inside our physics bubble.Finally, thanks to friends near and far, you kept me sane through this ordeal. I couldn\u00E2\u0080\u0099t havedone this without you!xxvChapter 1IntroductionThe current data taking at the Large Hadron Collider (LHC) in Geneva, Switzerland has provenparticularly fruitful for particle physics research since its official start in 2010, the announcement ofthe discovery of a particle consistent with the standard model Higgs Boson by ATLAS (A ToroidalLHC Apparatus) and CMS (Compact Muon Solenoid) in 2013 being chief amongst them. However,this discovery and the multitude of standard model precision measurements that have been done areonly half the story. The Standard Model, being the theory that classifies and explains the fundamen-tal particles and forces of the world, has a multitude of issues that have been heavily investigated inthe past decades. This includes its inability to be unified with General Relativity and thus its lackof explanation for the gravitational force; a related problem is the lack of a particle in the standardmodel consistent with a dark matter candidate. Other issues include the \u00E2\u0080\u0098Hierarchy problem\u00E2\u0080\u0099, whichboils down to the fact that there is no theoretical basis for why all fundamental particles have themasses that have been experimentally determined, or even to why fundamental particle masses aredifferent at all. This host of problems leads us to the second half of the LHC\u00E2\u0080\u0099s programme - toprobe the boundaries of new physics. Whether through new theories such as Supersymmetry orextra dimensions or extensions to the standard model, ATLAS and the LHC are at the forefront ofthis quest for better understanding of the universe.For the dual goals of fantastic precision to standard model processes and thorough searchesfor new physics to be achieved, massive amounts of particle collision data needs to be produced.The High-Luminosity LHC (HL-LHC) is a planned upgrade to the accelerator complex at CERN inGeneva, Switzerland, which plans to deliver about an order of magnitude higher collisions per unittime than current (2016) performance from 1\u00C3\u00971034 cm2s\u00E2\u0088\u00921 to 7.5\u00C3\u00971034 cm2s\u00E2\u0088\u00921. This will allowfor much higher statistics leading in turn to the probing of phase spaces of new theories inaccessibledue to their low cross-section - which is their probability of occurring. However, this increase inhard-scatter collisions, which are the ones of interest, means an increase in pileup collisions, lowerenergy proton collisions at the same time as those of interest, leading to difficult environments inwhich to reconstruct particles of interest.To solve this problem, it is planned to completely remove the Inner Tracker of the ATLASdetector during the HL-LHC shutdown in 2024. It will be replaced by a new particle tracker,1named ITk. Particle trackers follow the trajectory of charged particle from the collisions and areinvaluable for both particle identification and kinematic variable measurements such as momentum,charge and vertex position. It is planned to be more granular and extend further than the currentdetector, lending it much greater power in identifying pileup vertices from the hard-scatter verticesof interest. However, the design of this tracking detector should be optimised in order to get thebest possible performance out of the detector.One of the most challenging performance indicators for a tracking detector is performancein dense environments. Dense environments in a particle physics context means environmentswhere particles\u00E2\u0080\u0099 separation is very close to the separation between individual detector elementssuch as pixels. As such, the detector layout should take into account this performance when beingdesigned. This thesis will motivate, construct and validate a tool to do exactly this in simulation,as well as show results that optimise the detector element sizes, thickness, type and distance fromthe interaction point with the goal of investigating optimal ITk layout for performance in denseenvironments, with the additional constraints that come with having to have excellent kinematicmeasurement capabilities at the same time.2Chapter 2Theory2.1 The Standard ModelThe Standard Model at its core is a theory of the particles which inhabit our world and the inter-actions between them. The Standard Model is the combination of our theoretical understanding ofquantum field theory and the combined experimental knowledge we have acquired over a centuryof experimental research into the elementary particles that make up matter. It can, at the risk ofover-simplification, be broken down into two categories - the fundamental particles that make upmatter and the forces of interaction between them.2.1.1 Fundamental ParticlesThe first category of fundamental particles is the group of fermions, made up of leptons and quarks,all with spin 1/2. These particles follow Fermi-Dirac statistics and obey the Pauli exclusion prin-ciple. There are three generations of leptons: the electron and the electron neutrino; the muon andthe muon neutrino; and finally the tau and the tau neutrino. Each of these have an antiparticle, andfurthermore the electron, muon and tau have a \u00E2\u0088\u00921 charge while the neutrinos are neutral, for a totalof 12 different leptons - the antiparticles will have opposite charge. The quarks also have threegenerations: the up (u) and down (d) quarks; the strange (s) and charm (c) quarks; and finally thebottom (b) and top (t) quarks. The d, s and b quarks have charge \u00E2\u0088\u00921/3 while the u, c, and t quarkshave charge +2/3; all have anti-particles with the opposite charge. Furthermore, each quark cancarry one of three \u00E2\u0080\u0099colors\u00E2\u0080\u0099 - an intrinsic property not related to macroscopic color of visible light- of either blue, green or red, with anti-blue, anti-green or anti-red available to the antiquarks. Intotal, this gives 36 possibilities for different quarks. The quarks combine into colorless bound statecombinations of 3 quarks called a baryon or of 2 quarks called a meson - these must be colorlessfrom either having a color and its anti-color (meson) or a combination of all three colors (baryon).The familiar protons and neutrons which make up the atoms are the most stable discovered baryons.The second category of fundamental particles are bosons, with spin 1. These are the force car-riers of the theory and mediate all interactions. The photon mediates electromagnetic interactions3between charged particles, is massless, and is characterized by the theory of quantum electrody-namics (QED). The W+, W\u00E2\u0088\u0092 and Z gauge bosons mediate the weak interactions and are massive.Gluons are massless and mediate strong interactions between particles that carry colors - the quarksand themselves. The gluon interactions are characterized by quantum chromodynamics (QCD).Finally, the Higgs Boson was a long-standing mystery of the standard model before its discoveryby the LHC experiments ATLAS and CMS in 2012 as a 125 GeV particle [26]. The Higgs Bosons,unlike the other force carriers, is a scalar and has a spin of 0. It is responsible for the Higgsfield, which has a non-zero vacuum expectation value, allowing for spontaneous breaking of theelectroweak gauge symmetry. This leads to particles having mass through interaction with this field[27].These particles and these properties can be seen summarized in Figure 2.1.Figure 2.1: All the fundamental particles included in the Standard model. Not shown are theanti-particles described in text. [1]2.1.2 Fundamental ForcesThere are four fundamental forces of nature, at least at the energy scales of the world we live in;the three described by their mediating particles in Section 2.1.1 are the strong, electromagneticand weak forces; there is also the gravitational force, described by general relativity, for whichno mediating particle has been found yet. The strength of the gravitational force is on the order4of 10\u00E2\u0088\u009242 times weaker than the strong force - thus the effects of gravitation on particle physicsexperiments are negligible.The electromagnetic (EM) force is mediated by photons and involves the interaction betweencharged particles. A representation of the theory can be made using Feynman diagrams, whereinteractions between photons and and charged fermions are called vertices. The coupling, or fine-structure constant constant, \u00CE\u00B1 \u00E2\u0089\u0088 1137 characterizes the strength of the EM interaction between thefundamental particles. It also relates the number of vertices in an interaction with the probability ofit occurring, meaning that more complex EM interactions are much less likely to occur.The strong force is mediated by gluons and deals between particles containing colors, the quarksand gluons themselves. It can also be represented using Feynman diagrams, with the main differ-ence from EM force being that the gluon can interact with itself, and thus gluon-gluon vertices arepossible in the theory in addition to the regular quark-gluon vertices. The coupling constant in thestrong force, \u00CE\u00B1 , is greater than 1 at a low energy regime, meaning that in theory diagrams with moreloops have a higher chance of occuring. However, due to asymptotic freedom, the constant actualdepends on distance - the larger it is, the bigger the coupling. This means that, on the distancerange of bound states of quarks, such as protons, the coupling is small and thus simpler diagramscan describe the theory very well.Finally, the weak force is mediated by the W\u00C2\u00B1 bosons for charged interactions, and the Z bosonfor neutral interactions, and can also be described by Feynman diagrams. While lepton flavor(connecting same generations of leptons) is conserved, a weak interaction does not conserve flavorfor quarks, meaning a quark of a certain generation could turn into another generation (following allthe other rules) by interacting with a W boson. The flavour-changing weak decays are encapsulatedinto the Cabibbo-Kobayashi-Maskawa (CKM) matrix, which measures the coupling of quarks todifferent generations through the weak process [27, 28].2.2 Simulating Events in Particle PhysicsIn order to simulate the product of collisions in particle detectors event generators are used whichare based on perturbative quantum field theories such as QCD along with a phenomenological ap-proach, controlled by a large amounts of free parameters. The perturbative approaches are mostlyapplied to high-momentum interactions while softer ones use a more phenomenological approachdue to the breakdown of the current perturbative theories at low energy. The proton-proton un-derlying event involving the parton, particle decays, hadronization and particle showering are allmodelled using a Monte Carlo approach that generate distributions approaching real results on av-erage. This extends to generating a large number of particle decays within detectors for studies,such as single-particles not directly from a proton-proton collision. All these are generated in eventgenerators such as Pythia [29], Herwig [30], PowHeg [31], Sherpa [32], MadGraph [33] or othersuch programs; combined with a GEANT4 simulation of detectors this forms a very powerful wayof testing theories in particle physics experiments.52.2.1 Parton InteractionsParticle colliders such as the LHC collide protons going in opposite directions. Under the partonmodel, the proton, as a colored particle, will have three valence quarks, two up and one down quark,as well as a number of non-valence quarks and gluons that increase in number with increasingenergy. Thus, at low collision energy a proton-proton collision may appear like an elastic collisionbetween two particles, or with slightly more energy the valence quarks could interact [34]. Athigh energies such as the LHC, a proton-proton collision will result in interaction between eithervalence or non-valence quarks from both protons or gluons, which is required in order to study newdevelopments in the standard model or for precision measurements of the theory.In order to emulate this, a Parton Distribution function, which is the probability density forfinding a certain quark or gluon in a hadron as a function of the quark or gluon\u00E2\u0080\u0099s fraction of baryonmomentum, is computed using a mix of QCD and experimental data [35].6Chapter 3Large Hadron ColliderAccelerators used in particle physics research can be divided into two main categories - linearand circular. In both scenarios particles - usually protons, antiprotons, electrons or positrons - areaccelerated to relativistic speeds and then made to collide, normally either with particles going theother direction or onto a fixed target. The challenges are many but can be summarized into twobroad fields - accelerating the particles to the desired speed, and keeping the particles in a smallspace so they can collide exactly where you want it to. In most cases modern accelerators will useelectric and magnetic fields for these two purposes.The LHC itself is a synchrotron accelerator, the name for a ring of magnets bending and accel-erating particles until they are guided to collide. Due to the nature of the accelerator, particles to beaccelerated must have a minimum energy before being inserted into the main LHC ring, leading toa series of injection accelerators, most of which are themselves synchrotron accelerators.3.1 Current LHC Accelerator3.1.1 Principles of Synchrotron AcceleratorsThe operation of a synchrotron can be divided into accelerating and focusing phases. The acceler-ation is handled by a radiofrequency (RF) system in various cavities around the accelerator. Thecavity is a metallic chamber with an amplifier, in modern accelerators usually a klystron [36], pro-ducing a high power electromagnetic field at a certain frequency, normally in the MHz range. Theshape of the cavity is determined such that the EM waves become resonant within it.Particles going around the accelerator are carefully timed such that the frequency of their motionin the ring divided by the frequency of the EM field inside the cavity is an integer value. Then, itis just a matter of controlling the timing of the particles such that acceleration in the cavities occursuntil they are at the design velocity. After this, energy can be simply injected into the motion suchthat speed around the ring is constant, turning the accelerator into a storage ring.Of course, the world is not this ideal, and particles delivered to the accelerator are not perfectlysynchronous with the RF frequency. However, the concept of phase stability means this is not an7absolute necessity. This concept works by timing the arrival of particles on the rising edge of thevoltage wave in the cavity, then particles going slightly faster will arrive earlier and experiencesmaller energy transfer, whereas particles coming in later will receive more energy. Thus, all par-ticles will oscillate around the synchronous frequency desired - this is shown in Figure 3.1. Thisway, many bunches of particles can be accelerated at once around the ring such that each buncharrives near one of the rising edges of the voltage wave in the cavity, and will be kept at the designspeed. This gives rise to the concept of bunches, which is the largest size of a collection of protonsthat can be kept in equilibrium through this scheme [37].Figure 3.1: The concept of phase stability in a synchrotron accelerator. A bunch is charac-terized by the the synchronous particle (black dot) and the surrounding particles (greycircle) - as these go through cavities with a time-varying RF voltage, particles in thebunch leading in time will obtain a negative voltage and those lagging in time a positivevoltage compared to the synchronous particle, keeping the whole bunch in time. Thelength between RF waveforms is called a bucket. [2]The second main concept behind a synchrotron accelerator is that of focusing the beam into thecircular ring. As with all circular motion, there must be a force applied continuously to stay in thatmotion - this is done by magnets along the ring. The concept is very much similar to optical lensing,and in the case of most modern synchrotrons the lens are quadrupole magnets. It is impossible tofocus in two directions - ie to focus the beam of particles in the x and y direction if those are thetransverse axes - but each axis can be focused alternatively, this can be seen in Figure 3.2. Theadditive effect of this is eventual focusing in both directions, and thus a stable beam can be pilotedthrough a circular accelerator using these magnets [38].8Figure 3.2: Left: Labelled forces due to quadrupole magnets. In this example, thequadrupoles in the beam are set up such that the beam is focused on the x-direction.Right: Cumulative effect of magnetic lensing in the x (top) and y (bottom) directionsleads to a cumulative focusing of the beam. [2]Finally, synchrotron cannot accelerate particles from zero kinetic energy, and in fact as acceler-ators go to higher design energy, more injection steps are needed to obtain particles of the minimumenergy to be accelerated within the newest synchrotron.The injection of protons into the LHC begins with research grade hydrogen, from which theatoms are ionised and the protons kept. This is then injected with 50 MeV of energy through theLINAC2, the only linear accelerator in the injection scheme. The protons are then injected intoa booster ring and accelerated to 1.4 GeV; then injected into the Proton-Synchrotron (PS) systemand accelerated to 25 GeV, and finally to the Super-Proton-Synchrotron (SPS) and accelerated to450 GeV. This is the final step, as the 450 GeV protons are then injected into the LHC ring andaccelerated to design energy. The whole process is shown in Figure 3.33.1.2 LHC Injection System3.1.3 LHC AcceleratorThe LHC is not shaped as a perfect ring but has separate circular and straight sections, with 8straight sections approximately 528m long used for acceleration and beam crossings and 8 arcs tocomplete the circle, which can be seen in Figure 3.4. Acting as a collider, the LHC provides eachexperiment with a certain number of events of a particular type depending on the luminosity (L)achieved and the cross-section (\u00CF\u0083event of the particular process [39],Nevent/sec = L\u00CF\u0083event (3.1)The luminosity is a parameter of the machine and depends only on the beam configuration,assuming Gaussian distribution of protons,L =N2b nb frev\u00CE\u00B3r4pi\u00CF\u0083n\u00CE\u00B2\u00E2\u0088\u0097 F (3.2)9Figure 3.3: The LHC injection system. In normal proton-proton mode, the protons are firstaccelerated in the LINAC2, then in succesive sunchrotrons Booster, PS, SPS and finallyto the LHC.where Nb si the number of protons per bunch, nb is the amount of bunches per beam (2808nominally in the current LHC) frev is the frequency of revolution, \u00CE\u00B3r is the relativistic Lorentz factor,\u00CF\u0083n and \u00CE\u00B2\u00E2\u0088\u0097 beam parameters emittance and beta function respectively, and finally F is a geometricluminosity reduction factor, which depends on \u00CE\u00B8c which is the full crossing angle at the interactionpoint, \u00CF\u0083z the RMS bunch length and \u00CF\u0083\u00E2\u0088\u0097 the transverse RMS beam size at the interaction point, suchthatF =(1+(\u00CE\u00B8c\u00CF\u0083z2\u00CF\u0083\u00E2\u0088\u0097)2)\u00E2\u0088\u00921/2(3.3)10Figure 3.4: The two beams in the LHC, going in opposite directions - red (clockwise) andblue (counter-clockwise). The arc and straight sections, as well as the interaction pointsare all labelled. There is also a beam dump to cease operations and beam cleaning spotsalong the LHC.Both ATLAS and CMS experiments at the LHC require high luminosities for maximum searchand measurement potential - for LHC Runs prior to the 2024 upgrade the stated design luminosityis L = 1034 cm2s\u00E2\u0088\u00921 for proton collision, which has already been overtaken in 2016 with L\u00E2\u0089\u0088 1.37\u00C3\u00971034 cm2s\u00E2\u0088\u00921 . The decision was made early in the design of the LHC that this luminosity targetmeant a proton-anti proton collider would not be sufficient, as the rate of cost-effective anti- protonproduction could not match the desired luminosity. The advantage of a pp\u00C2\u00AF collider is that onlyone beam with one time-varying magnetic and electric field is needed as the different signs on theparticles mean the beams can go in opposite direction. The LHC is a proton-proton collider and thusneeds two separate beam pipes, with separate magnetic fields for focusing and RF electric fields foracceleration. Due to the small amount of tunnel space available for the LHC a twin-bore design isused, with beam channels in a common cryostat and opposing magnetic flux for each [40], as seenin Figure 3.5.11Figure 3.5: The magnetic field in a twin-bore beam pipe. The concept means there is oppositemagnetic fields in each pipe, both in the center left/right of the diagram, such that protonsbunches can travel in opposite directions.The magnets used at the LHC are NbTi Rutherford cables, cooled to below 2 K using superfluidhelium, to act as a superconductor and generate a field above 8 T. The accelerating RF cavitiesoperate at a frequency of 400 MHz, and the beam pipes are kept to such a vacuum that the densitieswill be below 1013 H2m\u00E2\u0088\u00923 - this is the least dense space in the Solar System. A number of differentquadrupole magnets are used at different spaces in the ring to keep the proton bunches in the beampipe, while dipole magnets are used bring the two beams together for collision in the interactionpoints and apart for travel in the other sections of the ring. Finally, each bunch has about 1.5\u00C3\u00971011protons at the beginning of each run, and the interactions points around the experiments will see abunch collision every 25 ns [41].3.2 High-Luminosity LHCThe High-Luminosity LHC (HL-LHC) is a planned upgrade for the LHC and injection complexplanned to take place during a shutdown in colliding operations between 2024 and 2026. The goalis to increase the luminosity to about L = 7.5\u00C3\u0097 1034 cm2s\u00E2\u0088\u00921. This would lead to an integratedluminosity of 3000 fb\u00E2\u0088\u00921 over the lifetime of the LHC, whereas prior to the upgrade the total inte-grated luminosity is slated to be around 300 fb\u00E2\u0088\u00921 [42]. This staggering increase in available datagives much greater potential to many of the physics goals of the LHC experiments such as AT-LAS and CMS. These physics studies include precision measurements of the Higgs Boson [43] andvector-boson scattering [44], as well as searches for physics beyond the standard model such assupersymmetric particles [45] and extra dimensions [15].Many of the beam characteristics will have to be changed in order to gain this increase inluminosity. First the amount of protons per beam will have to be increased to about 2.2\u00C3\u00971011, about12a 30% increase from current (Run 2) Performance. which can be done by increasing both the beamcurrent and brightness. Second, the \u00CE\u00B2\u00E2\u0088\u0097 factor in Equation 3.2, which is related to the transversesize of the beam at the interaction point, can be decreased which leads to increased luminosity.However, the changed geometry of interaction leads to a larger crossing angle \u00CE\u00B8C. The differentcrossing angle can be solved by techniques such as crab cavities [3]. Finally, the higher numberof protons leads to a faster \u00E2\u0080\u0099luminosity burn\u00E2\u0080\u0099, or number of protons consumed in the collisions.Luminosity levelling is a technique which is planned to keep the instantaneous luminosity stableover each colliding period, about 14 hours, such that the instantaneous luminosity goals can beachieved, as seen in Figure 3.6 [3].Figure 3.6: Left: The difference between nominal, or luminosity during LHC runs; levellingat HL-LHC and no levelling at HL-LHC. Both HL-LHC amounts of integrated luminos-ity over the 15 hours will be the same, and about five times higher than LHC, but withlevelling the pileuo will be constant. Right: Showing the average luminosity in solidlines and instantaneous luminosity with dashed lines for levelling and no levelling at theHL-LHC. [3]The effect of these upgrades and many more planned for the LHC on the detectors is to increasethe amount of proton interactions during each bunch crossing. The nominal LHC value for eventsper crossing is 27 which is the current average in Run 2. With an increase in instantaneous lumi-nosity of about an order of magnitude, the same increase in events per bunch crossing is expected,to an average of about 200 interactions per bunch crossing for HL-LHC - the massive increase canbe seen in Figure 3.7. Thus one of the main motivations for detector upgrades is optimizing per-formance in the dense environments of 200 proton-proton interactions in addition to the primaryinteraction that is being studied.13Figure 3.7: Left: A tt\u00C2\u00AF event from an ATLAS proton-proton collision during Run 2, with anumber of pileup events about 20. Right: A simulated tt\u00C2\u00AF event from an ATLAS proton-proton collision during the HL-LHC Run, with a number of pileup events of 200.14Chapter 4ATLAS4.1 Detector OverviewAs an instrument for particle physics research, ATLAS is well-suited for both precision measure-ments of fundamental physics as well as the search for new physics to answer some of the mostpressing issues in the field [9].Some of these precision measurements include tests of QCD, electroweak interactions and flavourphysics; as well as measurements of the coupling and spin of the top quark, which will be producedin high quantity at the LHC. The Standard Model Higgs Boson has been discovered [? ] throughdiphoton and ZZ searches, but other channels will contribute precise measurements of its proper-ties.Higgs bosons beyond the standard model, such as the A or H\u00C2\u00B1, decay preferentially to tau leptonsor b-jets. Heavy gauge bosons such as W \u00E2\u0080\u00B2 or Z\u00E2\u0080\u00B2 currently have been limited to masses above 3TeV. Excellent resolution of high-pT leptons and charge identification is needed in these searches.Flavour-changing neutral currents and lepton flavour violation through decays to muons are also apossible search avenue.Supersymmetric particles could be detected by a decay cascade down the to lightest supersymmetricparticle (LSP) which, given that it would only interact weakly with the detector, requires very goodmeasurements of the missing transverse energy in the detector, and as in other channels the iden-tification of leptons and jets from supersymmetric decays. The signature for gravitons, a theorisedparticle thought to be associated with gravity, could be missing energy due to extra dimensions orTeV-scale decays due to large separations in mass. Finally, miniature black holes decaying to jetsleptons, photons, neutrinos, W\u00E2\u0080\u0099s and Z\u00E2\u0080\u0099s is also a possible search avenue.Another challenge for the detector design arises from the fact that the high proton-proton crosssection means every event possibly tagged as new physics can be accompanied by a large num-ber (20 in 2015, up to 200 after 2024) of inelastic proton collisions from many protons collidingduring each bunch crossing. Many of these will be QCD jet production, which has a cross-sectionmuch higher the majority of processes of interest, meaning that the detector must have phenomenal15particle identification to extricate interesting events from the so-called background. Thus particleidentification is the crux of the many working parts of the ATLAS detector.As can be seen in Figure 4.1, the ATLAS detector is mostly cylindrical in shape, with forward-backward symmetry around the interaction point which is at its center. There are a number ofmagnets for particle momentum measurement - a thin superconducting solenoid around the innerdetector for momentum measurement of charged particles, and three large superconducting toroidalsystems, one in the central region and two on the endcaps, providing a magnetic field for the muonmomentum measurement. Many of the particle interactions can be seen in Figure 4.2.Figure 4.1: A fully labelled cut-away view of the ATLAS detector.Breaking down the necessary components from each part of the detector to achieve all thesegoals:\u00E2\u0080\u00A2 High-granularity particle tracking throughout the detector, fast and radiation-hard elementscloser to the interaction point to handle high particle occupancy;\u00E2\u0080\u00A2 Quasi-hermeticity in pseudorapidity in order to catch the largest possible fraction of particlescoming from the proton-proton interaction;\u00E2\u0080\u00A2 Good momentum resolution, reconstruction efficiency for charged particles, and vertex de-tection to identify displaced vertices;\u00E2\u0080\u00A2 Robust electromagnetic calorimetry to correctly identify and measure electrons and photons;\u00E2\u0080\u00A2 Hadronic calorimetry to accurately measure jet energy and for missing transverse energymeasurements;\u00E2\u0080\u00A2 Good muon identification, measurement of their momentum, as well as charge resolution.16Figure 4.2: A sketch of the role each part of ATLAS plays in particle identification and mea-surement. From the interaction point: the inner tracker detects charged particles and esti-mates their trajectory; the electromagnetic calorimeter measures the energy of electronsand photons; the hadronic calorimeter measures the energies of the numerous hadronsproduced - in this example protons and neutrons; finally the muon spectrometer actsas an extension of the inner tracker for precise muon measurements far from the denseenvironment close to the interaction point.The Inner detector, the first part of ATLAS particles will encounter as they fly away from theinteraction, is made up of both high granularity silicon pixel detectors close to the interaction pointand longer silicon strips further away. Currently, and until the ITk upgrade, it is also comprised ofthe Transition Radiation Tracker (TRT), straw-tube detectors filled with gas. Pattern recognition forparticle tracking, momentum measurement and vertex reconstruction are the main objectives of theinner detector, and in addition to this the TRT is a useful tool for electron identification [46].After the Inner Detector is the calorimeter system, divided into an electromagnetic calorimeterand a hadronic calorimeter. The electromagnetic calorimeter, the first element after the inner de-tector, is a sampling calorimeter made with liquid argon, optimized for good energy and positionresolution. The hadronic calorimeter, located after the EM calorimeter, is made of scintillator-tilesin the central region, and has a forward extention into extended barrel cylinders for better \u00CE\u00B7 cov-erage. The calorimeters have been designed such that they should stop most particles except formuons, meaning that the muon spectrometer should only see those particles [5, 7].Finally, the muon spectrometer is the last particle detector as you go away from the beamspot. The strong magnets mentioned previously bend the muons and three layers of high precisiontracking chambers give very good momentum resolution [8].Given that the design luminosity for proton interactions is \u00E2\u0088\u00BC 1034 cm \u00E2\u0088\u00922s\u00E2\u0088\u00921, this works out to17an event rate of 1 GHz. However, due to the way data is buffered and sent out of the detector,current technology, as of when ATLAS was first built, could only read out about 1 kHz of data, 6orders of magnitude lower. Given that most of the 1 GHz is in fact processes such as minimum-biasevents not relevant to most physics studies at the LHC, a way of choosing relevant physics eventsand discarding uninteresting ones is the job of the ATLAS trigger system. A Level-1 trigger, mostlybased on fast hardware inside the detector, reduces the output rate to the order of 100 kHz, whilethe next level, the High Level Trigger (HLT), is mostly software based and reduces the rate to 1kHz as seen in Figure 4.3 [4, 9].Figure 4.3: Data flow for ATLAS trigger during Run 2. The level 1 trigger receives data atabout 40 MHz which is the bunch crossing rate, filtering it down to 100 kHz as input tothe High Level Trigger (HLT). The HLT then only keeps 1 kHz for storage int he CERNdata networks. [4]4.2 ATLAS CalorimetersCalorimeters are a vital tool in detectors to measure the total energy of particles coming from acollision through the total absorption of their energy in some volume of matter. The absorption ofincident particle energy works on the principle of particle showers which occur when high energyparticles hit dense material; additionally two types of showers, electromagnetic and hadronic canoccur, meaning that calorimeters can be typically split up into EM and hadronic parts optimized todetect and measure each of these particle showers as shown in Figure 4.4. Both of these calorime-ters in ATLAS are sampling calorimeters, with alternating layers of absorbers to produce theseparticles showers and layers of active detector components to accurately measure the energy fromthe showers. The signal from the detector components will then be proportional to the energy ofthe incoming particle.The measurement, unlike the inner tracker, is completely destructive and absorbs all interactingparticles coming through the detector. Another key difference is that calorimeters will have a re-18Figure 4.4: A 3D representation of the ATLAS calorimeters, including the barrel Liquid Ar-gon EM calorimeter, the barrel Tile Hadronic calorimeter, the Liquid Argon endcaps forboth EM and Hadronic calorimetry and finally the forward Liquid Argon Calorimeter.sponse to both charged and neutral particles, and so are very useful in calculating the total missingenergy in an event, the key to identification of signals with neutrinos or of new, weakly interactingparticles. As the calorimeters respond to electromagnetic and hadronic showers differently, as wellas to different particles within those two types differently, they are vital in particle identification. Fi-nally, a high granularity and segmentation allows for the reconstruction of incident particle positionand angle, greatly increasing the quality of the event reconstruction.4.2.1 Electromagnetic CalorimetersThe electromagnetic calorimeter is the first element after the inner detector in ATLAS, and is op-timized to identify electrons and photons as well as measure their energy. In the energy regime ofATLAS, 1 GeV is roughly the threshold above which we expect to detect all photons and electronscoming from the interaction. In that energy range, electrons will lose most of their energy throughBremsstrahlung, and photons through pair production, and both of their cross section and dEdx areroughly independent of their energy.The reason this energy regime is important is because the EM calorimeter will measure theenergy of the EM shower of the incoming electron or photon. An electron of greater than 1 GeVwill produce secondary photons via Bremsstrahlung; meanwhile, photons of greater than 1 GeV willproduce secondary electron and positrons through pair production. At high energies, this will turninto a chain reaction - summarized in Figure 4.5, where each subsequent interaction will produce19more electrons and photons which will each then also produce more particles. If we treat thicknessthrough the material as t = xX0 , where x is the actual distance and X0 is, depending on the particle:\u00E2\u0080\u00A2 The distance over which an electron will lose everything but 1e of its energy from bremsstrahlung;\u00E2\u0080\u00A2 97 times the distance over which the number of photons will be reduced to 1e of the originalnumber by pair production;Figure 4.5: Diagram showing the chain reaction of an EM shower inside material. Each la-belled t = n interval is a radiation length for an electron inside the material.The number of particles left at thickness t is then approximatelyN(t) = 2t (4.1)and the energy of each of those particles at thickness t is approximatelyE(t) = E02\u00E2\u0088\u0092t , (4.2)where E0 is the original particle energy. The maximum thickness is thentmax =ln(E0/Ec)ln2, (4.3)where Ec is the critical energy, at which the energy lost by bremsstrahlung is equal to the energylost by ionization and excitation for an electron, and is the energy at which the shower will stop.It can then be shown that, by integrating over the number of particles, the total path length of allthe particles in the EM shower is L E0Ec , and so the calorimeter measures this path length L to get ameasure of the incident particle\u00E2\u0080\u0099s energy [47].To detect this, the ATLAS EM Calorimeter is made of a lead-steel absorber and liquid argonactive element sampling, divided into a barrel and two end caps. Liquid argon was the choice as the20active sensor element as it has an intrinsic linear behaviour as a function of deposited energy [DEFREF Particle identification with the ATLAS electromagnetic calorimeter], has stable response andis able to withstand large amounts of radiation for most of ATLAS\u00E2\u0080\u0099s life cycle. The barrel EMcalorimeter will cover |\u00CE\u00B7 | from 0 to 1.475, and the endcaps from |\u00CE\u00B7 | of 1.375 to 3.2, for a goodhermiticity to detect most incoming electrons and photons from the collision. A peculiar shapereminiscent of an accordion was chosen for the EM calorimeter design, which allows for complete\u00CF\u0086 coverage, reduces the length of the path needed to connect the readout cells to the electronics,and minimizes the inductance in the signal path [MORE REF] - the general makeup of the EMcalorimeter is shown in Figure 4.6. This makes it possible for the calorimeter to have a responsetime on the order of the 25ns between each bunch crossings of the LHC.Figure 4.6: Diagram showing details of the ATLAS LAr EM calorimeter. The accordionshape can be seen, as well as the segmentation in the \u00E2\u0088\u0086\u00CE\u00B7 and \u00E2\u0088\u0086\u00CF\u0086 directions. [5]The granularity of the EM calorimeter is vital to the identification of particles and their energyresolution. The calorimeter is divided along the \u00CE\u00B7 and \u00CF\u0086 directions. In the barrel, which has thefinest granularity, \u00E2\u0088\u0086\u00CE\u00B7\u00C3\u0097\u00E2\u0088\u0086\u00CF\u0086 = 0.003\u00C3\u00970.1, which has been optimized to help separate out differentparticles such as photons from pi0 background and electrons from jet background. In the end-cap, going from closest to furthest from interaction point, there are first constant thickness cells ofvarying \u00E2\u0088\u0086\u00CE\u00B7 and \u00E2\u0088\u0086\u00CF\u0086 , second \u00E2\u0088\u0086\u00CE\u00B7\u00C3\u0097\u00E2\u0088\u0086\u00CF\u0086 = 0.025\u00C3\u00970.025 and finally \u00E2\u0088\u0086\u00CE\u00B7\u00C3\u0097\u00E2\u0088\u0086\u00CF\u0086 = 0.050\u00C3\u00970.025.The energy resolution of an EM calorimeter can be estimated by\u00CF\u0083EE=a\u00E2\u0088\u009AE\u00E2\u008A\u0095 bE\u00E2\u008A\u0095c, (4.4)where the first observation is that the energy resolution gets better at higher energy. The first21term, a\u00E2\u0088\u009AE, is a stochastic term and is due mostly to sampling fluctuations due to not all chargedparticles crossing active layers. This uncertainty is also proportional to the thickness of the absorberlayer. The second term, bE , comes from the electronic noise of the readout and is dominant at lowenergy. Finally, the third, constant term, is an instrument effect from a number of instrumentalsources such as geometry, ageing, temperature gradient, and others. It is dominant at high energy.4.2.2 Hadronic CalorimetersHadronic calorimeters identify and measure the energy of hadrons coming from the collisions.They operate on much the same principle as the EM calorimeter, and detect a shower - hadronicin this case - of particles created by one incident hadron. However, unlike EM calorimeters, theshower produced by hadrons is much more complicated as it involves inelastic strong interactionsof particles, ending up with many different types of particles - shown in Figure 4.7, some of themweakly interacting which are not detected; furthermore, the shower has a much larger lateral spreadand can often go deeper into the calorimeter than the same energy particle detected in the EMcalorimeter.Figure 4.7: The proportion of each particle produced in a hadronic shower from an incident100 GeV proton in lead. [6]At low energy, much lower than 1 GeV, neutrons are the dominant particle created by the show-ering process. At intermediate energies, photons becomes the main component. At the energyATLAS deals with, pions dominate the hadronic shower. Neutral pions decay into photons whichwill produce EM cascades. Muons, neutrinos, neutrons and Kaons produced are stable and do not22interact much with the calorimeter, and inelastic collisions with the absorber will produce low en-ergy particles below the threshold needed for detection. In total, the energy missed through theseeffects can go up to 40% [47].The ATLAS hadronic calorimeter in the central region is a tile calorimeter, whose absorbermaterial is a laminated steel structure with pockets at regluar intervals to contain plastic scintillatingtiles. As the EM calorimeter, it is a sampling calorimeter, but with no accordion shape. In thebarrel, each tile is on the order of 100mm long in the radial direction, and form a segmentation of\u00E2\u0088\u0086\u00CE\u00B7 \u00C3\u0097\u00E2\u0088\u0086\u00CF\u0086 = 0.1\u00C3\u0097 0.1. A scintillator works by producing light when passed by ionizing particles,with impurities in the plastic converting the mostly UV light to visible light. This light propagatesto the edge of the tile, and is eventually collected by a photomultiplier tube (PMT) which detectsand measures the light. The general layout of the detector is shown in Figure 4.8.Figure 4.8: The segmentation of the hadronic calorimeter, showing the tiles that make-up thispart of the detector. [7]The Hadronic calorimeter system also includes an endcap detector from |\u00CE\u00B7 | of 1.5 to 3.2. Itis somewhat different from the barrel hadronic calorimeter, as it is a liquid argon calorimeter withcopper-plate absorbers. This allows for a cost-effective coverage of large eta to be as hermetic aspossible to most particles coming from the interaction .4.2.3 Muon SpectrometersThe final part of the ATLAS detector, the muon spectrometer is, as the name implies, a tool forprecisely and accurately measuring muon momentum, free from other particles due to the hermeticand dense calorimeters. Due to their weakly-interacting nature, muons are generally not stopped bythe detector and thus the large radius of the muon spectrometer offers a great chance to get precisionmeasurements on all muons coming from the interaction.23Three concentric cylinders form the barrel part of the muon spectrometer, at radii of 5, 7.5 and10 m from the interaction point, covering |\u00CE\u00B7 | < 1. Additional end-cap chamber are arranged infour disks at distances of 7, 10, 14, and 21-23 m from the interaction point in the z-axis, covering1 < |\u00CE\u00B7 |< 2.7; the disks are concentric with the beam axis.In the barrel, each cylinder has a number of sensitive layers, in this case there are 2\u00C3\u00974 layersin the first cylinder of the muon spectrometer, and 2\u00C3\u00973 layers in the two outer stations. MonitoredDrift Tube (MDT) chambers are in all barrel regions and all but the innermost ring of the end-capdisk closest to the interaction point, where the particle flux is too high. In this latter region, CathodeStrip Chambers (CSC) are used. For triggering purposes, three stations of Resistive Plate Chambers(RPC) are located in the middle and last cylinder of the barrel, and Thin Gap Chambers (TGC) areplaced in the end-caps. Their positions are labelled on Figure 4.9.Figure 4.9: A 3D view of the muon spectrometers in ATLAS, showing where each of the 4different detectors are placed in the barrel and endcaps.MDT\u00E2\u0080\u0099s are aluminum tubes with a central W-Re wire at 3270 V, with a mixture of Ar-CH4-N2gas and a single-wire resolution of 80 \u00C2\u00B5m and a drift time of about 50 ns. The tubes are arrangedwith multiple units per wire to improve resolution and also to create redundancy for the patternrecognition.CSC\u00E2\u0080\u0099s are multwire proportional chambers with a cathode strip readout, with a precision measure-ment obtained by measuring the charge induced on the cathode by the electron avalanche createdon the anode wire. Charge interpolation between neighbouring strips is used to improve spatialresolution. Resolutions of better than 60\u00C2\u00B5m are achieved with this setup, small drift time (\u00E2\u0088\u00BC 30 ns)and excellent time resolution (7 ns) are good for dense environment resolution. A second cathode,perpendicular to the strips, can be read out to measure the transverse coordinate. Diagrams of theMDT and CSC are shown in Figure 4.10.24\u00C2\u00B5 trackwirepathdriftAnode wiresCathode stripsddWSFigure 4.10: Left: Operation of MDT, with a wire in a gas-filled tube, and muon tracks ion-ization drifting to the wire. Right: Schematic of the CSC, with cathode strips and anoewires as readout. [8]RPC\u00E2\u0080\u0099s are made by from parallel resistive plates separated by a narrow gas gap, into whichprimary ionization electrons from the muon interactions will start an avalanche due to the uniformelectric field of about 4.5 kV/mm. A cross-section of the RPC can be seen in Figure 4.11. The de-tector provides a space-time resolution of 1 cm\u00C3\u0097 1 ns with a readout system of capacitive couplingon both sides of the detector. There are two sets of strips, \u00CE\u00B7 strips parallel to the MDT wires, and \u00CF\u0086strips orthogonal to the MDT wires, providing a second-coordinate measurement. These are usedin both trigger due to their excellent time resolution and for offline pattern recognition.Figure 4.11: Cross section of an RPC chamber. The strips and polysterene plates are shown.[8]TGC\u00E2\u0080\u0099s are similar to the MDT\u00E2\u0080\u0099s, but the distance between wires is larger than the distancefrom cathode (graphite on either ends of the gas gap) to the anode wire. Signals from the anodewire provide the trigger information together with the strips which are orthogonal to the wires.The muons will, like in the other gaseous detectors, ionize the gas and form an electron avalanchedetected by the wire, while the strips will detect the resulting ions. These chambers are themselves25constructed in doublets (two gaps) and triples (three gaps), and are filled with a carbon dioxide andn-pentane gas mixture. A gang of anode wires are grouped and fed to one readout channel, which isquickly read out for trigger information. The positions of the TGCs in ATLAS and a cross-sectionof the gaseous detector can be seen in Figure 4.12.200040006000800010000120006000 8000 10000 12000 14000 16000\u00CE\u00B7 = 1.05\u00CE\u00B7 = 1.60\u00CE\u00B7 = 2.00\u00CE\u00B7 = 2.40EMSEMLDouble gap TGCsEILFISFILFMSTriple gap TGCFML2nd coordinate TGC1.8 mm1.4 mm1.6 mm G-1050 \u00C2\u00B5m wirePick-up strip+HVGraphite layerFigure 4.12: Left: Location of the TGCs on the end-caps of ATLAS. Right: Schematic viewof the chamber, with the gap between graphite layers smaller than the space betweenwires, meant to give fast timing information for triggering purposes. [8]4.3 Current Inner DetectorThe general design of the ATLAS Inner Detector (ID) consists of both barrel layers and end-caplayers, with high precision pixels for vertexing closer to the interaction point and larger strips fur-ther away to maximize the number of points each track is made out of - a 3D view of the ID isshown in Figure 4.13. The purpose of an inner tracker is to turn interactions from charged particleswith material into detector signals which can be turned into a 3D coordinate for each interaction.Using a variety of track reconstruction techniques which will be described in Section 5.1, these 3Dpoints are combined into tracks, the trajectory of a charged particle from the interaction point all theway until the edge of the ID. From this trajectory, the bend due to a magnetic field to each particlecan be measured, leading to a calculation of its momentum. Furthermore, the origin of each particlecan be traced back to a vertex, either in the beam pipe or in the detector, leading to pile-up rejec-tion, long-lived particle identification and collision spot measurements. Furthermore, inner detectortracks can be combined with calorimeter and muon spectrometer to give a final decision on particleidentification as well as energy and momentum measurement.The current barrel Inner Detector is made up of 4 cylindrical layers of high granularity pixelsclosest to the beam spot - at radius of 39, 50.5, 88.5 and 122.5 mm - and four layers of dual-modulestrips at a radius of 299, 371, 443 and 514 mm. A dual-module strip layer includes two sets of stripsat a stereo angle for better position resolution, this will be explained thoroughly in Section 5.1.1.1.26The first layer of pixels, dubbed the Insertable B-Layer (or IBL) was added for the 2015 ATLASRun 2, while the three other pixel layers were present for the whole ATLAS run since 2008. Thestrips have been unchanged since the initial construction of ATLAS. The current ID also featuresthe TRT consisting of straw tubes filled with gas from a radius of 554 mm until 1082 mm. The Run1 Inner detector can be seen in Figure 4.14, and simplified with only sensor elements in Figure 4.15.Figure 4.13: 3D view of the ATLAS Inner Detector, showing the barrel and end-cap regions.The pixels, strips and TRT can all be seen.27Figure 4.14: Schematic of the entire ATLAS Inner Detector for Run 1 (valid until 2012).Pixels, SCT and TRT are all shown, with a zoom into the pixel layers. The radialdistance of each from the beam pipe is shown, as well as the \u00CE\u00B7 range of the barrel andend-cap parts of each detector. [9]Figure 4.15: a 3D diagram of the ATLAS Inner detector, valid up to Run 1 (2012). Variousbarrel and end-cap features are shown. [9]An important point is the coordinates used in describing the segmentation of the pixels andstrips in the Inner Detector. Silicon sensors are positioned essentially as 2D rectangles, as drawn inFigure 4.16 for the IBL. Given that the z-axis in ATLAS is defined as the axis along the beam pipe,one of the edges of all silicon detector elements will always be parallel to this axis - this is the localz direction of the element. The second edge of the silicon elements will be a combination of x and28y distance - this is called the R\u00E2\u0088\u0092\u00CF\u0086 coordinate, or local r coordinate of the detector element.Figure 4.16: An R-\u00CF\u0086 view of the IBL in ATLAS Run 2. The beam pipe goes in/out of thepage. The local r is thus along the stave plane shown here, and the local z in and out ofthe page on the pixels shown. [10]4.3.1 Silicon DetectorsThe general idea behind the silicon sensors in the ATLAS inner detector is the use of a dopedsemiconductor to achieve a depletion region through almost the totality of the silicon thickness; acharged particle going through this region will then ionise the silicon atoms and produce electronsand holes along its trajectory. An applied electric field makes these drift to either end of the silicon;one side has has sensors which then collects the charge. It is then possible to integrate the lengthof the pulse, which will be proportional to the amount of charge deposited - this is only donefor the pixel detector. This detection method allows for a high granularity and also offers a goodposition resolution which is crucial for vertex identification. For strips, only on/off informationabout a particular strip being above threshold is received - geometrical clustering thus gives a goodresolution but not as precise as the pixels.The silicon material is doped by introducing impurities. For a p-junction a material with fewervalence electrons is introduced, leading to the silicon losing valence electrons and becoming posi-tively charged which is labelled as a hole; for an n-junction the opposite is done, an element withmore valence electrons than silicon is introduced, which adds free electrons which can now freelymove through the silicon lattice. A depletion region is then created by implanting n-type materialon one side of the silicon and p-type material on the other side - this means positive charge willbuild up on one side of the silicon, and negative charge on the other. Once an equilibrium is built29up, the flow of charges will stop, and the region with only electrons or holes is called the depletionregion, as shown in Figure 4.17. This depletion region will lead to the free charges detected by thesensors and thus should be as large as possible to maximize the odds of detecting particles goingthrough the silicon.Figure 4.17: Left: An n-doped piece of silicon is attached to a p-doped piece of silicon. Thediffusion of electrons and holes create a depletion region. Right: The depletion regionis formed when diffusion and electric field due to charges reaches an equilibrium.An external voltage, or bias voltage, is applied to the silicon, with the positive on the side withthe n-type impurities and the negative on the p-type impurities; a large enough voltage will extendthe depletion region through most of the silicon, with a small current called leakage current whichcan be a source of noise. With this setup, a charged particle passing through the silicon will ionizethe atoms in the depletion region and the external electric field will lead the electrons and holes tothe edge of the sensor and the charge sensitive electronics. - this is shown in Figure 4.18 This designis ideal for single-pixel isolation and the reduction of radiation damage, which is significant due tothe small distance to the interaction point. The exact details of the construction of the pn junctionare different for pixels and strips and will be discussed in Section 4.3.1.2 and Section 4.3.1.3 respec-tively. Finally, the magnetic field in ATLAS causes an effect called the Lorentz angle, discussed inSection 4.3.1.1Figure 4.18: An idealized view of charge drift and diffusion in a silicon detector. The driftcauses charge carriers to follow the electric field to the sensors, while the diffusioncauses the charge carriers to spread out in the direction parallel to the drift.304.3.1.1 Lorentz AngleIn normal operation, as an ionising particle crosses the silicon depletion region, the electrons orholes ionised on the other side of the sensors would drift straight to the detector element due tothe electric field, albeit with some diffusion. However, due to the fact that ATLAS has a strongmagnetic field, the charge carriers from the particle interaction in the silicon will feel a force E\u00C3\u0097B,this has the largest impact on the barrel sensors where the electric field is perpendicular to themagnetic field. As the magnetic field is perpendicular to the R\u00E2\u0088\u0092 \u00CF\u0086 direction, charge drift will beaffected in this coordinate but not in the z-coordinate of the detector elements. The Lorentz angleis the angle the charge carriers will make to the normal to the silicon, and depends on the magneticfield and the Hall Mobility, such thattan(\u00CE\u00B8L) = \u00C2\u00B5HB, (4.5)where \u00CE\u00B8L is the Lorentz angle and \u00C2\u00B5H is the Hall mobility, which is a property of the siliconused. The Lorentz Angle in a way acts as a change in the incidence angle of each particle. As seenin Figure 4.19, the size of the charge deposit from an ionizing particle going through the siliconwill be at a minimum when the incidence angle is equal to the Lorentz angle, and wider whenhigher or lower than this. The Lorentz angle is usually measured from cosmic ray data before anew ATLAS data run, and cluster positions are corrected in reconstruction to account for it [11].Finally, during the detector construction, the sensors are usually angled so that most tracks comingfrom the interaction point will be incident at the Lorentz angle, reducing the cluster size and thusachieving greater separation in dense particle environments and better position resolution for bothpixels and strips.Figure 4.19: Diagram showing that a Lorentz angle is equivalent to a rotation of the detectorelement equal to that angle. The particle traversing the detector element is shown as anarrow, while the signal on the top sensors is shown as grey distributions. [11]314.3.1.2 Pixel SensorsThe silicon for the pixel is made of a majority n-type bulk, containing some oxygen impurities toincrease the tolerance of silicon against damage from charged hadrons, as shown in Figure 4.20.A high-positive (p+) region is put on the side opposite to the pixel sensors, and a high negativeregion (n+) is implanted on the sensor side of the silicon - this is called an n+-in-p sensor. Due tothe high reverse bias voltage, the majority of the region is depleted starting from the p+-n junctionextending almost to the edge of the sensors. The p+ side is connected to a high voltage, with then-side of the sensor at ground potential. The electrons ionised by passing charged particles willaccumulate at the n+ implants, and create a signal. The same technology is used for both the IBLand the 3 other pixel layers, with the IBL having a silicon thickness of 200 \u00C2\u00B5m while the next threehave a thickness of 256 \u00C2\u00B5m. The pixel detectors themselves are n+ material implanted on top of thesilicon and the readout electronics is bump-bonded to the silicon itself. A p-spray is used betweenthe n+ implants to isolate them to avoid low-resistance connections. A guard-ring structure is alsoimplemented at the edge of the sensor to avoid flashover. A typical sensor operates at a thresholdof about 4000 electrons for a signal due to thermal and other sources of noise in the electronics; atypical minimum ionising particle induces an average of 20000 electrons of signal [12].Figure 4.20: A cross-section of the silicon inside ATLAS\u00E2\u0080\u0099s pixel detector (not to scale). Then-bulk in grey is shown between the n+ of the pixels and the p+ on the other side of thesilicon. Guard-rings and p-sprays are two other prominent features shown here whichhelp protect against material buildup and radiation damage. The sensors are bumpbonded through the bum pad to the front-end electronics. [12]The size of the pixel detector elements are 50 \u00C2\u00B5m in the R\u00E2\u0088\u0092\u00CF\u0086 direction for all layers, 250 \u00C2\u00B5min the \u00CE\u00B7 direction for the IBL and 400 \u00C2\u00B5m in the \u00CE\u00B7 direction for the other 3 layers. The pixels arearranged in a tile, containing 144 columns and 328 rows of individual pixels, some pixels on theedges of the tile for the last 3 layers have a size of 600 \u00C2\u00B5m to fill all the space available. Each tilethus contains 47232 individual pixels, with some ganged to a common readout and everything onthe tile finally connected to 16 electronic front-end chips. The pixel system is kept to 0 \u00E2\u0097\u00A6C duringoperation and is connected to a common bias grid structure, ensuring isolation between pixels whilemaintaining a constant bias for the entire sensor [13].Each silicon tile is connected to a module, which contains also the front-end electronics chips,32services for routing signals and power, a module control chip and, only for the barrel, a flexible coilto provide connection to electric services - this is all shown in Figure 4.21. The modules in eachlayer are themselves mounted on mechanical supports known as staves, which can contain thirteenmodules - the staves are made of carbon-fiber composite material to reduce interactions as particlesgo through the detector. In the stave construction, the staves are the element that are rotated by theLorentz Angle with respect to the interaction point in order to minimize cluster size.Figure 4.21: A blown-up view of the various pixel electronics for hybrid pixel modules. Thepixel sensors are connected to front end electronic chips, and on the other side a printedcircuit to route signal and power, with above it a module control chip and finally con-nections to electrical services. [13]In total around 92 million output channels are used in the Run 2 Inner Detector, including the 3original pixel layers and the IBL around the barrel and the end-cap modules.4.3.1.3 Strip sensorsThe silicon for the strips is very similar to the pixels, with an n-type bulk as the primary material.However, for the current Inner Detector, the n+ type is on the other side of the sensors, and the p+type is on the sensor side, connected to electronics with AC-coupled read-out strips - this is shownin Figure 4.22. It has a bias voltage applied, around 150 V, making a large depletion region - this isat the n+ side, the p+ strips themselves are grounded. Since the strips are on the p-side, they willcollect holes as signal and not electrons. The threshold is set at around 6000 charge carriers for abinary signal to be triggered, signalling a particle has gone through a strip [48].33Figure 4.22: An R-\u00CF\u0086 view of the IBL in ATLAS Run 2. The beam pipe goes in/out of thepage. The local r is thus along the stave plane shown here, and the local z in and out ofthe page on the pixels shown. [14]The strips have a pitch in the R\u00E2\u0088\u0092\u00CF\u0086 direction of 80 \u00C2\u00B5m and in the \u00CE\u00B7 direction a dimension of126mm; the four barrel layers go from 299 to 514mm in the radial direction and have a length of1492mm in the z-direction. The end-caps have two sets of nine disks going out in z on either sideof the barrel. Each module in a layer has two sensors rotated by \u00C2\u00B120 mrad - shown in Figure 4.23- to obtain a space point, which will be explained further on in Section 5.1.1.1. Each strip sensoris made up of 768 strips. Like the pixels, each module is put on a mechanic stave around the beampipe.34Figure 4.23: Two SCT sensors glued together with a stereo angle of\u00C2\u00B120 mrad, also connectedto the services through the Hybrid assembly shown here. [14]4.3.1.4 Transition Radiation Tracker (TRT)The TRT, being large gaseous detectors, will not be able to scale to the high particle density of theHL-LHC and will thus be removed in the upgrade. Thus, only a cursory explanation is given here.In the current detector, its purpose is to give stand-alone pattern recognition capability due to itslarge distance from the interaction point, adding points to each track for momentum resolution andelectron-pion separation. It consists of 370,000 cylindrical drift tubes with a 30 \u00C2\u00B5m gold-platedtungsten sense wire in the center; the straw itself, 4mm in diameter, acts as a cathode and is athigh voltage. The TRT is filled with a gas mixture based on Xenon, with some CO2 and O2 toincrease electron drift velocity and for photon-quenching. The straws themselves are embedded inpolypropylene or polyethylene fibre to produce the transition radiation X-rays, through Cherenkovradiation, used for electron identification. In addition to a barrel component, the TRT also has twoend-caps on each side of the barrel, for a coverage up to \u00CE\u00B7 of 2.5 [49].4.4 ITk UpgradeAs explained in Section 3.2, in 2024 a high luminosity program for the LHC will begin, with a peakluminosity of \u00E2\u0089\u00A5 5\u00C3\u0097 1034 cm\u00E2\u0088\u00922s\u00E2\u0088\u00921 and an integrated luminosity up to 3000 fb\u00E2\u0088\u00921 over its 10 yearsof operation. This comes out to a mean number of interactions per bunch crossing of \u00C2\u00B5 140 with adistribution tail over \u00C2\u00B5 = 200. Compared to to the 23 pile-up events seen at the current Run 2 LHC,it is clear that the complete Inner Detector will need a rework to cope with this new environment.This rework is given the name ITk, for Inner Tracker.The current pixel detector was designed to withstand 1015 neq/cm2 and the strips 2\u00C3\u0097 1014neq/cm2 of radiation, or around 400 fb\u00E2\u0088\u00921, which is about an order of magnitude lower than the35total fluence under HL-LHC conditions. Furthermore, the electronics for pixels and strips in thecurrent detector were designed for an occupancy in the detector of up to 50 bunch crossing inter-actions - the HL-LHC delivering tails of up to 200 pile-up events limits the buffering and linkingbetween on-module electronics which will lead to inefficiencies, saturating the electronics and los-ing vast amounts of data. Finally, high particle density in the core of high-pT jets and tau leptondecays added to the high pile-up at the HL-LHC, the strips would be unable to resolve many ofthese decays and the TRT would reach 100% occupancy, which it is not designed for.For these reasons, the current Inner detector will be completely removed and replaced with asilicon-only detector for HL-LHC, with no TRT replacement due to its inability to cope with thehigh pile-up environment. The expectation is that the new Inner Detector performs as well or betterthan the current Inner Detector but with the harder constraints from HL-LHC such as the 200 pile-up event tails and longer beam spot which will make it much more difficult to associate each trackto the correct primary and secondary vertices which is essential to particle identification and pile-uprejection. To this end, the main requirements of the new ITk are, as stated in the Letter of Intent[50]:\u00E2\u0080\u00A2 High efficiency for the reconstruction of isolated particles like electrons and muons.\u00E2\u0080\u00A2 Reconstructing both vertices of pile-up events and the hard scatter interaction.\u00E2\u0080\u00A2 Identify secondary vertices from long-lived particles such as b-jets, even when highly boosted.\u00E2\u0080\u00A2 Resolve tracks in jet cores, even with the anticipated high occupancy.\u00E2\u0080\u00A2 Identify and resolve tracks from tau leptons with good impact parameter resolution.\u00E2\u0080\u00A2 Reconstruct tracks from converted photons.This thesis will focus on the tau lepton track reconstruction requirements in order to informdecisions on detector layouts. The ITk has gone through a number of iterations since a letter ofintent was published in 2012 [50]. The main goals are to increase the detector granularity, especiallyin the pixels; to better resolve the tracks in the dense environment created by the HL-LHC; andto make sure each particle coming from the interaction point passes enough silicon detector toconfidently use pattern recognition in order to reconstruct the many more tracks coming from pile-up, given the absence of the large TRT from the Inner Detector. However, this higher granularitymust be achieved with minimal material, as the higher number of particles mean any excess materialin the ID will lead to incredible additions of secondary particles and multiple scattering, adding toan already taxed dense environment and pattern recognition.The general design of the ITk has remained fundamentally unchanged since the Letter of Intent;a number of pixel detectors followed by several strip detectors, both simulated as using the sameproven technology as used in the IBL.The exact performance requirements sought with this design is:36\u00E2\u0080\u00A2 Minimum 14 hits on all layers for all \u00CE\u00B7 \u00E2\u0089\u00A4 2.5\u00E2\u0080\u00A2 Minimum 4 pixel hits for precise reconstruction and extrapolation to the strips\u00E2\u0080\u00A2 Minimum 5 strip hits, each hit being a combination of the two strip modules in one layer,such that 10 interactions with strip detectors occur on each track\u00E2\u0080\u00A2 An optimized pixel granularity, studied with full detector simulation, such that track recon-struction is on the levels of Run 2 including high-pT tracks which create the most denseenvironments, and to equal the Run 2 precision for secondary and primary vertex resolutionThe initial design specification for the 2012 Letter of Intent for the pixels was a size of 50\u00C3\u0097250 \u00C2\u00B5m2, same as the IBL due to experience with the technology. However, to meet the aboverequirements, it was found that a smaller pixel size would be necessary due to loss of resolution forimpact parameters due to the fact that the first layer would be further in radius that the current IBL;furthermore, the loss of efficiency due to collimated tracks in high-pT jets was an issue that neededfiner granularity in all pixels to solve.In work done since the 2012 Letter of Intent, an \u00CE\u00B7 coverage of 4.0 has been decided as the bestcompromise between particle hermeticity and constraints such as space and material - one of thefirst designs is seen in Figure 4.24. Lower level scenarios were considered for cost purposes, buthave been discarded due to the need for hermetic coverage for all tracks.37Figure 4.24: The obsolete LoI-VF (Very Forward) layout showing the ITk with pseudo-rapidity coverage up to |\u00CE\u00B7 | = 4.0. The red are pixels, while blue are strips. The xand y axes are both in units of meter. [15]Final discussions in 2016 have led to the development of a Step 1 layout, on a roadmap to finalITk layouts being included in both strip (late 2016) and pixel (2017) Technical Design Reports.The major change from the LOI and Scoping Document layout shown previously is the change of4 pixel and 5 strips layers to 5 pixel and 4 strip layers. Furthermore, two different types of Innerdetector are being considered for the barrel - an Extended Layout, shown in Figure 4.25, whichmimics the current Inner Detector, with cylindrical staves and end-cap rings further out in z - andan Inclined Layout, shown in Figure 4.26, with rings facing the interaction point in the barrel in anattempt to reduce cluster sizes close to the interaction point.38Figure 4.25: T The Extended 4.0 Layout concept for Step 1 ITk. 5 pixel layers in the centralregion are perpendicular to the beam pipe, with endcaps extending to a pseudo-rapidityof 4.0. The strips have a similar format.Figure 4.26: The Fully Inclined 4.0 Layout concept for Step 1 ITk. The 5 pixel layers inthe barrel region have inclined sensors at pseudo-rapidity above 1, leading to smallercluster sizes there. The rest of the layout is similar to the Extended 4.0.39Table 4.1: Design specification for Step 1 ITk pixel elements. The radius is the distance fromthe beam pipe of each layer, the R and Z-dimensions are the size of the individual deteec-tor elements, and the thickness is the thickness of active silicon.Radius [mm] R-dimension [\u00C2\u00B5m] Z-dimension [\u00C2\u00B5m] Thickness [\u00C2\u00B5m]Layer 1 39 50 50 150Layer 2 75 50 50 150Layer 3 155 50 50 150Layer 4 213 50 50 150Layer 5 271 50 50 150Table 4.2: Design specification for Step 1 ITk strip elements. The radius is the distance fromthe beam pipe of each layer, the R and Z-dimensions are the size of the individual deteec-tor elements, and the thickness is the thickness of active silicon.Radius [mm] R-dimension [\u00C2\u00B5m] Z-dimension [\u00C2\u00B5m] Thickness [\u00C2\u00B5m]Layer 1 405 74.6 23.82 320Layer 2 562 74.6 23.82 320Layer 3 762 74.6 47.64 320Layer 4 1000 74.6 47.64 3204.4.0.5 Silicon DetectorsThe current, Step 1 layout pixel sensors have a 50\u00C3\u0097 50 \u00C2\u00B5m-sized pixel elements, and a siliconthickness of 150 \u00C2\u00B5m in both barrel and end-caps. Similar to the current pixel detectors in theInner Detector, the sensors are planar with n-in-p electron carriers. The modules are on a stavetilted \u00E2\u0088\u009214.00 degrees with respect to the beam spot to minimize Lorentz Angle effects. The sensortechnology is still in flux, and many options are being tested currently for radiation hardness to3000 fb\u00E2\u0088\u00921 and for their impact on cluster size.The Step 1 strip sensors, unlike the current Inner Detector, also use n-in-p planar silicon sensorswith a Float zone in both barrel and end-caps. This means that the strips also collect electrons andnot holes. The strips have a silicon thickness of 320 \u00C2\u00B5m, a pitch of 74.5 \u00C2\u00B5m in the R direction andstrips in the Z direction of 23.82mm in the first 2 layers, and 47.64mm in the last 2 layers. The stavetilt in the barrel here is 10.0 degrees, to account for the fact that strips are upside down from wherethe pixels are located on the sensors.For the pixel barrel detectors, Table 4.1 gives the relevant details, and for the strip barrel detec-tors, Table 4.2 gives the relevant details for the Step 1 baseline layout.4.5 Event ReconstructionThe purpose of a particle detector is to reconstruct the underlying event with as much information aspossible. This information is both kinematic, such as momentum, energy; or particle identificationusing charge, decays or interactions. Every single event, both in simulation and in data goes throughmultiple steps of reconstruction to end up as a collection of identified particles to be analysed by40the ATLAS community. As seen in Figure 4.27, data and simulation diverge in the first steps, andmeet at the point of reconstructing physics objects from detector interactions.Figure 4.27: The data flow for the ATLAS data infrastructure. The top left shows the particlegenerators, which first create the particles, and finally the top reight shows the end-goal,raw data for reconstruction. Simulation goes through Hits, which is where particles de-posit energy, to digitization, which simulates detector response, to be eventually turnedinto Raw Data Objects (RDO). The bottom ATLAS detector diagrams shows whereATLAS data starts, output through the electronics into RDO for further reconstruction- this is where data and simulation converge. [16]Four vectors for simulated particles are normally generated by Pythia or other generators in-troduced in Section 2.2, and run through a full detector simulation based on a GEANT4 package,simulating the many effects each particle experiences through the detector, such as the magneticfield, interactions with detector material, decays and conversions. The Energy deposited in the ac-tual sensors such as the pixels or calorimeters is stored in the HITS file. These are then converted toa Raw Data Object file, which stores the signals from either simulation or data. Finally, these rawsignals are reconstructed into the measurements we are used to, such as momentum, position andenergy of each particle detected through the detector.The chain is moderated by a program called ATHENA, which is a modular program combiningall of the ATLAS digitisation for simulation and reconstruction for simulation and data [16].41Chapter 5Tracking5.1 ATLAS Track ReconstructionTrack reconstruction in particle detectors turns the raw signal from the tracking detectors into tra-jectories of charged particles as they move away from the interaction point; these trajectories arecalled tracks. These tracks are used as part of particle identification and kinematic parameter mea-surements of the particles in the ATLAS event reconstruction. As explained in Section 4.3.1,charged particles deposit energy through ionisation in the active silicon element of the tracking de-tector as they pass through it. Each of these energy deposits is called a hit - these form the backboneof track reconstruction. There are two main algorithms at play when building tracks from hits, thefirst is pattern recognition - joining hits in different layers as a proto-track - and track fitting - forfinding the final track parameters. Current track fitting involves both a global pattern recognitionwhich is combined with a local track fit to better connect hit candidates. In order for this complexsystem to work, both the material inside the detector - with which the particles may interact andscatter from - and the magnetic field which bends the track must be finely and accurately recorded.Putting all these elements together, a complex ambiguity solving program is the final step in anattempts to separate fake tracks - usually from random combinations of hits - from the tracks de-scribing particle trajectories through the detector [51].In Section 5.1.1.2 I will describe the current pattern recognition techniques, then in Section 5.1.1.3the track fitting strategies will be discussed, and finally the ambiguity solving, with emphasis ondense environments will be analysed in Section 5.1.1.5.5.1.1 Pattern Recognition5.1.1.1 Space PointsTo first reconstruct particles going through the three-dimensional detector, each hit on a pixel orstrip should be mapped to a 3D point. In this case the position corresponding to the 3D locationof the hit is called a space point [21]. A detailed geometry of the whole Inner Detector has been42mapped out, complete with alignment correction and material estimation to give each individualpixel or strip a 3D coordinate in the ATLAS detector [52]. Each track will then be made up ofa multitude of space points as shown in Figure 5.2.For the pixel detectors, each hit can have anintrinsic resolution which is one pixels\u00E2\u0080\u0099 size if a hit is one pixel large; in large clusters of pixels,time over threshold information can be used to deduce the location of the hit within the clusterto a much better resolution. After this is measured, a local to global transformation is applied toobtain a global 3D measurement of the position of a hit. To identify clusters, an algorithm calledConnected Component Analysis (CCA) is run, for which an example is shown in Figure 5.1. Thealgorithm is based on a technique for image reconstruction [17] which looks at every individualpixel above threshold, then looks at the 8 pixels surrounding it for signal over threshold - if that isindeed the case, then that pixel is added to the cluster. The algorithm continues until no more cellsabove threshold are found in the so-called eight-cell connectivity area around all the pixels abovethreshold.Figure 5.1: In examples (a), (b) and (d), the points x are connected through CCA. In example(c), the two x\u00E2\u0080\u0099s are not connected. [17]For the strips, the large length parallel to the beam-direction means overall worse resolution inthat axis if each individual strip were converted 1-to-1 to a 3D position. However, as each strip layerconsists of two modules at a small stereo angles, a combination of two strip hits in one layer is usedto obtain a space point, giving good resolution along all three axes for each hit. A local-to-globaltransformation using the tracker geometry is then used to map the local strip coordinates to a 3Dpoint [18].43Figure 5.2: Example of space points on different layers leading to an estimate of the tracktrajectory [18]5.1.1.2 Track Seed FindingATLAS employs a combination of local and global pattern recognition algorithms to constructtracks. Using highly cpu-consuming global pattern recognition [18] to link hits across all layers isnot used due to CPU time being a sparce resource during reconstruction. Instead, three consecutivesilicon layers are first considered using a fast technique which estimates the momentum and impactparameters, which are a set of parameters that fully describe the measured trajectory of the particle,of the proto-track using a rudimentary helical trajectory which assumes no multiple scattering anda constant magnetic field. This method is shown in Figure 5.3. Different layer combinations havedifferent requirements on the fitted parameters so that they may be accepted as good so-called seeds- this can be a very large number per event, as shown in Figure 5.5.44Figure 5.3: Diagram of simplified patter recognition in the Run 2 ATLAS Inner Detector.Space Points are seen in yellow, and rejected seeds frin global pattern recognition outputare shown with circles. The green circled track candidate as well as the blue dashed lineare rejected since they do not fit with the nominal interaction point. Red tracks showfully fitted track candidates, while the dashed circle shows a seed which shares spacepoints with another accepted track candiddate, shown as a black line. [19]The estimated parameters are given at the point of closest approach to the beam line, or z-axis,are called perigee parameters [20] and are shown in Figure 5.4:\u00E2\u0080\u00A2 qp - charge of the particle over the momentum;\u00E2\u0080\u00A2 \u00CF\u00860 - the angle the track makes with the x-axis at the perigee;\u00E2\u0080\u00A2 \u00CE\u00B80 - the angle the track makes with the z-axis in the r-z plane at the perigee;\u00E2\u0080\u00A2 d0 - the distance to the origin (z-axis) in the x-y plane;\u00E2\u0080\u00A2 z0 - the distance, along z, of the track at the perigee to the z-axis.45Figure 5.4: The perigee parameters in the x-y plane (left) and in the r-z plane (right). [20]To obtain the transverse momentum, first the charge is estimated from the direction of thecurvature. Then, assuming a homogeneous magnetic field of 2T parallel to the beam line, the radiusof the circle (\u00CF\u0081) made by the track is estimated [18]:\u00CF\u0081[mm] =pT [GeV ]3\u00C3\u009710\u00E2\u0088\u00924\u00C3\u0097q[e]\u00C3\u0097B[T ] (5.1)The parameter d0 is then calculated by finding the coordinates of the circle center, cx and cy,then usingd0 =\u00E2\u0088\u009Ac2X + c2Y \u00E2\u0088\u0092\u00CF\u0081 (5.2)This global pattern recognition for 3-layer seeds, as seen in Figure 5.5, leads to a large numberof seeds being made in the ID.Figure 5.5: Example of the large number of seeds created, in Run 1 with only 3 pixel layersand 4 strips, and low number of pile-up. [21]465.1.1.3 Local Pattern recognitionOnce track candidates are found using this fast global approach, a local pattern recognition methodis utilized with the help of a Kalman filter [53]. A Kalman filter approach allows for first a filtering- estimating the current state vector based on previous measurements; then a prediction - whichestimates the state vector at another layer; and finally smoothing - to update past state vectors basedon new information.The major challenges of the local track fitting and extrapolation are the presence of an inho-mogeneous magnetic field, multiple scattering through detector material, energy loss in material aswell as radiative energy loss throughout the detector. Each of these add multiple nuisance param-eters to any track fit; in many cases adding parameters each time a track candidate goes through alayer or any other material such as services or magnets. These must all be considered when creatingtrack candidates from seeds.In order to have a robust Kalman filtering algorithm for local pattern recognition, various tech-niques have been developed to propagate charged particles through the ATLAS detector takinginto account the inhomogeneous magnetic field and material [22]. Here, only some details on theRunge-Kutta-Nystrom propagator used in both the Kalman filter and in further studies in this thesiswill be mentioned. Other methods, such as STEP or Helical are left to the reader\u00E2\u0080\u0099s curiosity [22].The Runge-Kutta Propagator uses the parameter s, the arc length of the propagated track to thedestination surface, as a free parameter. The equation of motion for particles going through theB-field of the detector, derived form the Lorentz Force isd2rds2=qp[drds\u00C3\u0097B(r)](5.3)The magnetic field being inhomogeneous, as shown in Figure 5.6, analytical solutions to thisequation of motion are impossible. The Runge-Kutta propagator is thus a tool for recursive numer-ical solving of the equation of motion in an inhomogeneous electric field. Thus, the arc distance sfrom the initial surface where track parameters are known is divided into a number of steps, whichwill be solved in such order that the beginning steps, once solved, will give positions which will beused as an input to further steps, and so on until the desired surface is reached.47Figure 5.6: Illustration of the inhomogeneous magnetic field in ATLAS for Run 1. The topimage is for the an r- screenshot of the field for the whole detector. Bottom left showshow the magnetic field changes for both radius and andlge \u00CF\u0086 , the field here is at z=0.Bottom right is a zoomed in diagram of the magnetic field in the inner detector. [22]This method is used to propagate a charged particle through the ATLAS detector from onesurface to the next, as shown in Figure 5.7. Many surfaces have been defined in reconstruction code,such as cylinders to approximate barrel layers and planes to represent individual detector elements.Track parameters can be defined locally on each of these surfaces or globally with respect to the aglobal set of axes. The propagator is thus also able to switch between local and global frames inorder to propagate correctly to a surface and also output correct global coordinates of the track andsurface intersection.48Figure 5.7: Example of navigation of a track through the full inner detector geometry setup.The track parameters are calculated and fitted at each surface using the propagatormethod of choice. [22]An adaptive method is used where the number of steps is variable. An initial step size in s ischosen, then the propagation of this one step is done in full and then divided into two steps. Thedifference between the two solutions is defined as the local error, which can be checked againstoptimized error tolerance. If this criteria is not met, the step is shortened and the whole calculationdone again. A constant error tolerance is achieved throughout the propagation by keeping the localerror as close as possible to the optimized error tolerance during the whole propagation.Each individual step is solved at different points, or stages, labelled k along the arc, as shownin Figure 5.8. The number of stages per step has been set to 4 in the ATLAS propagation as it hasbeen shown that, while the number of stages produces a solution correct to the order of the numberof stages, any improvement beyond fourth order is negligible.49Figure 5.8: The equation of motion is evaluated at four point k along the trajectory for afourth-order Runge-Kutta propagator. The position r and tangent vector to the trackT are calculated at the initial step point, the two steps midway through and the final steppoint. [23]The solutions to the parameters in a single step are [23]:y\u00E2\u0080\u00B2n+1 = y\u00E2\u0080\u00B2n+h6(k1+2k2+2k3+ k4), (5.4)yn+1 = yn+hy\u00E2\u0080\u00B2n+h26(k1+ k2+ k3), (5.5)where ki are the equation of motion calculated at each of the four stages i, and h is the steplength. y\u00E2\u0080\u00B2n+1 is the tangent vectordrds at step n+1 and yn+1 is the position of the particle at the end ofthat step. Finally, the numerical integration is stopped when the propagation is closer to the surfacethan a chosen cut value, and the last step is calculated using:r f inal = r f\u00E2\u0088\u00921+hdrds+12h2d2rds2. (5.6)In this case h is the final distance to the surface, and r is the position vector at that step.In addition to the inhomogeneous magnetic field the track extrapolator also takes into accountmaterial effects. A simplified version of the material contained in the ATLAS detector is used inall track reconstructions used for both the Kalman filter propagating to a subsequent layer or duringthe smoothing algorithm when the fit on a previous point is re-evaluated using new information.Multiple Scattering is one of the main effects, causing small angle deflections when a chargedparticle encounters detector material as shown in Figure 5.9. These are modelled as a Gaussiandistribution with a center at 0. Using the Highland formula, the root mean square of the projectedscattering angle is shown, empirically, to be [54]:50Figure 5.9: Multiple scattering example for a 5 GeV muon through a silicon detector, showingprojected scattering angle \u00CE\u00B8 pro j . The left shows Monte Carlo simulations of 25000muon events using Geant4, compared to two models, Highland and Gaussian mixturemodel. On the right is an illustration of multiple scattering and the effect on the particles\u00E2\u0080\u0099direction. [22]\u00CF\u0083 pro jms =13.6MeV\u00CE\u00B2cpZ\u00E2\u0088\u009At/X0[1+0.038ln(t/X0)], (5.7)where X0 is the radiation length, Z is the charge and p is the momentum of the particle. The rootmean square is thus a function of t, the path length through the material. For particles of interest ,mainly charged poins and other hadrons in jets, the assumption made in the derivation of the aboveformula, which is that the deflection of a particle is an elastic process and does not change theabsolute momentum of the track particle is valid.The energy loss of charged particles going through the detector is mostly described by ioni-sation, bremsstrahlung, pair production and photonuclear interaction (written here in order of de-scending effect on heavy particles studied here). The ionisation loss, which dominates, is treated asdeterministic with respect to the amount of material traversed using the Bethe-Bloch formula. Bymodelling the energy loss as a Landau distribution, with fluctuations around a most probable value,the most probable energy loss (L\u00E2\u0088\u0086p) can be simplified to [22]:L\u00E2\u0088\u0086p = \u00CE\u00BE[ln2mc2\u00CE\u00B32I+ ln\u00CE\u00BEI\u00E2\u0088\u00920.8+4.447], (5.8)where \u00CE\u00BE is a parameter dependent on properties of the traversed medium and the momentumand energy of the particle, and I is the mean ionisation potential of the medium.Being used for both extrapolation through the inhomogeneous magnetic field as well as a modelof multiple scattering and energy loss through material, the ATLAS track extrapolation will bereferenced frequently in both the track fitting as well as the in propagation of tracks through activesilicon area.The Runge-Kutta propagator incorporates all these material effects as point-like material up-51dates to the track when crossing material as seen in Figure 5.10, decoupling the equation of motionfrom these effects.Figure 5.10: Material in each layer is modelled as surfaces with a certain thickness each trackgoes through as seen on left, with exact material descriptions contained in databasesfor the extraplation and reconstruction. On the right is shown the agreement of trackingmaterial with the full simulation. [22]5.1.1.4 Kalman Fitter stepsPutting all of these steps together is a Kalman Fitting procedure which begins with the initial globalpattern recognition and uses track extrapolation to form complete tracks through the detector [46].The Kalman fitting in this case is divided into two parts, a filtering to extend the fit and a smoothingto incorporate the new information into the fit of earlier points.The Filtering procedure can be broken down into these main steps [53, 55]:\u00E2\u0080\u00A2 Propagate the track parameters and their covariance matrix from layer k\u00E2\u0088\u00921 to k using previ-ous track extrapolation methods.\u00E2\u0080\u00A2 Compare predicted position to the hits on that layer, taking into account material effects intothe uncertainty on the measurement.\u00E2\u0080\u00A2 Add hit to the current fit.Track parameters used in fitting and extrapolating are bundled into a state vector for purposesof the Kalman filter. They are continuously fitted and updated throughout the kalman procedure asoutliend in Figure 5.11.52Figure 5.11: Diagram showing the propagation of track parameters through the detector lay-ers. At each layer, the propagated position and covariance matrix make up the whitecircles, with the track parameters and their covariance matrix make up the cylinderpredicting the extrapolation to the next layer. [22]In its simplest form a state vector is a matrix of parameters (in ATLAS 5 the tracking parame-ters) as a function of the position, eg. [56]x = x(z) (5.9)Where z can be a discrete set of points, in this case each layer with a measurement. The systemcan thus be described asx(zl) = fl\u00E2\u0088\u00921(xl\u00E2\u0088\u00921+wk\u00E2\u0088\u00921), (5.10)where x(zl) is the aforementioned state vector at layer zl , l is a label for each layer, f is thetrack propagator described above, and w is a description of the variation in track parameters due tomultiple scattering and other material effects. Furthermore, the actual observed state vector, ml , isml = hl(xl)+\u00CF\u0083l, (5.11)where h is a mapping from the state vector to the measurement, and \u00CF\u0083 is the measurement noise.In the ATLAS environment, the propagator fl is nonlinear, and thus the filtering is approximatedby a Taylor expansion of the extrapolating functionfl(x\u00E2\u0088\u0097l ) = fl(xl)+\u00E2\u0088\u0082 fl\u00E2\u0088\u0082xl(x\u00E2\u0088\u0097l \u00E2\u0088\u0092 xl) (5.12)Additionally, the measurement can be considered linear with a certain choice of parameters forthe state vector. The state vector propagation now reads as53xl\u00E2\u0088\u00921l = Fl\u00E2\u0088\u00921(xl\u00E2\u0088\u00921) (5.13)where F is now a transformation matrix, analogue to the extrapolating function f described inEquation 5.10. With this linear approximation the usual Kalman filtering formalism can be used.In the prediction step, the function fl , described above as the extrapolation to a new layer l viaTaylor expansion, is used to extrapolate the state vector. The covariance matrix is also transportedto the new layer viacl\u00E2\u0088\u00921l = Fl\u00E2\u0088\u00921Cl\u00E2\u0088\u00921FTl\u00E2\u0088\u00921+Ql\u00E2\u0088\u00921 (5.14)where Ql\u00E2\u0088\u00921 is the covariance matrix of wl\u00E2\u0088\u00921, the process noise included in the state vectorequation. The residuals for the extrapolation are found using function a Hl , the mapping functionfrom state vector to measurement. Keeping in mind xil is the estimate of the state vector xl using themeasurements in the algorithm up to the current extrapolation i, the residual r is defined as:rl\u00E2\u0088\u00921l = ml\u00E2\u0088\u0092Hlxl\u00E2\u0088\u00921l . (5.15)And the covariance of the above residuals isRl\u00E2\u0088\u00921l =Vl +HlCl\u00E2\u0088\u00921l HTl (5.16)where Vl is covariance of the measurement noise at point l.In the second, filtering step, the state of the fit at the current layer is estimated based on theprevious measurements made. Using the filtered residuals in Equation 5.15, and computing theircovariance matrixRl =Vl\u00E2\u0088\u0092HlClHTl (5.17)which is input to the calculation for \u00CF\u00872, which essentially calculates the total distance betweeneach measured point and fitted value to give an overall score. For each point k, chi2k is calculated,and iteratively added up to give a total \u00CF\u00872 of the fit.\u00CF\u00872k = rTk R\u00E2\u0088\u00921k rk (5.18)Finally, the smoothing operation is used to refine the state vector at each previous point based onthe new information, starting with a smoother gain matrix. A gain matrix depends on the covarianceand can be understood as how much to change each prior measurement due to new information, inthis case a new measurement in the algorithm. The smoother gain matrix, Al , for measurement l:Al =ClFTl (Cll\u00E2\u0088\u00921)\u00E2\u0088\u00921, (5.19)54which is used to smooth the state vector at point nxnl = xl +Ak(xnl+1\u00E2\u0088\u0092 xll+1) (5.20)The covariance matrix and residuals are similarly smoothed.We can see that, starting with a small number of hits in a seed in the inner detector, trackextrapolation using Runge-Kutta-Nystrom numerical methods can be used in a Kalman filter topropagate the state vector to new measurement layers in order to obtain the next most probable hitin the track; this is combined with an error estimate in the form of a covariance matrix that includeseffects such as multiple scattering and energy loss in the detector material. We are thus able to fit atrack from a seed anywhere in the inner detector. Additionally, the \u00CF\u00872 computed at each step can beused to discard outliers on the track given certain constraints on the goodness of fit and individuallayer residuals. In Run 1, about a third of the initial seeds were successfully fitted and became trackcandidates input to the ambiguity solver.5.1.1.5 Ambiguity SolvingOnce seeds are made using the global pattern recognition described in Section 5.1.1.2, the trackcandidate formation using the Kalman filter works independently of whether or not a hit is usedby another track or not. However, many of these track candidates can be incomplete, a wrongcombination of hits or fake tracks. Incomplete implies that they should be merged with furtherhits to correctly describe the path of a particle; wrong combinations means they use hits that don\u00E2\u0080\u0099tbelong to the particle being tracked, or fake meaning a track is made entirely of hits from differentparticles, noise or other means. This issue is addressed in two steps: first, each track is given ascore which corresponds to how likely the track is to describe a single particle trajectory throughthe Inner Detector, second, by using the score, tracks which share too many hits or have too manyoutliers are rejected by an optimized algorithm to maximize reconstruction efficiency and minimizethe amount of incomplete, wrong or fake tracks [18].The first component of the ambiguity solver, the track score, depends on two of the propertiesof the track. First, it is scored based on which detector elements it hits. With a now-complete trackfit, we can model as accurately as possible the trajectory of each track through the Inner Detector.Thus, each track candidate will have an expected hit in a number of both pixel and strip layers. Amissing hit in either of those will be a detriment to the score. Furthermore, a missing hit in the twomodules of a strip layer is an even stronger penalty, as the odds of being missed in both are verysmall [21] . Additionally, tracks with an overlap hit, that is two hits in one layer, have a strongincrease in score. This all benefits fully reconstructed tracks rather than smaller, segmented tracks.The pixel detector, being more precise, usually carries a higher score if a track has a hit in it, anda higher penalty for a miss. Finally, the \u00CF\u00872 of the track is incorporated into this score by way ofcalculating the log of the probability given the \u00CF\u00872 calculated and the number of degrees of freedom,such that [57]55Score = [Scores from hits]+ logP(\u00CF\u00872,ndf) (5.21)ignoring all constants.The final part of track reconstruction now uses this score to make an ordered list of tracks. Eachhit on a track is given a label:\u00E2\u0080\u00A2 Unused - does not share cluster with other tracks;\u00E2\u0080\u00A2 Shared - shares cluster with other tracks\u00E2\u0080\u00A2 Split - shares cluster with other tracks, but lesser penalty (to be explained in Section 5.2);\u00E2\u0080\u00A2 Outlier - hit probably not consistent with track, usually rejected unless the track is re-fitted;\u00E2\u0080\u00A2 Rejected - hit does not belong to the track, usually because it shares the cluster with toomany other tracks or it is an outlier and refitting has not changed this.A track candidate with only unused hits would pass the ambiguity solver and be accepted asa track. The track with highest score which has split or shared hits will not know about the othertrack candidates which share that hit, and so will not be affected. As the Ambiguity solver movesdown the track candidates by score, tracks with too many shared or split hits, that are not consistentwith the cuts in the ambiguity solver, will be rejected. Some tracks with too many shared hits canalso have those hits removed and if consistent with a good track candidate, will be refit, re-scoredand re-inserted into the ambiguity solver. Finally, if tracks that could have a shared hit, but addingthat track to that cluster would mean previous tracks with a higher score would be rejected due tothat cluster being shared by too many tracks, that hit is deemed incompatible with being shared, andis rejected. The Pixel and Strip detectors both have different limits on the number of tracks whichcan share a cluster, which has been optimized to maximize the number of real tracks accepted andminimize the number of fake tracks accepted.5.2 Tracking in Dense EnvironmentsPattern recognition, track fitting, extrapolation and ambiguity solving is already a challenge in theusual track reconstruction environment of ATLAS. A further wrinkle occurs in boosted decays,principally in high-pT jets and \u00CF\u0084 lepton decays. In these cases, it is possible that the ConnectedComponent Analysis (CCA) defined in Section 5.1.1.1 merges the pixels with deposits from dif-ferent particles together into one cluster, or that the separation between the charged particles is sosmall the energy deposits can be within the same pixel, as shown in Figure 5.12. For these extremecases an additional algorithm is used, called tracking in dense environments (TIDE).56Figure 5.12: Simulation of charged particle in jets, showing the average separation betweenthe two closest charged particles in both the transverse and longitudinal direction, inthe first pixel layer (R= 50.5 mm) as a function of transverse momentum of jets. Thehorizontal lines shown illustrate the size of a 50\u00C3\u0097400 \u00C2\u00B5m pixel. [24]The strategy behind TIDE in ATLAS is to identify which clusters could belong to multiplecharged particles, such that the penalty for having shared hits is lessened on tracks in these col-limated environments. This is done through the use of a Neural Network to estimate the numberof particles going through a cluster. In the pixel detector, this Neural Network takes as input thetime-over-threshold charge in the pixels as well as the location of each pixel in the detector to de-termine which clusters are consistent with multiple charged particles going through it. The inputto the Neural Network is in the form of a 7\u00C3\u0097 7 matrix - a 7\u00C3\u0097 7 pixel grid - containing time overthreshold information for each pixel, as well as additional inputs such as track candidate incidenceangle to the cluster. This Neural Network is trained on the probability of 1, 2, or 3 particles goingthrough the cluster, higher multiplicities are not considered. The output is the probability of thecluster containing energy deposits for 1, 2 or more than 2 charged particles. The possible grid oftime over threshold pixels is shown in Figure 5.13 on the left, with a typical shared hit from twotracks on the right.57Figure 5.13: Left figure is a pictorial representation of multiple tracks deposing energy andforming one cluster. Right figure - (a) shows the perspective from the silicon thicknesswhere 1 particle deposits energy and (b) where multiple particles do. [24]The algorithm unfortunately cannot detect each cluster with deposits from multiple particlescompletely accurately, nor can it determine which clusters only have 1 particle with 100% certainty.Given that the identification rate for both of these scenarios depends on the probability cut on theprobability output by the Neural Network, a working point has to be determined to decide betweenmaximizing identification of multi-particle clusters or minimizing incorrectly labelled 1-particlecluster. The working point for Run 1 is shown in Figure 5.14. In Run 2, cuts were loosed to 0.35for the fraction of correctly split 2-particle clusters, and 0.4 for three-particle clusters.Figure 5.14: A working point plot for the Run 1 NN clustering. Determined through MonteCarlo, the cuts chosen split 71% of clusters from 2 particles correctly, while 7.5% ifclusters from 1 particle are incorrectly split. [24]This Neural Network is run at the Ambiguity Solver stage, where track candidate parametersare considered precise enough such that delaying it from the pattern recognition to the AmbiguitySolver gives a gain in performance. Furthermore, the Neural Network only runs when a cluster58has multiple track candidates sharing it, meaning each shared cluster in the pixel detector can beflagged as split. Additionally, information on other layers can be used for better ambiguity solving- given that separation between particles tends to increase as they go further away from the collisionpoint, requiring two tracks sharing a cluster in one layer to also share it in the previous layers isan excellent discriminant. The robustness of the Neural Network cluster identification has beenstudied and validated for most variations in NN inputs [58].With the optimization of both the Neural Network and Ambiguity Solver, track reconstructioncan benefit from better identification of shared clusters. This is shown in Figure 5.15, where theaverage amount of pixel clusters per track when using TIDE increases relative to the baseline, closerto the ideal, in the high-pT decays of \u00CF\u0081 and \u00CF\u0084 particles because of a higher fraction of correctlyidentified split clusters.Figure 5.15: The average number of pixel clusters per track is shown for (a) \u00CF\u0081 sample and(b) \u00CF\u0084 sample. Baseline shows track reconstruction without track splitting in the Am-biguity Solver, while Ideal shows a truth-based reconstruction showing the maximumalgorithmic efficiency. The \u00CF\u0081 has a two-prong decay while the \u00CF\u0084 has a three-prong de-cay. This plot shows how the two-particle splitting of the TIDE NN has a much betteridentification rate than the three-particle splitting. [25]This same method cannot be used for the strips as there is no time-over-threshold charge in-formation. With the larger z-axis dimension on the strips, tighter cuts must be applied on sharedclusters, such that a track can only have two shared clusters - the efficiency relative to the amount ofallowed shared strip clusters is shown in Figure 5.16 - and must have a minimum of 9 silicon cluster(pixels + strips) before a track can have shared hits. This is due to fake rates increasing when short,incorrectly split clusters in the pixel detector make a track with strip hits.59Figure 5.16: Ideal, or truth-based reconstruction efficiency for reconstructing all charged de-cay products of (a) \u00CF\u0081 and (b) \u00CF\u0084 is shown shown. The dependence on the maximumnumber of shared SCT clusters is clearly outlined. [25]The largest effect of TIDE impact on track reconstruction can be seen for reconstruction effi-ciency of \u00CF\u0084 decays as shown in Figure 5.17, and for simulated Z\u00E2\u0080\u0099 jet events as shown in Figure 5.18.Figure 5.17: Algorithmic Reconstruction efficiency for single-\u00CF\u0084 to 3 charged pion events, de-fined as reconstruction efficiency when all clusters are not shared by more than 2 parti-cles in the truth record. [25]60Figure 5.18: Track Reconstruction efficiency for 3 TeV Z\u00E2\u0080\u0099 events where all tracks consideredhave a production vertex before the first layer. [25]In conclusion, the combination of global and local pattern recognition, track fitting and ambi-guity solving as well as identifying shared pixel clusters in dense environments with TIDE formsthe chain ATLAS uses for track reconstruction. These tracks are crucial for particle identificationand kinematic parameter resolution, and thus the tools used and detector make-up form a crucialpart of how accurately ATLAS can reconstruct events.61Chapter 6Emulation Methods6.1 GoalsAs stated in Section 4.4, one of the goals of the upgraded Inner Detector for the HL-LHC is tobe able to reconstruct tracks in dense environments with a same or better efficiency than than thecurrent, Run 2 Inner Detector. These dense environments come from decays of high momentumparticles into several charged particles before the inner detector. These will be collimated due tothe kinematics of the decay, as shown in Figure 6.1. This can be a tau lepton decaying to multiplecharged pions, or a bare quark hadronizing to several hadrons due to color confinement. The radialdistance between the decay and each layer means a greater separation between each decay product,and thus less of a chance to lead to a shared track on a layer as particles move away from each other.A finer granularity in either or both of the detector element directions will also lower the number ofshared clusters on a track. Finally, a smaller silicon thickness will lead to a smaller charge depositwidth, making it less likely that two collimated particles will share a cluster.Figure 6.1: Pictorial representation of particle decays. In this case, a particle labelled \u00CF\u0081 decaysinto two charged particles. In (a), this decay is seen in the \u00CF\u0081 rest frame - the decayproducts are back to back due to conservation of momentum. In (b), we boost to the labframe of a \u00CF\u0081 with low momentum - the two decay products are well separated. In (c),we boost to the lab frame of a high momentum \u00CF\u0081 - the two decay products are emittedclose together and have little separation - they are highly collimated.In Section 5.2, it was shown how these kinds of dense environments lead to tracks from real62particles being rejected due to their number of shared hits being too high and thus mistaken for afake track. Shared hits are a very important flag for fake tracks as a dense environment like the HL-LHC, with \u00C2\u00B5 = 200, leads to very high combinatorics for the pattern recognition, meaning manytracks can be made from random assortments of hits. However, particles such as the Z\u00E2\u0080\u0099 boson areactively searched for, and current limits already reach 4 TeV [59]. A 5 TeV Z\u00E2\u0080\u0099 decaying to two topquarks would result in incredibly collimated jets, with the outcome that many of the tracks, crucialfor reconstructing the invariant mass of the Z\u00E2\u0080\u0099, sharing hits due to the dense environment.Due to severe limitations on computing time and manpower, a full simulation of every singlelayout being considered for the ITk is completely impossible. The move from \u00E2\u0080\u009DLOI Layout\u00E2\u0080\u009D with4 pixel layers and 5 strip layers to the \u00E2\u0080\u009DStep 1\u00E2\u0080\u009D layout with 5 pixel and 4 strip layers took a fewmonths, a time-scale which would leave little room for further study of the silicon detector prop-erties outlined previously - such as distance from the interaction point, detector element size andthickness of the silicon active area. Since the optimization of two-track resolution is a prime man-date for the ITk, this is a topic which needs to be addressed before finalizing the detector layoutsfor construction.The solution, which forms the basis of this thesis, is a fast emulation using the already fully-simulated layouts as a baseline and the full ATHENA reconstruction apparatus to approximate theeffects of different layouts on the efficiency of track reconstruction. It is labelled an emulation asit does not simulate a full, new geometry, but instead approximates new layouts using tracks fromthe full simulation and a simplified sensor interaction model. Thus, only a few values will describea new inner detector geometry and not a complicated, fully engineered geometry. The procedure,to be fully explained in Section 6.3, extrapolates the tracks to each layer with a variable distancefor each, emulates the ionisation of the silicon by the charged particle and the subsequent electrondrift to the pixels and strips, and finally corrects for diffusion and sensor edge effects by comparingthe baseline simulated energy deposit width to the emulated width using the same geometry. Thisis all done at the Ambiguity Solving stage, thereby determining which tracks have shared clustersand emulating the passage of this new information through the ambiguity solver, resulting in anapproximation of the tracks which would be output if the detector were in the new, emulated layout.Throughout this section, the single \u00CF\u0084 lepton to 3 pions samples will be used to gain the factorsneeded to scale energy deposit width and cluster separation widths. To do this, the same layout asin the fully simulated samples will be emulated, and both energy deposit width and clustering willbe studied to find the right values for the emulation. This will then allow the program to emulatedifferent layouts from the baseline for a multitude of ITk studies.6.2 Samples UsedThe sample used to calibrate the TIDETester emulation as well as to test various layout configu-rations is a single tau lepton decaying to three charged pions, either \u00CF\u0084\u00C2\u00B1\u00E2\u0086\u0092 pi\u00C2\u00B1+pi\u00C2\u00B1+pi\u00E2\u0088\u0093+\u00CE\u00BD\u00CF\u0084 or\u00CF\u0084\u00C2\u00B1\u00E2\u0086\u0092 pi\u00C2\u00B1+pi\u00C2\u00B1+pi\u00E2\u0088\u0093+pi0 +\u00CE\u00BD\u00CF\u0084 . Since only the ATLAS Inner Detector is being studied, and bothpi0 and \u00CE\u00BD\u00CF\u0084 are neutral, they will not be detected and thus the production process of the three charged63pions will not affect the studied being performed. The program Pythia, which was introduced inSection 2.2 is used to make a \u00E2\u0080\u0098particle gun\u00E2\u0080\u0099 sample of a single tau forced to decay into the threeprong final states described above. A Geant4 simulation [16] is used to propagate the resultingparticles through the ATLAS detector using Monte Carlo methods, with appropriate productionof secondary particle from material interaction and detector response. This produces a Raw DataObject (RDO) sample containing the detector output from the simulated particles - this can thenbe used to calibrate the TIDETester emulation and furthermore to study different layouts in DenseEnvironments.6.3 MethodologyAs outlined in Section 5.1.1.5, the ambiguity solver takes as input all track candidates from thepattern recognition. The function of the ambiguity solver is to reject tracks which share clusterswith too many other tracks. Thus the assumption is made that, regardless of detector layouts, thesame tracks will be output to the ambiguity solver.Every hit from every track is examined in the ambiguity solver to determine if it shares a clusterwith any other track in the event. These other tracks are only tracks that have been accepted by theambiguity solver; a rejected track does not count as a track sharing a particular cluster. This way a\u00E2\u0080\u0099bank\u00E2\u0080\u0099 of accepted tracks is kept through each event to decide whether or not each cluster is shared.The TIDETester algorithm is the tool developed in the context of this thesis to emulate clustersat the ambiguity solver level and determine if they are shared by multiple tracks. TIDETester hasbeen developed in the ATHENA framework, briefly introduced in Section 4.5, as a modular toolthat can be used for a number of investigations involving ITk layouts and their effects on the outputtracks and thus the overall reconstruction quality of each event.The first step is emulating the energy deposit width from all tracks on the detector layers theytraverse. This is done by finding the exit and entry points of each track on a hypothetical layer, andestimating the contribution of electron diffusion due to Lorentz angle to the width. This procedureis described in detail in the following sections.6.3.1 Energy Deposit WidthFirst the minimum silicon radius, which is when the track would first interact with the active silicon,is found by fetching the global coordinates of the silicon module of the detector element crossed byeach track; the x and y coordinates can then be converted to a radial direction in the r-axis. Then,a cylindrical surface is created at that radius. The coordinates of interaction are then converted toa global position, giving the global (x1,y1,z1) coordinates of where a track first meets the siliconelement of a detector layer. After this, taking into account the thickness of the silicon and theincidence angle, another cylindrical surface is created at a new, further radius which is where thetrack would exit the silicon. The track is extrapolated to that cylinder, and the global (x2,y2,z2)coordinates of the track exiting the silicon are found; the process is illustrated in Figure 6.2.64Figure 6.2: A 2D projection onto the x-y axis of a track is shown going through a layer ofsilicon. with one inner cylinder used find the track\u00E2\u0080\u0099s coordinates at the inner edge, andthe outer cylinder to find the track\u00E2\u0080\u0099s coordinates at the outer edge. The incidence angle isaccounted for, but no multiple scattering effects are considered for the cylinder\u00E2\u0080\u0099s radiusfor extrapolation. Diagram is not to scale.Charged particles traversing the silicon sensor will leave a signal width, as shown in Figure 6.3.After finding the entry and exit points of the track through the silicon, the width of the drift of thesignal electrons created by the charged particle traversing the silicon must be estimated. This widthis then calculated along both axes of the individual silicon elements.65Figure 6.3: From TIDE section - a projection onto the local r axis - the energy deposit widthfor one particle on that axis is shown on (a), and for a cluster of two particles on (b).There are two important local detector element axes as shown in Figure 6.4, the z-axis and the r-axis. These follow the segmentation of the pixels and strips, and are the coordinate system in whichthe energy deposit width will be calculated. The r-axis has the complication of having the electronsdrift in the direction of the Lorentz Angle [11]. Initially, the energy deposit width is modelled asthe distance between the coordinates where the track crosses the top of the silicon, the track edge;and the coordinates where the electrons emitted from the bottom of the track silicon drift to the top,the drift edge.Figure 6.4: A 3D representation of a detector element, showing the local r and local z axis onthe detector element as well as the global (x,y,z) coordinate system.66In the r-axis, the electrons are modelled to drift following the Lorentz Angle, and in the z-axisthey will be modelled to drift following the electric field, so following the normal to the silicon.This calculation is illustrated in Figure 6.5.Figure 6.5: Left:A charged particle going through silicon projected onto the local r axis ofthe detector element. The first approximation to the energy deposit width is the space inr between where the track exits the silicon and the point where electrons, travelling atthe Lorentz angle, reach the edge of the silicon. Right: Energy deposit width projectedonto the local z axis, in this case the electrons at the drift edge travel straight up to theedge of the silicon, following the electric field.There are other effects at play here, including the electron diffusion for smaller silicon thickness(pixels) and threshold effects for larger silicon thickness (strips). The strategy here be to look atthe average energy deposit widths in the simulation, for each layer, and correct the emulated energydeposit width from TIDETester to account for these effects.In order to calibrate the emulation done in TIDETester, the energy deposit width as calculatedpreviously will have to be compared to the width obtained in full simulation. To obtain the simulatedenergy deposit width in each detector element dimension, the central coordinates of each individualpixel or strip in each cluster is found. Only clusters that have only had one real particle pass throughthem are chosen here, so that the true, single particle width is the one being studied. Then, eachcentroid is compared to all the others in both z and r to find the largest distances. This would be thewidth in each of the detector elements\u00E2\u0080\u0099 local axes. This procedure is outlined in Figure 6.6.Figure 6.6: Left: A 3D representation of a track depositing energy (red) in a cluster of detectorelements. The local r and z axes are shown along the edges of the elements. Right: Atfirst the center coordinates of each track are found, then the distance in r (\u00E2\u0088\u009A\u00E2\u0088\u0086x2+\u00E2\u0088\u0086y2)is found between each, as well as the distance in z ( \u00E2\u0088\u0086z ). The maximum of each is thewidth of the cluster in r and z respectively.67Looking at Figure 6.7, there is different behaviour seen in the first two layers which are ex-tremely close to the interaction point, and the three last pixels layers which are further away. Thefurther distance reduces the range of possible incidence angles, and thus leads to smaller deviationsin cluster size for tracks incident on those outer pixel layers. To find a correction to the emulatedwitdth, the ratio of emulated over simulated is found at each point, and fit with a polynomial ofdegree 2. This function was chosen as it was a good approximation to the shape, with a larger dis-crepancy near the Lorentz angle where electron drift is most prevalent. The polynomial degree 2 fitis shown to be in good agreement with the difference between the emulation model and simulation,as shown in the accompanying plots for each layer.68Figure 6.7: Cluster width in the r-dimension, as a function of incidence angle, for the variouspixel layers (0-4). The fully simulated width is shown as red points whereas the em-ulation, without correciton, is shown as a blue line. The lower plot shows the ratio ofemulated over simulated width. The black line in the ratio plot is a polynomial fit tothe difference, which will be the correction applied to the emulation in order to properlyemulate the width.Looking at Figure 6.8 and Figure 6.9, the equivalent to Figure 6.7 but for strips, due to therelatively larger radius of each strip layer, the incidence angle range is roughly constant for alllayers. The model appears to agree very well close to the incidence angle but overestimates thewidth further from this minimum. This leads to the conclusion that electron diffusion is not a largefactor in the strips, possibly due to the fact that the large silicon width leads to too much diffusion,69meaning electrons adjacent on other strips are too few to pass over the threshold to register as a hit.The polynomial degree 2 again models the discrepancy well, as it is used as a correction factor.Figure 6.8: Cluster width in the r-dimension, as a function of incidence angle, for the various striplayers. Due to each strip layer being a combination of two strip detectors, there are eightcorrections instead of four. Layers 5-8 denote the strip detector closest to the interaction pointfor strip layer 0-3 respectively. The fully simulated width is shown as red points whereas theemulation, without correciton, is shown as a blue line. The lower plot shows the ratio ofemulated over simulated width. The black line in the ratio plot is a polynomial fit to thedifference, which will be the correction applied to the emulation in order to properly emulatethe width.70Figure 6.9: Cluster width in the r-dimension, as a function of incidence angle, for the variousstrip layers. Due to each strip layer being a combination of two strip detectors, there areeight corrections instead of four. Layers 9-12 denote the strip detector further from theinteraction point for strip layer 0-3 respectively. The fully simulated width is shown asred points whereas the emulation, without correciton, is shown as a blue line. The lowerplot shows the ratio of emulated over simulated width. The black line in the ratio plot isa polynomial fit to the difference, which will be the correction applied to the emulationin order to properly emulate the width.As was the case for the phi coordinate, the eta coordinate for the pixel emulation shows inFigure 6.10 an underestimation near the lorentz angle and a slight overestimation of the widthfurther from that angle. A polynomial degree 2 fit corrects this well, except in the tails where itmay over-correct the width . Given that this is a rare case, this is a very minor effect and thus thegood agreement for most angles supports the use of this fit. No strip eta correction is applied, asthe large strip length means that there are no occurances when two strip lengths are included inone cluster. Given that the three other cases were successful in roughly predicting the width evenwithout correction, the method is assumed valid in the strip eta coordinate as well.71Figure 6.10: Cluster width in the z-dimension, as a function of incidence angle, for the var-ious pixel layers (0-4). The fully simulated width is shown as red points whereas theemulation, without correciton, is shown as a blue line. The lower plot shows the ratio ofemulated over simulated width. The black line in the ratio plot is a polynomial fit to thedifference, which will be the correction applied to the emulation in order to properlyemulate the width. 72However, correcting this width is not as simple as adding a distance to the total energy deposit- it cannot be assumed that both edges of the energy deposit will be corrected by the same amount.When comparing energy deposits from different particles, the edges that are closest to each othermust be corrected with the right factor. This will be discussed in Section 6.3.2.6.3.2 Re-clusteringTIDETester re-clustering involves a complete emulation of every track\u00E2\u0080\u0099s interaction with every innerdetector tracking layer in order to find which tracks share clusters in each layer. First, the edges ofthe energy deposit are found using the technique outlined in Section 6.3.1, but not yet corrected.Then, once the distance between each track\u00E2\u0080\u0099s energy deposit in the layer is found in both of thepixels\u00E2\u0080\u0099 local coordinates, that distance is corrected using the correction factors found from the 2nddegree polynomial fit. Finally, the average distance needed to resolve two different energy depositsas a single or shared cluster needs to be computed. This will complete all the information neededto emulate any ITk layout.6.3.2.1 Correcting distances between tracksThe way track information is processed, all the clusters that make up a single track are checked forbeing shared with other tracks. Thus, we will refer to this track as the reference track. Its energydeposit on each layer will be compared to all the other energy deposits in that layer in order todetermine if each cluster was shared or not, as illustrated in Figure 6.11.73Figure 6.11: Two tracks are shown going through 3 pixel layers. Their emulated energy de-posit is shown in red, whereas the true simulated deposit is shown in green. In Layer(1), the energy deposit of the reference track overlaps in both local r and local z withanother track, so this cluster will be shared - this matches the clustering from the base-line simulation. In Layer (2), there is overlap in the local z, but not in r - however, thedistance in r is small, less than 1 detector element - the simulated cluster is thus alsoshared between the two tracks. In Layer (3), there is overlap in local r only as well, butthe distance is much greater than in (2) - there is one simulated cluster per track in thiscase. To re-cluster each energy deposit, the distance in r and z below which two tracksshare one cluster must be determined.First the global coordinates of each edge of all energy deposits of the track on the layer beinginvestigated are found using the algorithm outlined in Section 6.3.1. Then, the deposits for eachtrack and the reference track are checked for overlap - this is an easy check as it is certain thatoverlapping energy deposits will share a cluster, and no correction needs to be done. If the referencetrack overlaps in both z and r local reference frame, then the cluster will be considered sharedbetween these two tracks. If it overlaps in only one local dimension, then the correction fromSection 6.3.1 is applied.The electrons which will be detected in the pixel or strip will also have a diffusion effect,diffusing at an angle \u00CE\u00B8D from both edges of the deposit. However, depending on both the Lorentzangle and incidence angle of the track, the contribution of the diffusion may be different on both74edges of the energy deposit. It is assumed that the correction factors found previously are mostlydue to diffusion. Thus, the correction must be appropriately divided into two for each edge ofthe deposit. The rest of this section concerns itself with first finding the diffusion angle, and thencorrectin the energy deposits with this information.The possible asymmetry of the correction on both sides of the deposit is investigated by firstfinding the diffusion angle of the track, using the assumption that, at the Lorentz Angle, the onlycontribution to the width is electron diffusion which is assumed to be the contributing factor to thediscrepancy between model and simulated in Section 6.3.1. Due to only knowing the thickness anddeposit width at the Lorentz angle, the computation uses mathematica [60] code to solve for this,as shown in Section A.1. The result is an equation which returns the diffusion angle \u00CE\u00B8D given theLorentz Angle of the layer.\u00CE\u00B8D = cos\u00E2\u0088\u00921\u00EF\u00A3\u00AB\u00EF\u00A3\u00AC\u00EF\u00A3\u00AC\u00EF\u00A3\u00AD\u00E2\u0088\u0092\u00E2\u0088\u009A(l2 sin2(\u00CE\u00B8L)(l2+4t2) \u00E2\u0088\u0092(l2 cos2(\u00CE\u00B8L))(l2+4t2) +(\u00E2\u0088\u009A2\u00E2\u0088\u009A\u00E2\u0088\u0092t2(l2cos(4\u00CE\u00B8L)\u00E2\u0088\u0092l2\u00E2\u0088\u00928t2))(l2+4t2) +l2(l2+4t2)+(4t2)(l2+4t2))\u00E2\u0088\u009A2\u00EF\u00A3\u00B6\u00EF\u00A3\u00B7\u00EF\u00A3\u00B7\u00EF\u00A3\u00B8 (6.1)where \u00CE\u00B8L is the Lorentz Angle, t is the active silicon thickness and l is the width of the simulatedcluster size for that particular layer, as shown in Figure 6.12. In the r local detector element axisthe lorentz angle simulated is input, whereas in the z axis this angle is set to 0.Figure 6.12: Left: The previously shown energy deposit width diagram in local r, with theadded diffusion at the Lorentz angle. Right: Previously shown energy deposit widthdiagram in local z, with the added diffusion at the incidence angle of 0.With the ability to estimate the diffusion angle for every track, given the variables describedabove, now we must estimate how each edge of the energy deposit form each track contributes tothe width correction as calculated in Section 6.3.1. The edges will be labelled as \u00E2\u0080\u0099drift\u00E2\u0080\u0099 edge forthe contribution from the electron drift from the track\u00E2\u0080\u0099s first interaction with the silicon, and \u00E2\u0080\u0099track\u00E2\u0080\u0099edge for the contribution from the track\u00E2\u0080\u0099s last interaction with the silicon. Figure 6.13 shows howto geometrically estimate the contribution from each, by finding the ratio of the width of the Trackedge (wT E) and the Drift edge (wDE):75Figure 6.13: The relevant geometry for calculating contributions for both edges of diffusionis shown, as projected onto the local r axis of the silicon. The same calculation canbe done for any positive or negative Lorentz Angle, and positive or negative incidenceangle. In the z direction, \u00CE\u00B8L is simply 0.wT EwDE= x =tan(\u00CE\u00B8i+\u00CE\u00B8D)\u00E2\u0088\u0092 tan(\u00CE\u00B8i)tan(\u00CE\u00B8L+\u00CE\u00B8D)\u00E2\u0088\u0092 tan(\u00CE\u00B8L) (6.2)Track edge =x1+ x(6.3)Drift edge =11+ x(6.4)where x is the ratio between how much the correction factor should be added to the track edgeover the drift edge, as shown in Figure 6.13. For example, if x = 2, and the correction is 1 pixelwidth, then in the track direction the direction should be x/(1+ x) = 2/3 and in the drift direction1/(1+ x) = 1/3, thus the track edge will be corrected to be 23 of a pixel wider and the drift edgewill be 13 of a pixel wider.Finally, the distance in r and z between each track\u00E2\u0080\u0099s drift and track edge coordinates and thereference track\u00E2\u0080\u0099s drift and track edge coordinates are computed, and corrected with the computa-tion factor found above. The minimum distance for each track and reference track combination isretained as being the real, closest parts of the energy deposit and thus the ones which will determineif the cluster is shared or not.6.3.2.2 Ideal track separationThe idea behind ideal track separation is that, once the actual distance between a reference track andeach other track\u00E2\u0080\u0099s energy deposit are found, there must be a cut on these distances below which thetracks form a shared cluster, and above which the tracks form two separate, individually resolvedcluster. The assumption will be made that, at least in the pixels, this cut will be the same in boththe detector element\u00E2\u0080\u0099s local axes r and z. For the strips, given the order of magnitude increase in zdirection, we will focus on the r cut, and leave the z cut as the geometrically obvious 1.5 element76width. The cut will be as follows: if two energy deposits are below the selected distance in boththe r and z local axes of the stave where the reference track deposited energy - the cluster will beshared; if either or both are further than the cut distance, the clusters are resolved.The cut value be chosen by comparing the emulation to the number of tracks per cluster in thesimulated event, using the exact same layout (silicon thickness and layer distances equal). The cutvalue acts as both a validation of the method and an approximation of clusterization for TIDETester.Geometrically, it would make sense to set this cut at 1.5 detector element sizes; however, edgeeffects, detector effects and diffusion may change this value. The expectation is that the cut shouldbe between 0 and 2 detector element sizes (in each axis). The way to do this will be:1. Run the reconstruction of single \u00CF\u0084 events.2. For each cluster, get (a) the number of tracks sharing the cluster as simulated in Geant4, and(b) the distance of each track\u00E2\u0080\u0099s energy deposit from the reference track in the cluster, in bothr and z local axes of the cluster\u00E2\u0080\u0099s detector element.3. Do a scan from 0 to 2 for cut values of separation between energy deposits in r and z. If thisdistance, along both axes, is smaller than the cut value being scanned, the other track sharesthe cluster.4. For each cut value being scanned, take the ratio of simulation tracks in shared clusters overemulation tracks in shared cluster.5. The cut value for which that ratio is one, means that this is the cut distance in emulation forwhich you have the same amount of tracks in shared clusters as the baseline simulation.6. Do this separately for each layer.This procedure is outlined in Figure 6.14.77Figure 6.14: Depiction of the scan to find ideal cut values for clustering. Left: In the baselinesimulation, the two tracks share a cluster on this particular layer. After finding theenergy deposit width, a scan in both r and z local axes is started, going from 0 (theenergy deposit width) until 1 pixel width away from the energy deposit width, wherea deposit from another track is. Thus, if the cut value was 1 pixel width in both axes,emulation would consider this a shared cluster - in which case, the simulated clusterwould have two tracks and the emulated cluster would have two tracks; leading to asimulated over emulated ratio of 1. Right: Same scan, but in this case simulation hasthe two tracks having different, singular clusters. The cut value would need to be twodetector elements in r and z for emulation to consider this a shared cluster.This scan is shown in Figure 6.15 for the pixels and in Figure 6.16 for the strips.Figure 6.15: The scan, as described in Figure 6.14, is done for all 5 pixel layers. A ratio on they-axis of 1 means that emulation has the same number of shared clusters as the baselinesimulation of the layout. On the x-axis is the scanned distance, in both local r and z,below which two energy deposits from two tracks would be considered a single sharedcluster.The optimal pixel track separation is between 0.8 and 1 pixel width for all pixel layers in bothr and z. For layers 0-3 a distance of 1 pixel width (50 \u00C2\u00B5m in the Step 1 layout) will be used as thedistance cut, and 0.9 pixel widths will be used for layer 4.78Figure 6.16: The scan, as described in Figure 6.14, is done for all 4 strip layers - due to thefact that each strip consists of two detectors, this means 8 total detector layers must bescanned over. A ratio on the y-axis of 1 means that emulation has the same number ofshared clusters as the baseline simulation of the layout. On the x-axis is the scanneddistance, in both local r and z, below which two energy deposits from two tracks wouldbe considered a single shared cluster.The strips all converge on ideal track separation between 1.5 and 2. In order to avoid overly fine-tuning, a strip width of 1.5 was chosen in the r direction as the ideal track separation for all layers;in the z direction the strips are too large to make any determination - the ideal track separation is setto 1.5 as well.With the calculation of the energy deposit width and now the track separation needed in eachlayer, the emulation has been completed and can now be validated and then used for physics studieson ITk geometries. The energy deposit has been shown to be correctly modelled using a simplifiedmodel with small corrections, and clustering values to separate shared from singular clusters havebeen found.6.3.3 Truth Matching and ITk TIDE Neural NetworkThe definition of truth in the context of ATLAS is the direct information of the particles simulatedthrough the detector, and not the reconstruction information which is a \u00E2\u0080\u0098best guess\u00E2\u0080\u0099 after the fact.This is accessible in simulation as the particles being propagated through the detector originatingfrom Pythia. These particles are being stored in the event itself, allowing for the access to truth-level information of the particle, such as its type, momentum and detector elements traversed. Truthinformation is crucial for two methods to be described below, truth matching and TIDE NeuralNetwork emulation.796.3.3.1 Truth MatchingTruth matching is a way to match a track reconstructed in the inner detector to a truth particle insimulation. This is done to identify which tracks are created from a real particle going throughthe detector and which are fakes, created by combinatorics, detector noise or other means. It alsoallows for the identification of which particle creates which track. Given the single tau lepton tothree charged pions sample being analysed, other than the very small chance of long-lived taus orhigh momentum secondary, all tracks will be charged pions.Truth matching is possible because the Geant 4 simulation saves which truth particles depositenergy in which detector element. Thus, during track reconstruction, each cluster which makesup tracks can then be matched to zero, one or more truth particles. Thus, by looping over eachcluster comprising each track, the truth matching probability of each specific track to a specifictruth particle is calculated as:Ptrk,truth =10\u00E2\u0088\u0097Tp+5\u00E2\u0088\u0097Ts10\u00E2\u0088\u0097Hp+5\u00E2\u0088\u0097Hs , (6.5)where Tp is the number of pixel hits which a track shares with a specific truth particle and Hpis the total number of pixel hits the track is made of; the subscript s denotes strip clusters. Thenumbers 5 and 10 have been optimized for best truth matching results. Thus it is possible for atrack to have multiple truth matching probabilities - only the highest is kept, with one exception.This exception is if a truth particle is matched to multiple tracks - in this eventuality, the track withthe highest score is truth matched to that particle, and no other track will be. A track with a truthmatching probability greater than 0.5 is accepted as matched to that specific truth particle.6.3.3.2 ITk TIDE Neural NetworkThe TIDE Neural Network for ATLAS Run 2 was described in Section 5.2. It acts as a clusteridentifier, using time over threshold and other pixel information to output probabilities of a specificpixel cluster having one, two or three particles depositing energy into it. This Neural Network,however, has only been optimized for the previous ATLAS pixel layouts and detector dimensionsand thus cannot be used for ITk track reconstruction.By the time of the construction of the ITk, however, this Neural Network will certainly be op-timized and working for the chosen ITk geometry. Thus, any performance study should take thisinto account when investigating new layouts. A truth emulation of the TIDE Neural Network wasimplemented to solve this. Using the truth information stored in each cluster, it is possible to knowhow many charged particles traversed a specific cluster in simulation. Thus, using the confusionmatrix from the Run 2 TIDE Neural Network, that knowledge can be smeared using the Run 2efficiencies in order to emulate the performance of the Run 2 cluster identification neural network.A confusion matrix, shown in Table 6.1, is a matrix that has 1, 2 or 3 truth particles in a cluster asrows, and the highest probability output by the Neural Network as columns. Thus, each element ina row is the fraction of time - for a given number of truth particles in a cluster - the cluster was iden-80Table 6.1: The Run 2 TIDE Neural Network confusion matrix. Each row shows the numberof truth charged particles going through a cluster, while each column shows the fractionof the time the NN determined that particular cluster was from 1, 2 or 3 particles.1-Particle NN 2-Particle NN 3-Particle NNTruth 1-particle 0.958 0.034 0.007Truth 2-particle 0.260 0.366 0.374Truth 3-particle 0.063 0.112 0.825tified as 1 (left column), 2 (middle column) or 3 (right column) by the TIDE NN. A perfect neuralnetwork would have values of 1 in the diagonal and 0 everywhere else; reality is not as efficient butan extraordinary achievement nonetheless.These numbers are used during the track reconstruction, such that split hits are also created bythe ITk with the same efficiency as Run 2. Effects such as momentum and angle dependence areignored as these have been found to be small in Run 2 studies.6.4 ValidationThe validation of the TIDETester emulation will take place in 2 steps: 1) checking that the amountof shared hits output from the event in simulation and emulation matches; 2) checking that theamount of real tracks output from simulation and emulation are consistent. The first check comparesif the output after the total machination of the ambiguity solver are similar between simulation andemulation by comparing ratios of shared hits. The second check is to see if the actual total numberof truth-matched tracks in single \u00CF\u0084 to 3 charged pions event is correctly replicated in emulation.6.4.1 Shared HitsFor a shared hit to be allowed on a track in the ambiguity solver, there are a number of requirements,as explained in Section 5.2. The most important is that each track must have a minimum number ofunshared silicon hits, and that shared hits must come from tracks that were shared in earlier layers -putting an emphasis on finding shared hits from collimated tracks and not from fake tracks. In thisvalidation, a split hit will also be considered a shared cluster. Thus, for every layer, the fraction ofshared clusters on track will be computed and compared to the simulation. This will be done byemulating only the pixels, only the strips, and finally emulating all inner detector layers.Figure 6.17 shows the difference in fraction of shared clusters between full simulation and theTIDETester emulation. The emulation shows a slight under-prediction of shared clusters for mostlayers. However, this under-prediction is limited to about 5%, given uncertainty, from the nominalfull simulation fraction of shared clusters. Given the number of variables to control, as well as thecomplicated nature of the shared hit determination throughout the track reconstruction procedure,81this is well within the acceptable range for emulation.Figure 6.17: Comparing the fraction of shared clusters on each layer for the simulation versusthe emulation of TIDETester. The y-axis is the fraction of shared clusters while thex-axis is the radius of each layer from the beam pipe - thus each data point is thefraction of shared clusters at a specific layer. The black points are full simulation forall tracking detectors, while red only has pixel detector emulated, green has only stripdetector emulated, and blue data points have both pixel and strip detectors emulatedusing TIDETester. The bottom insert shows the ratio of shared clusters for TIDETesterover the nominal (black) layout.After comparing emulation and simulation another sanity check for TIDETester is to test whetheror not the results obtained match what is expected. The way to do this is to emulated one layer be-ing at the position of another, and compare the fraction of shared clusters. If TIDETester scalesas expected, the results should match. This is done for pixels in Figure 6.18 and for the strips inFigure 6.19.For the pixel scaling results shown in Figure 6.18, only tau leptons which decay before the firstlayer are kept, in an attempt to compare the same tracks for every layer. Given detector acceptanceconstraints, the agreement shown here is remarkable as each layer scales to the next very well. Thusthe pixels can be considered validated for TIDETester emulation.82Figure 6.18: Comparing the fraction of shared clusters on each pixel layer predicted by TIDE-Tester depending on distance. The y-axis is the fraction of shared clusters while thex-axis is the radius of each layer from the beam pipe. In this test all layers are movedaway from the beam pipe to compare to the next layer - black data points are the firstpixel layer, red the second, green the third, blue the fourth and brown the fifth.For the strip scaling results shown in Figure 6.19, there is a slight underestimation when scalingone layer to the previous one - this may be due to complex detector acceptance issues or to the wayshared hits are only allowed in certain circumstances. However, given good agreement between thefirst three layers given uncertainty as well as the trend of decreasing fraction of shared clusters withdistance, the strips can also be considered validated for TIDETester.83Figure 6.19: Comparing the fraction of shared clusters on each strip layer predicted by TIDE-Tester depending on distance. The y-axis is the fraction of shared clusters while thex-axis is the radius of each layer from the beam pipe. In this test all layers are movedtowards the beam pipe to compare to the previous layer - black data points are the firststrip layer, red the second, green the third and blue the fourth.6.4.2 Pion Tracks AcceptedNow that we know we can emulate the right fraction of shared clusters, the amount of truth-matchedtracks reconstructed after emulation should be compared to those after full simulation. This is doneby running over all events, truth matching (as shown in Section 6.3.3) each track, and countingthe number of tracks truth matched to a charged pion from the \u00CF\u0084 lepton. Then, we take a ratio ofall events which have all 3 pion tracks accepted, and bin this as a function of truth tau transversemomentum as shown in Figure 6.20.84Figure 6.20: Comparing the track reconstruction efficiency for the simulation versus the emu-lation of TIDETester. The y-axis is the fraction of events where all three charged pionsfrom the \u00CF\u0084 were reconstructed as tracks, while the x-axis is the truth transverse momen-tum of the \u00CF\u0084 lepton. The black points are full simulation for all tracking detectors, whilered only has pixel detector emulated, green has only strip detector emulated, and bluedata points have both pixel and strip detectors emulated using TIDETester. The bottominsert shows the ratio of shared clusters for TIDETester over the nominal (black) layout.As can be seen, for the individual pixel or strip emulation, the efficiency is always within 8%of the simulation. For combined emulation of pixel and strips by TIDETester, this never dropsbelow 6%. Given the numerous challenges of fully emulating particle interaction with matter andthe complex track reconstruction for ATLAS, obtaining an efficiency within 5% given uncertaintyis an excellent result. Given the good shared cluster fraction prediction and scaling as well as theexcellent track reconstruction results, the TIDETester emulation algorithm can now be used to studylayouts differing from the baseline for ITk layout decisions.85Chapter 7Results7.1 Layout Studies Using Single TauThis section will cover the results of multiple studies done on ITk layouts using the TIDETester em-ulation tool described in Section 6.3.3. The sample used is the simulated single tau lepton decayingto three charged pions - with a flat pT distribution to ensure enough statistics in the momentumregions studied. The track reconstruction efficiency will be the figure of merit to study the differentlayouts. As in Section 6.1, track reconstruction efficiency for this specific sample is defined asEfficiency =Events with three tracks truth matched to pions from tauEvents with three truth pions from tau(7.1)where truth matching is as defined in Section 6.3.3. The studies will be restricted to tau leptonsdecaying in the barrel region ( |\u00CE\u00B7 |< 1.3 ) as this is the region of the detector where dense environ-ments have the largest effect - thus making sure to highlight effects of different ITk geometries.In order to compare different layouts, specific layout settings will be changed in emulation,however, in all situations TIDETester will be used to emulate every single layer, such that anychange is due to a change in ITk layout and not to the use of TIDETester. When comparing layoutsusing TIDETester, the same samples will be compared to each other using different emulationsettings - this means that the data will be completely correlated. First the standard deviation ofeach geometry in each bin is found, then, each different geometry is modelled as a variable in amultivariate distribution - due to the large sample sizes, with over 1000 events in most bins, thefollowing confidence interval calculation can be used [61]:x\u00C2\u00AF\u00C2\u00B1\u00E2\u0088\u009A\u00CF\u00872p(\u00CE\u00B1)\u00E2\u0088\u009As11n(7.2)where x is the mean value, \u00CF\u00872 is the chi-square distribution, p is the number of different geome-tries considered, \u00CE\u00B1 is the confidence interval, s11 is the variance and n is the amount of data pointsin the bin. This provides a confidence interval for each efficiency value that can then be used tocompare different geometries, and will be used for uncertainties in this section.867.1.1 Letter of Intent ResultsThe first set of results uses the Letter of Intent (LOI) Layout, described in Section 4.4, which is, atthe time of writing, obsolete. However, as a further exercise in validation, it is valuable to study theeffect of layout changes in this ITk geometry. The main feature of the LOI is the four pixel layersand five strip layers, as opposed to the five pixel and four strips in latter versions of the ITk tracker.The version of TIDETester used to make this plot was a preliminary version and thus this studyshould not be directly compared to any subsequent result using newer layouts. The ideal studyto do is to change the inner strip layers to pixels and compare the performance - this is shown inFigure 7.1.Figure 7.1: LOI Layout ITk simulation. Testing the change of strip layers into pixels. They-axis shows the average efficiency to reconstruct the three charged pions from the taulepton decay, as a function of the truth tau transverse momentum on the x-axis. Thebottom insert shows the ratio of efficiency over the nominal (black) efficiency. Blackpoint are baseline layout, red point have the first strip layer changed into a pixel (50\u00C3\u0097150mum), green points have first two strip layers changed to pixels, blue points have firstthree strip layers changed to pixels.These results show a clear difference, event at low momentum, between the different layouts.Above 500 GeV, when only changing one strip layer to a pixel layer, the efficiency is shown toimprove by as much as 2\u00E2\u0088\u0092 4% at high momenta. If more strips were to be changed to pixels, theincrease could be as high as 8% increase at 1 TeV. This is good validation for the change from LOILayout to the present ITk Step 1 layout, which has two versions each shown in Section 4.4 andwhose main difference from LOI is the inner-most strip layer which is changed to a pixel layer. The87ITk Step 1 layout will be considered the baseline for further studies.7.1.2 CMOS PixelsUsing the full power of the layout emulation methods outlined in Section 6.1, the first study doneon the Step 1 layout is to investigate the effect of including CMOS sensors in some pixel layers asopposed to the RD53 [15] in all current baseline designs of the ITk. A Monolothic CMOS sensor[62] replaces the sensor and active area of the current silicon chip with a single monolithic CMOSchip. The advantages of this are smaller pixel granularity, thinner charge collection area, and asimpler and possibly cheaper production.The study is thus looking at the effects of changing some of the current RD53 chip [63] pixellayers to CMOS. It is assumed that all properties are the same, such that diffusion and drift ofelectrons in the active area are not affected, other than by the decreased thickness. The resultsshown are in Figure 7.2.Figure 7.2: STEP 1 ITk Layout - Baseline. The y-axis shows the average efficiency to recon-struct the three charged pions from the tau lepton decay, as a function of the truth tautransverse momentum on the x-axis. The baseline layout is shown in black, while theoutermost (red) and two outermost (green) pixel layers are emulate with CMOS sensors.The bottom insert shows the ratio of efficiency over the nominal (black) efficiency.From this figure it can be seen that very little improvement is seen when one or even two layersare converted to CMOS - the maximum being a 1% efficiency gain in intermediate momentumbins. When changing three layers the effect appears to be more pronounced, with a constant 1\u00E2\u0088\u00924%increase in efficiency. However this is a very minimal effect for such a drastic change in detec-88tor design. The reason for the only small improvement is likely to be is because the use of theTIDE Neural Network to identify 2 and 3-particle clusters already compensated for most of theimprovements that could be gained from smaller pixels.To quantify this, the same study is repeated but turning off the TIDE Neural Network for alllayers, shown in Figure 7.3.Figure 7.3: STEP 1 ITk Layout - the truth TIDE Neural Network splitting has been turnedoff for all pixel layers. The y-axis shows the average efficiency to reconstruct the threecharged pions from the tau lepton decay, as a function of the truth tau transverse momen-tum on the x-axis. The baseline layout is shown in black, while the outermost (red) andtwo outermost (green) pixel layers are emulate with CMOS sensors. The bottom insertshows the ratio of efficiency over the nominal (black) efficiency.The effect seen here is more pronounced - the efficiency drops extremely rapidly with increasingtau lepton transverse momentum, while the relative effect of the CMOS pixel geometry increasesdrastically. However, since the increase in efficiency due to CMOS sensors is only relatively highdue to the huge drop in efficiency with momentum, it does not recapture the loss due to the turningoff of the Neural Network. This suggests that, at higher momentum, a large fraction of lost effi-ciency is due to tracks depositing energy in overlapping patterns, which is difficult to solve usingsmaller detector elements. Thus the effect of CMOS on track reconstruction efficiency in dense en-vironments is much smaller than would be expected given the drastic change in size of the detectorelement.One downside of a CMOS sensor is the challenge of including Time-over-Threshold (ToT)readout, meaning that the particle Neural Network implemented may not be possible to apply.89Thus, the most realistic scenario for a CMOS sensor in the ATLAS upgrade would be the last twolayers without a Neural Network but with CMOS sensors - this is shown in Figure 7.4. From theprevious study with no Neural Network it is clear that some efficiency is lost - this study will thustest how much efficiency can be recovered from the use of CMOS sensors in pixel layers with noToT information.Figure 7.4: STEP 1 ITk Layout - Baseline. The y-axis shows the average efficiency to recon-struct the three charged pions from the tau lepton decay, as a function of the truth tautransverse momentum on the x-axis. The baseline layout is shown in black, with thesame baseline with TIDE NN turned off in last two pixel layers in red, with NN turnedoff and CMOS in last pixel layer in green, and finally NN turned off and CMOS in lasttwo pixel layers in blue. The bottom insert shows the ratio of efficiency over the nominal(black) efficiency.The baseline here is the normal layout with all pixel layers including a Neural Network; the restof the data sets have the Neural Network for the last two layers turned off to simulate the lack oftime-over-threshold information. As can be seen, at about 1 TeV tau is when the efficiency startsto drop due to the lack of the split hits. Some recovery of efficiency can be regained with CMOSdimensions in those layers but this does not recover it completely.7.1.3 Strip LengthThe next study using TIDETester was investigating the effect of strip length on track reconstructionin dense environments. The strip length is the long axis of the strips, and in the baseline layout is23.82 mm for the first two layers, and 47.64 mm in the last two strip layers. The two extreme sce-90narios are considered (all 23.82 or all 47.64) and compared to nominal - this is shown in Figure 7.5.Figure 7.5: STEP 1 ITk Layout - Baseline. The y-axis shows the average efficiency to recon-struct the three charged pions from the tau lepton decay, as a function of the truth tautransverse momentum on the x-axis. The baseline geometry is in black, while largeststrip lengths (47.64 mm) in all layers is in red, and shortest strip length (23.82 mm) ingreen. The bottom insert shows the ratio of efficiency over the nominal (black) efficiency.The results are unambiguous - there is less than a 0.2% change from the baseline across thewhole transverse momentum spectrum. Any deviation is more likely to be due to statistical fluctu-ation than to a real effect. This shows that, due to the very large size of the strips in the z-direction,there will be no impact on dense environment performance unless changed to a very small size -the change of strips to pixels has already been investigated for the LOI in Section 7.1.1 and will beinvestigated for newer layouts in Section 7.1.4.7.1.4 Converting Strips to PixelsAn idea with some traction in the strip community is to replace the first or first two strip layerswith pixels similar to the ones used in the current pixel detector (non-IBL), measuring 50\u00C3\u0097400 \u00C2\u00B5min the R-Z plane. They would be relatively easy to produce given the experience from the currentATLAS detector and could give increased resolution in the z axis of the detector.A study was thus done to quantify the effect of this change on dense environment track recon-struction. Material effects were outside the scope of this study, as pixels generally require morematerial than strips; however, a good estimate can be made using a change of geometry only. Theresults are shown in Figure 7.6.91Figure 7.6: STEP 1 ITk Layout - Baseline. The y-axis shows the average efficiency to recon-struct the three charged pions from the tau lepton decay, as a function of the truth tautransverse momentum on the x-axis. The baseline geometry is in black, while the firststrip layer is changed to a 50\u00C3\u0097400 \u00C2\u00B5m pixel in the red data, and the first two strip layersare changed to a 50\u00C3\u0097400 \u00C2\u00B5m pixel in the green data. The bottom insert shows the ratioof efficiency over the nominal (black) efficiency.The results show a drastic improvement - about 3\u00E2\u0088\u0092 4% increase throughout most of the mo-mentum range when modifying the first strip layer, and 6\u00E2\u0088\u009210% increase in efficiency for most ofthe range when modifying the first two strip layers. Thus, as with the switch from 4 pixel and 5strip layers to 5 pixels and 4 strip layers, a switch to include more pixel layers would be beneficialto reconstruction of dense environments.7.1.5 Pixel SizeAnother point of discussion the size of the pixels for the ITk. Most simulations use a pixel size of50\u00C3\u0097 50 \u00C2\u00B5m, but a 25\u00C3\u0097 100 \u00C2\u00B5m pixel, in the R-Z direction, is also being considered. This wouldallow for better resolution in the transverse plane, which is most important for track reconstruction.The results of this study are shown in in Figure 7.7, with a 100\u00C3\u009725\u00C2\u00B5m option in the R-z directionincluded for comparison purposes.92Figure 7.7: STEP 1 ITk Layout - Baseline. The y-axis shows the average efficiency to recon-struct the three charged pions from the tau lepton decay, as a function of the truth tautransverse momentum on the x-axis. The baseline geometry is in black, while in red arepixel dimensions 25\u00C3\u0097100 \u00C2\u00B5m, and in green pixel dimensions 100\u00C3\u009725\u00C2\u00B5m. The bottominsert shows the ratio of efficiency over the nominal (black) efficiency.The results show that changing pixel sizes from the current default to 25\u00C3\u0097100\u00C2\u00B5m pixel in theR-Z direction has very little effect on track reconstruction in dense environments. However, theother study, with the directions reversed, has the effect of a drastic reduction in efficiency. To betterunderstand this, the efficiency was also plotted as a function of \u00CE\u00B7 in Figure 7.8.93Figure 7.8: STEP 1 ITk Layout - Baseline. This plot is binned in \u00CE\u00B7 to show the discrepancy inbehaviour between the two tested pixel sizes. The baseline geometry is in black, whilein red are pixel dimensions 25\u00C3\u0097 100 \u00C2\u00B5m, and in green pixel dimensions 100\u00C3\u0097 25\u00C2\u00B5m.The bottom insert shows the ratio of efficiency over the nominal (black) efficiency.This plot showing the efficiency behaviour with \u00CE\u00B7 implies that a larger absolute value of \u00CE\u00B7corresponds to the drop in efficiency for the 100\u00C3\u0097 25 scenario, but not for the 25\u00C3\u0097 100. As \u00CE\u00B7grows, in the central barrel region, the size of clusters grow as tracks go through a larger amountof active area through each layer. These results clearly support either the 50\u00C3\u009750 or 25\u00C3\u0097100 \u00C2\u00B5mpixels for the ITk.7.1.6 Pixel DistanceThe radial distance of each layer should also be considered when designing a tracking detector fodense environments. The further out in radius a layer is, the more separation between neighbouringtracks simply from geometry. In an ideal detector for resolving individual tracks, each layer wouldbe as far as possible from the interaction point to separate each charged particle. However, otherconsiderations, such as momentum and vertex reconstruction require measurements as close to thebeam pipe as possible. Within these constraints a study of changes to both pixel and strip barrel layerdistance from the beam pipe is a good way to optimise a detector for dense environments. In thissection we present the results of studying pixel distance effects on track reconstruction efficiency -for a broad overview of distance\u00E2\u0080\u0099s effect, Figure 7.9 shows all pixel layers being moved outwardsby the same fixed amount.94Figure 7.9: STEP 1 ITk Layout - Baseline. The y-axis shows the average efficiency to re-construct the three charged pions from the tau lepton decay, as a function of the truthtau transverse momentum on the x-axis. The baseline geometry is in black, while datapoints in red move each pixel layer 20mm radially from the beam pipe, in green 40mm,blue 60mm and brown 80mm. The bottom insert shows the ratio of efficiency over thenominal (black) efficiency.The results here clearly show a turn-on curve until about 600 GeV in tau pT . After this, alltau momentum bins show a very constant efficiency increase between 4 and 6 %. This is rathersignificant, though the negative impact on kinematic variable resolution would undoubtedly be toogreat for this option to be considered. Another major point to note is the lack of a difference betweenmovement of 20mm to 80mm - from the plot there is completely diminishing returns after about40mm. Even moving further seems to impact the efficiency less at high momentum - this may bedue to angular effects, such as longer clusters being formed at higher radius, which begin being thelimiting factor at this distance.The next study is thus to study the impact of movement of the first two layers, which are themost important for studies of the kinematic variables discussed earlier. We will thus study theimpact of moving both towards the beam pipe and away to gauge the effect on dense environmenttrack reconstruction - this is shown in Figure 7.10.95Figure 7.10: STEP 1 ITk Layout - Baseline. The y-axis shows the average efficiency to re-construct the three charged pions from the tau lepton decay, as a function of the truthtau transverse momentum on the x-axis. The baseline geometry is in black, while datapoints in red move the first two pixel layers 5mm away radially from the beam pipe,in green 10mm away, blue 5mm towards the beam pipe and brown 10mm towards thebeam pipe. The bottom insert shows the ratio of efficiency over the nominal (black)efficiency.There are quite a few interesting features to this plot. The first is the small effect of movingeach layer back - no more than 1% for 5mm, and no more than 2% for 10mm. Since this is an effectseen through the momentum range it can be quite significant. Second, when layers are movedtowards the beam pipe, a pronounced effect is seen but peaking at about 500 GeV in tau pT , andnot constant throughout the range. This can be explained by the fact that tracks which will gofrom sharing hits to being separate clusters when changing the first layer do not have shared hitsin subsequent layers, and thus will be at lower momentum. This is why the effect is very small athigh momentum. However, the effect is quite pronounced; between 200 and 1000 GeV where theefficiency is lowered by 3-5%, this decrease will have to be weighed against any improvement inprimary vertex and b-tagging performance from this change in layout.Finally, we can study the performance when moving the last three pixel layers, as shown inFigure 7.11.96Figure 7.11: STEP 1 ITk Layout - Baseline. The y-axis shows the average efficiency to re-construct the three charged pions from the tau lepton decay, as a function of the truthtau transverse momentum on the x-axis. The baseline geometry is in black, while datapoints in red move the last three pixel layers 10mm radially towards from the beampipe, in green 10mm away, blue 20mm and brown 30mm away. The bottom insertshows the ratio of efficiency over the nominal (black) efficiency.Here the negligible effects at low momentum is apparent, as well as the very minimal effectabove 1 TeV tau pT , which is around 2%. However, this would also indicate that moving the lastthree layers towards the beam pipe has little effect on dense environment track reconstruction, whichcould be used to increase precision on kinematic variables by moving them towards the interactionpoint.7.1.7 Strip DistanceThe strips can also be studied for the effect of their radial position on track reconstruction efficiencyin dense environments. In contrast to the pixels, being at a much higher radius means that movingstrip layers will have an impact mostly on high momentum tau decays. Furthermore, the last striplayer, being at 1m from the interaction point right inside the magnet cryostat, cannot be moved to ahigher radius. Thus, we will study the effect of moving the first three strip layers towards and awayfrom the beam pipe, as shown in Figure 7.12.97Figure 7.12: STEP 1 ITk Layout - Baseline. The y-axis shows the average efficiency to re-construct the three charged pions from the tau lepton decay, as a function of the truthtau transverse momentum on the x-axis. The baseline geometry is in black, while datapoints in red move the first three strips layers 50mm radially away from the beam pipe,in green 100mm away, blue 50mm towards the beam pipe and brown 100mm towards.The bottom insert shows the ratio of efficiency over the nominal (black) efficiency.This figure shows a rather symmetric looking effect, with a move of 50mm towards or awaygives a roughly 5% decrease or increase in efficiency respectively, at tau pT around 1 TeV. For100mm move, the effect can go up to 15% at very high momentum, but is generally within the5-10% range above 1 TeV. It is likely not to be worth the efficiency drop to move strips closer,as any effect this would have on kinematic variable resolution would be very low - however, therather large effect of moving layers away from the beam pipe is encouraging, and warrants furtherinvestigation.98Chapter 8ConclusionsAn emulation method was created to study different tracker layouts for the ATLAS ITk Upgradein 2024. The response of active silicon areas in both pixels and strips was modelled using bandgap theory and electromagnetic principles to approximate the passage of charged particles throughthe detector elements of a tracker. Then, electron diffusion was modelled using data from ATLASITk simulation and energy deposit widths were tuned such that emulation of each detector layergave results congruent with full simulation. Finally, geometrical arguments were used to optimisethe separation distance needed, in each detector axis, for multiple charged particles to leave oneshared cluster or individual clusters in a detector layer. This emulation allows for a tracker of anydetector element size, thickness or distance from the interaction point to be studied in the context ofdense environments - meaning that the valid tracks output from track creation will be the result ofthe emulated geometry. The emulation results are propagated through the full ATLAS simulationchain in order to give a precise estimate of the performance of the track reconstruction in denseenvironments for the many ITk layout changes being considered.This emulation was validated using both cluster data and track data. First, the amount of sharedclusters between full simulation and emulation were shown to be equal within uncertainty across alllayers. Second, the number of tracks output was shown to be consistent within 5% across the wholerange of tau lepton transverse momentum studied, a great accuracy given the multiple challenges ofparticle interaction emulation.When emulating smaller, thinner CMOS pixels, it was found that only minimal gains wereobtained due to the TIDE Neural Network drowning out any improvements due to smaller pixelsby identifying which clusters were shared. As such, when modifying the last three pixel layers withCMOS the relative change in efficiency was around 2%, but when turning off the Neural Networkthis relative increase was up to 60%, though never gaining back the efficiency lost with the NeuralNetwork off. It was also found that CMOS sensors in the last two pixel layers could make up aroundhalf of the relative efficiency lost at high momentum (from 0.87 to 0.93 of baseline efficiency) ifthe Neural Network was turned off in those same layers, which is a realistic scenario.When studying the change of strip length, which is the long z-axis of the strip detectors, itwas found that regardless of the distribution, whether all strip lengths are 23.82 or 47.64 mm, the99efficiency was consistent within uncertainty. Thus it can be concluded that strip lengths decisionsbetween 23.82 or 47.64 mm do not affect the dense environment performance in ITk.Converting the first two strip layers to Run 2-size pixels was also studied, pixel size being50\u00C3\u0097400 \u00C2\u00B5m in the R-Z axes respectively. It was found that changing the first strip layer led to 4%increase in efficiency in a large range of tau momentum, and the first two strip layers to an 8-10%increase for much of the tau momentum range. Thus it can be concluded that changing strips topixels has a large and positive impact on TIDE performance in ITk.Investigating the impact of pixel size on track reconstruction efficiency in dense environmentsfound that there is no difference in efficiency between 50\u00C3\u0097 50 \u00C2\u00B5m or 25\u00C3\u0097 100 \u00C2\u00B5m in the R-Zaxes. The 100\u00C3\u009725 \u00C2\u00B5m pixel geometry performed worse by about 5% above 1 TeV tau transversemomentum, but is not being considered for ITk Layouts.Studying the distance of pixel layers led to the conclusion that moving the first two layersforward by either 5 or 10 mm would lead to a rather large decrease in efficiency at low momentum,peaking at a 2% decrease for the 5mm and 5% decrease for the 10mm at around 600 GeV taumomentum. The impact on kinematic variable resolution would have to be considered along withthe loss of efficiency to make a decision on whether this loss of tracks is acceptable. For the lastthree layers, it was found that movement did not have much effect on the reconstruction efficiency.Finally, for strip distance studies, it was found that a 5-10% increase in efficiency can be gainedwhen moving the first three strip layers 100 mm away from the beam pipe, while moving the samedistance away would yield a 10-15% decrease in the same momentum range. Because of this, itcan be concluded that moving forward would have negative impact as the very probable minimalincrease in kinematic precision due to the distance from the vertex would lead to a large drop inefficiency in high momentum particle decays. Moving the layers back would be beneficial to theefficiency but would have to be investigated with respect to the actual space in the barrel, alreadybeing filled with material and services to the layers being built.100Bibliography[1] A. Purcell, Go on a particle quest at the first CERN webfest. Le premier webfest du CERN selance a` la conque\u00CB\u0086te des particules, https://cds.cern.ch/record/1473657. \u00E2\u0086\u0092 pages viii, 4[2] S. Baird, Accelerators for pedestrians; rev. version, Tech. Rep. AB-Note-2007-014.CERN-AB-Note-2007-014. PS-OP-Note-95-17-Rev-2. CERN-PS-OP-Note-95-17-Rev-2,CERN, Geneva, Feb, 2007. https://cds.cern.ch/record/1017689. \u00E2\u0086\u0092 pages viii, 8, 9[3] G. Apollinari, I. Bjar Alonso, O. Brning, M. Lamont, and L. Rossi, High-Luminosity LargeHadron Collider (HL-LHC): Preliminary Design Report. CERN, Geneva, 2015.https://cds.cern.ch/record/2116337. \u00E2\u0086\u0092 pages viii, 13[4] ATLAS Collaboration, The ATLAS Data Flow System for LHC Run II, Tech. Rep.ATL-DAQ-PROC-2015-064, CERN, Geneva, Dec, 2015.https://cds.cern.ch/record/2112127. \u00E2\u0086\u0092 pages ix, 18[5] ATLAS Collaboration, ATLAS liquid-argon calorimeter: Technical Design Report. TechnicalDesign Report ATLAS. CERN, Geneva, 1996. https://cds.cern.ch/record/331061. \u00E2\u0086\u0092 pagesix, 17, 21[6] C. W. Fabjan and F. Gianotti, Calorimetry for particle physics, Rev. Mod. Phys. 75 (2003)1243\u00E2\u0080\u00931286, http://link.aps.org/doi/10.1103/RevModPhys.75.1243. \u00E2\u0086\u0092 pages ix, 22[7] ATLAS Collaboration, ATLAS tile calorimeter: Technical Design Report. Technical DesignReport ATLAS. CERN, Geneva, 1996. https://cds.cern.ch/record/331062. \u00E2\u0086\u0092 pages ix, 17,23[8] ATLAS Collaboration, ATLAS muon spectrometer: Technical Design Report. TechnicalDesign Report ATLAS. CERN, Geneva, 1997. https://cds.cern.ch/record/331068. \u00E2\u0086\u0092 pagesix, 17, 25, 26[9] ATLAS Collaboration, The ATLAS Experiment at the CERN Large Hadron Collider, J.Instrum. 3 (2008) S08003. 437 p, https://cds.cern.ch/record/1129811, Also published byCERN Geneva in 2010. \u00E2\u0086\u0092 pages x, 15, 18, 28[10] ATLAS Collaboration, The ATLAS Pixel Insertable B-Layer (IBL), Tech. Rep.ATL-INDET-PROC-2010-034, CERN, Geneva, Oct, 2010.https://cds.cern.ch/record/1303015. \u00E2\u0086\u0092 pages x, 29[11] ATLAS Collaboration, Measurement of Lorentz angle and depletion depth in the ATLASPixel Detector with cosmic rays data, Tech. Rep. ATL-COM-INDET-2010-041, CERN,Geneva, Mar, 2010. https://cds.cern.ch/record/1248606. \u00E2\u0086\u0092 pages x, 31, 66101[12] D. A. Dobos, C. Gossling, and R. Klingenberg, Commissioning Perspectives for the ATLASPixel Detector. PhD thesis, Dortmund U., Dortmund, 2007.https://cds.cern.ch/record/1092108. Presented on 1 Sep 2007. \u00E2\u0086\u0092 pages x, 32[13] ATLAS Collaboration, ATLAS pixel detector electronics and sensors, Journal ofInstrumentation 3 (2008) P07007. \u00E2\u0086\u0092 pages x, 32, 33[14] T. G. Cornelissen, P. F. van der Heijden, F. L. Linde, S. C. M. Bentvelsen, and P. M. Kluit,Track Fitting in the ATLAS Experiment. PhD thesis, U. Amsterdam, Amsterdam, 2006.https://cds.cern.ch/record/1005181. Presented on 12 Dec 2006. \u00E2\u0086\u0092 pages x, 34, 35[15] ATLAS Collaboration, ATLAS Phase-II Upgrade Scoping Document, Tech. Rep.CERN-LHCC-2015-020. LHCC-G-166, CERN, Geneva, Sep, 2015.https://cds.cern.ch/record/2055248. \u00E2\u0086\u0092 pages xi, 12, 38, 88[16] ATLAS Collaboration, The ATLAS simulation infrastructure, The European Physical JournalC 70 (2010) 823\u00E2\u0080\u0093874. \u00E2\u0086\u0092 pages xi, 41, 64[17] A. Rosenfeld and J. A. Ofaltz, Sequential operations in digital picture processing, Journal ofthe ACM (JACM) 13 (1966) 471\u00E2\u0080\u0093494. \u00E2\u0086\u0092 pages xi, 43[18] ATLAS Collaboration, Performance of the ATLAS Silicon Pattern Recognition Algorithm inData and Simulation at\u00E2\u0088\u009As = 7 TeV, Tech. Rep. ATLAS-CONF-2010-072, CERN, Geneva,Jul, 2010. https://cds.cern.ch/record/1281363. \u00E2\u0086\u0092 pages xi, 43, 44, 46, 55[19] H. M. Gray and E. W. Hughes, The Charged Particle Multiplicity at Center of Mass Energiesfrom 900 GeV to 7 TeV measured with the ATLAS Experiment at the Large Hadron Collider.PhD thesis, Pasadena, USA, California Institute of Technology, Pasadena, USA, 2010.https://cds.cern.ch/record/1309943. Presented on 09 Nov 2010. \u00E2\u0086\u0092 pages xi, 45[20] M. Limper, S. Bentvelsen, and A. P. Colijn, Track and vertex reconstruction in the ATLASinner detector. PhD thesis, Amsterdam U., Amsterdam, 2009.https://cds.cern.ch/record/1202457. Presented on 12 Oct 2009. \u00E2\u0086\u0092 pages xi, 45, 46[21] ATLAS Collaboration, Concepts, Design and Implementation of the ATLAS New Tracking(NEWT), Tech. Rep. ATL-SOFT-PUB-2007-007. ATL-COM-SOFT-2007-002, CERN,Geneva, Mar, 2007. https://cds.cern.ch/record/1020106. \u00E2\u0086\u0092 pages xi, 42, 46, 55[22] ATLAS Collaboration, The Track Extrapolation Package, Tech. Rep.ATL-SOFT-PUB-2007-005. ATL-COM-SOFT-2007-010, CERN, Geneva, Jun, 2007.https://cds.cern.ch/record/1038100. \u00E2\u0086\u0092 pages xi, xii, 47, 48, 49, 51, 52, 53[23] E. Lund, L. Bugge, I. Gavrilenko, and A. Strandlie, Track parameter propagation through theapplication of a new adaptive Runge-Kutta-Nystro\u00C2\u00A8m method in the ATLAS experiment,Journal of Instrumentation 4 (2009) P04001. \u00E2\u0086\u0092 pages xii, 50[24] ATLAS Collaboration, A neural network clustering algorithm for the ATLAS silicon pixeldetector, J. Instrum. 9 (2014) P09009. 38 p, https://cds.cern.ch/record/1712337. \u00E2\u0086\u0092 pagesxii, 57, 58[25] ATLAS Collaboration, The Optimization of ATLAS Track Reconstruction in DenseEnvironments, Tech. Rep. ATL-PHYS-PUB-2015-006, CERN, Geneva, Mar, 2015.https://cds.cern.ch/record/2002609. \u00E2\u0086\u0092 pages xii, xiii, 59, 60, 61102[26] ATLAS Collaboration, Observation of a new particle in the search for the Standard ModelHiggs boson with the ATLAS detector at the LHC, Physics Letters B 716 (2012) 1\u00E2\u0080\u009329. \u00E2\u0086\u0092pages 4[27] D. J. Griffiths, Introduction to Elementary Particles. John Wiley and Sons, Inc., 1987. \u00E2\u0086\u0092pages 4, 5[28] M. Peskin and D. Schroeder, An introduction to quantum field theory. Addison-Wesley,1995. \u00E2\u0086\u0092 pages 5[29] T. Sjo\u00C2\u00A8strand, S. Mrenna, and P. Skands, A brief introduction to PYTHIA 8.1, ComputerPhysics Communications 178 (2008) 852\u00E2\u0080\u0093867. \u00E2\u0086\u0092 pages 5[30] G. Corcella, I. G. Knowles, G. Marchesini, S. Moretti, K. Odagiri, P. Richardson, M. H.Seymour, and B. R. Webber, HERWIG 6: an event generator for hadron emission reactionswith interfering gluons (including supersymmetric processes), Journal of High EnergyPhysics 2001 (2001) 010. \u00E2\u0086\u0092 pages 5[31] S. Frixione, P. Nason, and C. Oleari, Matching NLO QCD computations with Parton Showersimulations: the POWHEG method, Journal of High Energy Physics 2007 (2007) 070. \u00E2\u0086\u0092pages 5[32] T. Gleisberg, S. Ho\u00C2\u00A8che, F. Krauss, M. Scho\u00C2\u00A8nherr, S. Schumann, F. Siegert, and J. Winter,Event generation with SHERPA 1.1, Journal of High Energy Physics 2009 (2009) 007. \u00E2\u0086\u0092pages 5[33] J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer, and T. Stelzer, MadGraph 5: going beyond,Journal of High Energy Physics 2011 (2011) 1\u00E2\u0080\u009340. \u00E2\u0086\u0092 pages 5[34] J. D. Bjorken and E. A. Paschos, Inelastic electron-proton and \u00CE\u00B3-proton scattering and thestructure of the nucleon, Physical Review 185 (1969) 1975. \u00E2\u0086\u0092 pages 6[35] J. C. Collins and D. E. Soper, Parton distribution and decay functions, Nuclear Physics B194 (1982) 445\u00E2\u0080\u0093492. \u00E2\u0086\u0092 pages 6[36] O. Brunner, H. Frischholz, and D. Valuch, RF power generation in LHC, tech. rep., 2003. \u00E2\u0086\u0092pages 7[37] A. W. Chao, K. H. Mess, M. Tigner, and F. Zimmermann, Handbook of accelerator physicsand engineering. World scientific, 2013. \u00E2\u0086\u0092 pages 8[38] E. J. N. Wilson, Proton-synchrotron accelerator theory, tech. rep., Geneva, 1975. CERN,Geneva, 1975 - 1976. \u00E2\u0086\u0092 pages 8[39] L. Evans and P. Bryant, LHC machine, Journal of Instrumentation 3 (2008) S08001. \u00E2\u0086\u0092 pages9[40] J. P. Blewett, 200 GeV intersecting storage accelerators, in Proceedings of the 8thinternational conference on high-energy accelerators, vol. 28. 1971. \u00E2\u0086\u0092 pages 11[41] O. S. Brning, P. Collier, P. Lebrun, S. Myers, R. Ostojic, J. Poole, and P. Proudlock, LHCDesign Report. CERN, Geneva, 2004. https://cds.cern.ch/record/815187. \u00E2\u0086\u0092 pages 12103[42] L. Rossi, LHC Upgrade Plans: Options and Strategy, https://cds.cern.ch/record/1407911.\u00E2\u0086\u0092 pages 12[43] ATLAS Collaboration, Projections for measurements of Higgs boson signal strengths andcoupling parameters with the ATLAS detector at a HL-LHC, Tech. Rep.ATL-PHYS-PUB-2014-016, CERN, Geneva, Oct, 2014. https://cds.cern.ch/record/1956710.\u00E2\u0086\u0092 pages 12[44] ATLAS Collaboration, Studies of Vector Boson Scattering And Triboson Production with anUpgraded ATLAS Detector at a High-Luminosity LHC, Tech. Rep.ATL-PHYS-PUB-2013-006, CERN, Geneva, Jun, 2013. https://cds.cern.ch/record/1558703.\u00E2\u0086\u0092 pages 12[45] ATLAS Collaboration, Prospect for a search for direct pair production of a chargino and aneutralino decaying via a W boson and the lightest Higgs boson in final states with onelepton, two b-jets and missing transverse momentum at the high luminosity LHC with theATLAS Detector., Tech. Rep. ATL-PHYS-PUB-2015-032, CERN, Geneva, Jul, 2015.https://cds.cern.ch/record/2038565. \u00E2\u0086\u0092 pages 12[46] ATLAS Collaboration, ATLAS inner detector: Technical Design Report, 1. Technical DesignReport ATLAS. CERN, Geneva, 1997. https://cds.cern.ch/record/331063. \u00E2\u0086\u0092 pages 17, 52[47] B. Vachon, TRISEP Summer School Particle Detection Methods, , 2016. \u00E2\u0086\u0092 pages 20, 23[48] ATLAS Collaboration, The silicon microstrip sensors of the ATLAS semiconductor tracker,Nuclear Instruments and Methods in Physics Research Section A: Accelerators,Spectrometers, Detectors and Associated Equipment 578 (2007) 98\u00E2\u0080\u0093118. \u00E2\u0086\u0092 pages 33[49] A. Collaboration, TRT performance in Run 1, Tech. Rep. ATL-COM-INDET-2015-041,CERN, Geneva, Jun, 2015. https://cds.cern.ch/record/2021497. \u00E2\u0086\u0092 pages 35[50] ATLAS Collaboration, Letter of Intent for the Phase-II Upgrade of the ATLAS Experiment,Tech. Rep. CERN-LHCC-2012-022. LHCC-I-023, CERN, Geneva, Dec, 2012.https://cds.cern.ch/record/1502664. \u00E2\u0086\u0092 pages 36[51] A. Salzburger, Fermilab-CERN Hadron Collider Physics Summer School Tracking Lectures, ,2014. \u00E2\u0086\u0092 pages 42[52] A. Salzburger, S. Todorova, and M. Wolter, The ATLAS Tracking Geometry Description,Tech. Rep. ATL-SOFT-PUB-2007-004. ATL-COM-SOFT-2007-009, CERN, Geneva, Jun,2007. https://cds.cern.ch/record/1038098. \u00E2\u0086\u0092 pages 43[53] I. Gavrilenko, XKALMAN algorithm description, ATLAS note (1996). \u00E2\u0086\u0092 pages 47, 52[54] ATLAS Collaboration, Treatment of energy loss and multiple scattering in the context oftrack parameter and covariance matrix propagation in continuous material in the ATLASexperiment, Tech. Rep. ATL-SOFT-PUB-2008-003. ATL-COM-SOFT-2008-008, CERN,Geneva, Jul, 2008. https://cds.cern.ch/record/1114577. \u00E2\u0086\u0092 pages 50[55] R. Fru\u00C2\u00A8hwirth, Application of Kalman filtering to track and vertex fitting, Nuclear Instrumentsand Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors andAssociated Equipment 262 (1987) 444\u00E2\u0080\u0093450. \u00E2\u0086\u0092 pages 52104[56] R. Mankel, Pattern recognition and event reconstruction in particle physics experiments,Reports on Progress in Physics 67 (2004) 553. \u00E2\u0086\u0092 pages 53[57] D. Wicke, A new algorithm for solving tracking ambiguities, DELPHI 236 (1998) 98\u00E2\u0080\u0093163.\u00E2\u0086\u0092 pages 55[58] ATLAS Collaboration, Robustness of the Artificial Neural Networks Used for Clustering inthe ATLAS Pixel Detector, Tech. Rep. ATL-PHYS-PUB-2015-052, CERN, Geneva, Dec,2015. https://cds.cern.ch/record/2116350. \u00E2\u0086\u0092 pages 59[59] A. Collaboration, Search for high-mass new phenomena in the dilepton final state usingprotonproton collisions at with the {ATLAS} detector, Physics Letters B 761 (2016) 372 \u00E2\u0080\u0093392. \u00E2\u0086\u0092 pages 63[60] S. Wolfram, Mathematica: a system for doing mathematics by computer. Addison WesleyLongman Publishing Co., Inc., 1991. \u00E2\u0086\u0092 pages 75[61] R. A. Johnson, D. W. Wichern, et al., Applied multivariate statistical analysis, vol. 5.Prentice hall Upper Saddle River, NJ, 2002. \u00E2\u0086\u0092 pages 86[62] I. Peric, Active pixel sensors in high-voltage CMOS technologies for ATLAS, Journal ofInstrumentation 7 (2012) C08002. \u00E2\u0086\u0092 pages 88[63] M. Garcia-Sciveres, A. Mekkaoui, and D. Ganani, Towards third generation pixel readoutchips, Nuclear Instruments and Methods in Physics Research Section A: Accelerators,Spectrometers, Detectors and Associated Equipment 731 (2013) 83\u00E2\u0080\u009387. \u00E2\u0086\u0092 pages 88105Appendix ASupporting MaterialsA.1 Diffusion Width Angle DerivationFigure A.1 will be used as reference for the derivation. This shows the derivation for one quadrant,projected onto the x-y axis of the detector - for other quadrants the calculations will be identical.Two assumptions are made: first that if a track strikes the active area of the silicon at the lorentzangle, the electron diffusion will be at equal angles on either side of the track; second that theelectron diffusion angle does not depend on incidence angle of the track.Figure A.1: Diagram with necessary labels to carry out the derivation of angle of electron dif-fusion in silicon. The track, in red, traverses at the Lorentz Angle, leaving a measurableenergy deposit width l. Thickness t is known, as well as the Lorentz angle. Trianglelengths a and b are unknown but will be used in the derivation; \u00CE\u00B8D is the wanted variable.First start with an equation for diffusion width angle, \u00CE\u00B8D, in terms of a, b and l, of which l canbe measured but a and b are temporary, using the elementary cosine law:cos(2\u00CE\u00B8D) =a2+b2\u00E2\u0088\u0092 l22ab. (A.1)Then using right-angle trigonometry:106a =tcos(\u00CE\u00B8L\u00E2\u0088\u0092\u00CE\u00B8D , (A.2)b =tcos(\u00CE\u00B8L+\u00CE\u00B8D, (A.3)and thus Equation A.1 has the electron diffusion width term, in a cosine, in both the left andright hand side of the equation. Using mathematica, as shown in Figure A.2, to solve this:Figure A.2: Result of solving the equations of this section with mathematica.The final result is\u00CE\u00B8D = cos\u00E2\u0088\u00921\u00EF\u00A3\u00AB\u00EF\u00A3\u00AC\u00EF\u00A3\u00AC\u00EF\u00A3\u00AD\u00E2\u0088\u0092\u00E2\u0088\u009A(l2 sin2(\u00CE\u00B8L)(l2+4t2) \u00E2\u0088\u0092(l2 cos2(\u00CE\u00B8L))(l2+4t2) +(\u00E2\u0088\u009A2\u00E2\u0088\u009A\u00E2\u0088\u0092t2(l2cos(4\u00CE\u00B8L)\u00E2\u0088\u0092l2\u00E2\u0088\u00928t2))(l2+4t2) +l2(l2+4t2)+(4t2)(l2+4t2))\u00E2\u0088\u009A2\u00EF\u00A3\u00B6\u00EF\u00A3\u00B7\u00EF\u00A3\u00B7\u00EF\u00A3\u00B8 . (A.4)107"@en . "Thesis/Dissertation"@en . "2017-02"@en . "10.14288/1.0340666"@en . "eng"@en . "Physics"@en . "Vancouver : University of British Columbia Library"@en . "University of British Columbia"@en . "Attribution-NonCommercial-NoDerivatives 4.0 International"@* . "http://creativecommons.org/licenses/by-nc-nd/4.0/"@* . "Graduate"@en . "Simulating the next generation of the ATLAS inner detector : tracking in dense environments"@en . "Text"@en . "http://hdl.handle.net/2429/60267"@en .