# A high-granularity timing detector for the ATLAS phase-II upgrade

M.P. Casado, C. Adam Bourdarios, M. Belfkir, N. Berger, F. Costanza, A.

Cueto, M. Delmastro, L. Di Ciaccio, L. Franco, C. Goy, et al.

► To cite this version:

M.P. Casado, C. Adam Bourdarios, M. Belfkir, N. Berger, F. Costanza, et al. A high-granularity timing detector for the ATLAS phase-II upgrade: Technical design report. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2022, 1032, pp.166628. 10.1016/j.nima.2022.166628. hal-03978531

HAL Id: hal-03978531

https://hal.science/hal-03978531

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ATLAS-TDR-031 · LHCC-2020-007

# ATLAS
A High-Granularity Timing Detector
for the ATLAS Phase-II Upgrade

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Technical Design Report
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# Technical Design Report:
A High-Granularity Timing Detector for the
ATLAS Phase-II Upgrade

Reference: CERN-LHCC-2020-007
ATLAS-TDR-031

Created: 27th July 2020

Last modified: 27th July 2020

Prepared by: The ATLAS Collaboration

© 2020 CERN for the benefit of the ATLAS Collaboration.

Reproduction of this article or parts of it is allowed as specified in the CC-BY-4.0 license.
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Abstract

The large increase of pileup interactions is one of the main experimental
challenges for the HL-LHC physics programme. A powerful new way to
mitigate the effects of pileup is to use high-precision timing information to
distinguish between collisions occurring close in space but well-separated in
time. A High-Granularity Timing Detector, based on low gain avalanche
detector technology, is therefore proposed for the ATLAS Phase-II upgrade.
Covering the pseudorapidity region between 2.4 and 4.0, this device will
improve the detector physics performance in the forward region. The typical
number of hits per track in the detector was optimized so that the target average
time resolution per track for a minimum-ionising particle is 30 ps at the start of
lifetime, increasing to 50 ps at the end of HL-LHC operation. The high-precision
timing information improves the pileup reduction to improve the forward object
reconstruction, complementing the capabilities of the upgraded Inner Tracker
(ITk) in the forward regions of ATLAS and leading to an improved performance
for both jet and lepton reconstruction. These improvements in object
reconstruction performance translate into sensitivity gains and enhance the
reach of the ATLAS physics programme at the HL-LHC. In addition, the HGTD
offers unique capabilities for the online and offline luminosity determination, an
important requirement for precision physics measurements.
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# The ATLAS Collaboration

## Argentina

Departamento de Física, Universidad de Buenos Aires, Buenos Aires, Argentina
Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata, Argentina

## Australia

Department of Physics, University of Adelaide, Adelaide, Australia
School of Physics, University of Melbourne, Victoria, Australia
School of Physics, University of Sydney, Sydney, Australia

## Austria

Institut für Astro- und Teilchenphysik, Leopold-Franzens-Universität, Innsbruck, Austria

## Azerbaijan

Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan

## Belarus

B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk, Belarus
Research Institute for Nuclear Problems of Byelorussian State University, Minsk, Belarus

## Brazil

Departamento de Engenharia Elétrica, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil
Universidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro, Brazil
Universidade Federal de São João del Rei (UFSJ), São João del Rei, Brazil
Instituto de Física, Universidade de São Paulo, São Paulo, Brazil

## Canada

Department of Physics, University of Alberta, Edmonton AB, Canada
Department of Physics, Carleton University, Ottawa ON, Canada
Department of Physics, McGill University, Montreal QC, Canada
Group of Particle Physics, University of Montreal, Montreal QC, Canada
Department of Physics, Simon Fraser University, Burnaby BC, Canada
Department of Physics, University of Toronto, Toronto ON, Canada
TRIUMF, Vancouver BC, Canada
Department of Physics and Astronomy, York University, Toronto ON, Canada
Department of Physics, University of British Columbia, Vancouver BC, Canada
Department of Physics and Astronomy, University of Victoria, Victoria BC, Canada

## Chile

Departamento de Física, Pontificia Universidad Católica de Chile, Santiago, Chile
Universidad Andrés Bello, Department of Physics, Santiago, Chile
Instituto de Alta Investigación, Universidad de Tarapacá, Chile
Departamento de Física, Universidad Técnica Federico Santa María, Valparaíso, Chile

## China

Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China

Physics Department, Tsinghua University, Beijing, China

Department of Physics, Nanjing University, Nanjing, China

University of Chinese Academy of Science (UCAS), Beijing, China

Department of Modern Physics and State Key Laboratory of Particle Detection and
Electronics, University of Science and Technology of China, Hefei, China

Institute of Frontier and Interdisciplinary Science and Key Laboratory of Particle Physics
and Particle Irradiation (MOE), Shandong University, Qingdao, China

School of Physics and Astronomy, Shanghai Jiao Tong University, KLPPAC-MoE, SKLPPC,
Shanghai, China

Tsung-Dao Lee Institute, Shanghai, China

Department of Physics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China

Department of Physics, University of Hong Kong, Hong Kong, China

Department of Physics and Institute for Advanced Study, Hong Kong University of Science
and Technology, Clear Water Bay, Kowloon, Hong Kong, China

Nanofabrication Facility, Suzhou Institute of Nano-Tech and Nano-Bionics (SINANO),
Chinese Academy of Sciences, China

## Colombia

Facultad de Ciencias y Centro de Investigaciónes, Universidad Antonio Nariño, Bogotá,
Colombia

Departamento de Física, Universidad Nacional de Colombia, Bogotá, Colombia, Colombia

## Czech Republic

Palacký University, RCPTM, Joint Laboratory of Optics, Olomouc, Czech Republic

Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic

Czech Technical University in Prague, Prague, Czech Republic

Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic

## Denmark

Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

## France

LAPP, Université Grenoble Alpes, Université Savoie Mont Blanc, CNRS/IN2P3, Annecy,
France

LPC, Université Clermont Auvergne, CNRS/IN2P3, Clermont-Ferrand, France

LPSC, Université Grenoble Alpes, CNRS/IN2P3, Grenoble INP, Grenoble, France

IJC Lab, Université Paris-Saclay, CNRS/IN2P3, 91405, Orsay, France

Centre de Calcul de l'Institut National de Physique Nucléaire et de Physique des Particules
(IN2P3), Villeurbanne, France

CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France

LPNHE, Sorbonne Université, Université de Paris, CNRS/IN2P3, Paris, France
IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
OMEGA, Ecole Polytechnique, CNRS, PALAISEAU, France

**Georgia**

E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia
High Energy Physics Institute, Tbilisi State University, Tbilisi, Georgia

**Germany**

Institut für Physik, Humboldt Universität zu Berlin, Berlin, Germany
Physikalisches Institut, Universität Bonn, Bonn, Germany
Deutsches Elektronen-Synchrotron DESY, Hamburg and Zeuthen, Germany
Lehrstuhl für Experimentelle Physik IV, Technische Universität Dortmund, Dortmund, Germany
Institut für Kern- und Teilchenphysik, Technische Universität Dresden, Dresden, Germany
Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany
II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany
II. Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany
Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
Institut für Physik, Universität Mainz, Mainz, Germany
Fakultät für Physik, Ludwig-Maximilians-Universität München, München, Germany
Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), München, Germany
Department Physik, Universität Siegen, Siegen, Germany
Fakultät für Physik und Astronomie, Julius-Maximilians-Universität Würzburg, Würzburg, Germany
Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal, Wuppertal, Germany

**Greece**

Physics Department, National and Kapodistrian University of Athens, Athens, Greece
Physics Department, National Technical University of Athens, Zografou, Greece
National Centre for Scientific Research "Demokritos", Agia Paraskevi, Greece
Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece

**Israel**

Department of Physics, Technion, Israel Institute of Technology, Haifa, Israel
Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel
Department of Particle Physics, Weizmann Institute of Science, Rehovot, Israel

**Italy**

INFN Bologna and Universita' di Bologna, Dipartimento di Fisica, Italy
INFN Sezione di Bologna, Italy
Dipartimento di Fisica, Università della Calabria, Rende, Italy
INFN Gruppo Collegato di Cosenza, Laboratori Nazionali di Frascati, Italy

INFN e Laboratori Nazionali di Frascati, Frascati, Italy

Dipartimento di Fisica, Università di Genova, Genova, Italy

INFN Sezione di Genova, Italy

INFN Gruppo Collegato di Udine, Sezione di Trieste, Udine, Italy

ICTP, Trieste, Italy

Dipartimento Politecnico di Ingegneria e Architettura, Università di Udine, Udine, Italy

INFN Sezione di Lecce, Italy

Dipartimento di Matematica e Fisica, Università del Salento, Lecce, Italy

INFN Sezione di Milano, Italy

Dipartimento di Fisica, Università di Milano, Milano, Italy

INFN Sezione di Napoli, Italy

Dipartimento di Fisica, Università di Napoli, Napoli, Italy

INFN Sezione di Pavia, Italy

Dipartimento di Fisica, Università di Pavia, Pavia, Italy

INFN Sezione di Pisa, Italy

Dipartimento di Fisica E. Fermi, Università di Pisa, Pisa, Italy

INFN Sezione di Roma, Italy

Dipartimento di Fisica, Sapienza Università di Roma, Roma, Italy

INFN Sezione di Roma Tor Vergata, Italy

Dipartimento di Fisica, Università di Roma Tor Vergata, Roma, Italy

INFN Sezione di Roma Tre, Italy

Dipartimento di Matematica e Fisica, Università Roma Tre, Roma, Italy

INFN-TIFPA, Italy

Università degli Studi di Trento, Trento, Italy

## Japan

Faculty of Applied Information Science, Hiroshima Institute of Technology, Hiroshima, Japan

KEK, High Energy Accelerator Research Organization, Tsukuba, Japan

Graduate School of Science, Kobe University, Kobe, Japan

Faculty of Science, Kyoto University, Kyoto, Japan

Kyoto University of Education, Kyoto, Japan

Research Center for Advanced Particle Physics and Department of Physics, Kyushu University, Fukuoka, Japan

Nagasaki Institute of Applied Science, Nagasaki, Japan

Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan

Ochanomizu University, Otsuka, Bunkyo-ku, Tokyo, Japan

Graduate School of Science, Osaka University, Osaka, Japan

Department of Physics, Shinshu University, Nagano, Japan

International Center for Elementary Particle Physics and Department of Physics, University
of Tokyo, Tokyo, Japan

Graduate School of Science and Technology, Tokyo Metropolitan University, Tokyo, Japan

Department of Physics, Tokyo Institute of Technology, Tokyo, Japan

Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure
and Applied Sciences, University of Tsukuba, Tsukuba, Japan

Waseda University, Tokyo, Japan

## Morocco

Faculté des Sciences Ain Chock, Réseau Universitaire de Physique des Hautes Energies -
Université Hassan II, Casablanca, Morocco

Faculté des Sciences, Université Ibn-Tofail, Kénitra, Morocco

Faculté des Sciences Semlalia, Université Cadi Ayyad, LPHEA-Marrakech, Morocco

Faculté des Sciences, Université Mohamed Premier and LPTPM, Oujda, Morocco

Faculté des sciences, Université Mohammed V, Rabat, Morocco

## Netherlands

Institute for Mathematics, Astrophysics and Particle Physics, Radboud University
Nijmegen/Nikhef, Nijmegen, Netherlands

Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam,
Netherlands

## Norway

Department for Physics and Technology, University of Bergen, Bergen, Norway

Department of Physics, University of Oslo, Oslo, Norway

## Poland

AGH University of Science and Technology, Faculty of Physics and Applied Computer
Science, Krakow, Poland

Marian Smoluchowski Institute of Physics, Jagiellonian University, Krakow, Poland

Institute of Nuclear Physics Polish Academy of Sciences, Krakow, Poland

## Portugal

Laboratório de Instrumentação e Física Experimental de Partículas - LIP, Lisboa, Portugal
Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal
Departamento de Física, Universidade de Coimbra, Coimbra, Portugal

Centro de Física Nuclear da Universidade de Lisboa, Lisboa, Portugal
Departamento de Física, Universidade do Minho, Braga, Portugal

Departamento de Física Teórica y del Cosmos, Universidad de Granada, Granada (Spain),
Spain

Dep Física and CEFITEC of Faculdade de Ciências e Tecnologia, Universidade Nova de
Lisboa, Caparica, Portugal

Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

## Romania

Transilvania University of Brasov, Brasov, Romania
Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania

Department of Physics, Alexandru Ioan Cuza University of Iasi, Iasi, Romania

National Institute for Research and Development of Isotopic and Molecular Technologies,
Physics Department, Cluj-Napoca, Romania

University Politehnica Bucharest, Bucharest, Romania

West University in Timisoara, Timisoara, Romania

Russia

Joint Institute for Nuclear Research, Dubna, Russia

P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia

National Research Nuclear University MEPhI, Moscow, Russia

D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University,
Moscow, Russia

Budker Institute of Nuclear Physics and NSU, SB RAS, Novosibirsk, Russia

Novosibirsk State University Novosibirsk, Russia

Institute for High Energy Physics of the National Research Centre Kurchatov Institute,
Protvino, Russia

Institute for Theoretical and Experimental Physics named by A.I. Alikhanov of National
Research Centre "Kurchatov Institute", Moscow, Russia

Konstantinov Nuclear Physics Institute of National Research Centre "Kurchatov Institute",
PNPI, St. Petersburg, Russia

Tomsk State University, Tomsk, Russia

Serbia

Institute of Physics, University of Belgrade, Belgrade, Serbia

Slovak Republic

Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovak
Republic

Department of Subnuclear Physics, Institute of Experimental Physics of the Slovak
Academy of Sciences, Kosice, Slovak Republic

Slovenia

Department of Experimental Particle Physics, Jožef Stefan Institute and Department of
Physics, University of Ljubljana, Ljubljana, Slovenia

South Africa

Department of Physics, University of Cape Town, Cape Town, South Africa

iThemba Labs, Western Cape, South Africa

Department of Mechanical Engineering Science, University of Johannesburg, Johannesburg,
South Africa

University of South Africa, Department of Physics, Pretoria, South Africa

School of Physics, University of the Witwatersrand, Johannesburg, South Africa

Spain
Institut de Física d'Altes Energies (IFAE), Barcelona Institute of Science and Technology,
Barcelona, Spain

Departamento de Física Teorica C-15 and CIAFF, Universidad Autónoma de Madrid,
Madrid, Spain

Departamento de Física Teórica y del Cosmos, Universidad de Granada, Granada (Spain),
Spain

Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia - CSIC,
Valencia, Spain

Centro Nacional de Microelectrónica (IMB-CNM-CSIC), Spain

Sweden

Department of Physics, Stockholm University, Sweden

Oskar Klein Centre, Stockholm, Sweden

Fysiska institutionen, Lunds universitet, Lund, Sweden

Physics Department, Royal Institute of Technology, Stockholm, Sweden

Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden

Switzerland

Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics,
University of Bern, Bern, Switzerland

CERN, Geneva, Switzerland

Département de Physique Nucléaire et Corpusculaire, Université de Genève, Genève,
Switzerland

Taiwan

Department of Physics, National Tsing Hua University, Hsinchu, Taiwan

Institute of Physics, Academia Sinica, Taipei, Taiwan

Turkey

Department of Physics, Ankara University, Ankara, Turkey

Istanbul Aydin University, Application and Research Center for Advanced Studies, Istanbul,
Turkey

Division of Physics, TOBB University of Economics and Technology, Ankara, Turkey

Bahcesehir University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey

Istanbul Bilgi University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey

Department of Physics, Bogazici University, Istanbul, Turkey

Department of Physics Engineering, Gaziantep University, Gaziantep, Turkey

United Kingdom

School of Physics and Astronomy, University of Birmingham, Birmingham, United
Kingdom

Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom

SUPA - School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom

SUPA - School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom
Physics Department, Lancaster University, Lancaster, United Kingdom

Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom

School of Physics and Astronomy, Queen Mary University of London, London, United Kingdom

Department of Physics, Royal Holloway University of London, Egham, United Kingdom

Department of Physics and Astronomy, University College London, London, United Kingdom

School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom

Department of Physics, Oxford University, Oxford, United Kingdom

Particle Physics Department, Rutherford Appleton Laboratory, Didcot, United Kingdom

Department of Physics and Astronomy, University of Sheffield, Sheffield, United Kingdom

Department of Physics and Astronomy, University of Sussex, Brighton, United Kingdom

Department of Physics, University of Warwick, Coventry, United Kingdom

## United States of America

Physics Department, SUNY Albany, Albany NY, United States of America

High Energy Physics Division, Argonne National Laboratory, Argonne IL, United States of America

Department of Physics, University of Arizona, Tucson AZ, United States of America

Department of Physics, University of Texas at Arlington, Arlington TX, United States of America

Department of Physics, University of Texas at Austin, Austin TX, United States of America

Physics Division, Lawrence Berkeley National Laboratory and University of California, Berkeley CA, United States of America

Department of Physics, Boston University, Boston MA, United States of America

Department of Physics, Brandeis University, Waltham MA, United States of America

Physics Department, Brookhaven National Laboratory, Upton NY, United States of America

California State University, CA, United States of America

Enrico Fermi Institute, University of Chicago, Chicago IL, United States of America

Nevis Laboratory, Columbia University, Irvington NY, United States of America

Physics Department, Southern Methodist University, Dallas TX, United States of America

Physics Department, University of Texas at Dallas, Richardson TX, United States of America

Department of Physics, Duke University, Durham NC, United States of America

Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge MA, United States of America

Department of Physics, Indiana University, Bloomington IN, United States of America

University of Iowa, Iowa City IA, United States of America

Department of Physics and Astronomy, Iowa State University, Ames IA, United States of America

Louisiana Tech University, Ruston LA, United States of America

Department of Physics, University of Massachusetts, Amherst MA, United States of America

Department of Physics, University of Michigan, Ann Arbor MI, United States of America
Department of Physics and Astronomy, Michigan State University, East Lansing MI, United States of America

Department of Physics and Astronomy, University of New Mexico, Albuquerque NM, United States of America

Department of Physics, Northern Illinois University, DeKalb IL, United States of America

Department of Physics, New York University, New York NY, United States of America

Ohio State University, Columbus OH, United States of America

Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman OK, United States of America

Department of Physics, Oklahoma State University, Stillwater OK, United States of America
Institute for Fundamental Science, University of Oregon, Eugene, OR, United States of America

Department of Physics, University of Pennsylvania, Philadelphia PA, United States of America

Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh PA, United States of America

Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz CA, United States of America

Department of Physics, University of Washington, Seattle WA, United States of America

SLAC National Accelerator Laboratory, Stanford CA, United States of America

Departments of Physics and Astronomy, Stony Brook University, Stony Brook NY, United States of America

Department of Physics and Astronomy, Tufts University, Medford MA, United States of America

Department of Physics and Astronomy, University of California Irvine, Irvine CA, United States of America

Department of Physics, University of Illinois, Urbana IL, United States of America

Department of Physics, University of Wisconsin, Madison WI, United States of America

Department of Physics, Yale University, New Haven CT, United States of America
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# Contents

<table><tr><td>1</td><td>Introduction</td><td>1</td></tr><tr><td>2</td><td>Detector Requirements and Layout</td><td>5</td></tr><tr><td>2.1</td><td>Beam conditions at the HL-LHC</td><td>5</td></tr><tr><td>2.2</td><td>Detector overview and requirements</td><td>7</td></tr><tr><td>2.3</td><td>Detector layout and optimisation</td><td>8</td></tr><tr><td>2.4</td><td>Radiation hardness</td><td>15</td></tr><tr><td>3</td><td>Performance and Physics Benchmarks</td><td>19</td></tr><tr><td>3.1</td><td>Simulation and hit-level detector response</td><td>20</td></tr><tr><td>3.1.1</td><td>Detector geometry</td><td>21</td></tr><tr><td>3.1.2</td><td>Sensor simulation</td><td>23</td></tr><tr><td>3.1.3</td><td>Simulation of digitised readout signals</td><td>24</td></tr><tr><td>3.1.4</td><td>Occupancy</td><td>27</td></tr><tr><td>3.1.5</td><td>Detector-level reconstruction</td><td>29</td></tr><tr><td>3.2</td><td>Reconstruction and detector performance</td><td>30</td></tr><tr><td>3.2.1</td><td>Association of HGTD timing measurements to tracks</td><td>30</td></tr><tr><td>3.2.2</td><td>Determination of the time of the primary vertex</td><td>37</td></tr><tr><td>3.3</td><td>Physics object performance</td><td>39</td></tr><tr><td>3.3.1</td><td>Challenges for associating tracks to vertices</td><td>41</td></tr><tr><td>3.3.2</td><td>Strategy of improving physics object performance</td><td>42</td></tr><tr><td>3.3.3</td><td>Suppression of pileup jets</td><td>43</td></tr><tr><td>3.3.4</td><td>Lepton track isolation</td><td>46</td></tr><tr><td>3.3.5</td><td>Additional applications</td><td>47</td></tr><tr><td>3.4</td><td>Physics</td><td>49</td></tr><tr><td>3.4.1</td><td>Vector boson fusion Higgs production</td><td>51</td></tr><tr><td>3.4.2</td><td>Vector boson scattering</td><td>54</td></tr><tr><td>3.4.3</td><td>Measurement of sin<sup>2</sup> θ<sub>eff</sub></td><td>58</td></tr><tr><td>3.4.4</td><td>Impact of the luminosity uncertainty</td><td>59</td></tr><tr><td>3.4.5</td><td>Trigger for magnetic monopole searches</td><td>62</td></tr><tr><td>3.4.6</td><td>Limitations in the Monte Carlo modeling</td><td>63</td></tr><tr><td>4</td><td>Technical Overview</td><td>65</td></tr><tr><td>4.1</td><td>Introduction</td><td>65</td></tr></table>
Contents

<table><tbody><tr><td>4.2</td><td>Detector overview and key requirements</td><td>65</td></tr><tr><td>4.2.1</td><td>Expected Radiation levels</td><td>66</td></tr><tr><td>4.2.2</td><td>Key requirements</td><td>68</td></tr><tr><td>4.2.3</td><td>Read-out bandwidth</td><td>68</td></tr><tr><td>4.3</td><td>Hybrid HGTD module</td><td>69</td></tr><tr><td>4.3.1</td><td>Sensors</td><td>70</td></tr><tr><td>4.3.2</td><td>Front End ASIC</td><td>72</td></tr><tr><td>4.3.3</td><td>Module assembly</td><td>75</td></tr><tr><td>4.4</td><td>Module loading on support structure</td><td>77</td></tr><tr><td>4.5</td><td>Off detector electronics, calibration and luminosity</td><td>78</td></tr><tr><td>4.5.1</td><td>Peripheral Electronics Boards</td><td>79</td></tr><tr><td>4.5.2</td><td>Luminosity</td><td>79</td></tr><tr><td>4.5.3</td><td>t<sub>0</sub> time calibration</td><td>80</td></tr><tr><td>4.6</td><td>Power distribution and detector control system</td><td>81</td></tr><tr><td>4.6.1</td><td>HV system</td><td>81</td></tr><tr><td>4.6.2</td><td>LV system</td><td>81</td></tr><tr><td>4.6.3</td><td>Monitoring and Controls</td><td>82</td></tr><tr><td>4.7</td><td>Mechanics, Services and Infrastructure</td><td>82</td></tr><tr><td>4.8</td><td>Assembly, Installation and Commissioning</td><td>83</td></tr><tr><td>4.9</td><td>Next steps towards construction</td><td>84</td></tr><tr><td>5</td><td>Sensors</td><td>87</td></tr><tr><td>5.1</td><td>Sensor parameters and requirements</td><td>87</td></tr><tr><td>5.2</td><td>Low Gain Avalanche Detectors</td><td>88</td></tr><tr><td>5.2.1</td><td>Overview</td><td>88</td></tr><tr><td>5.2.2</td><td>LGAD productions</td><td>91</td></tr><tr><td>5.3</td><td>Radiation damage and irradiations</td><td>92</td></tr><tr><td>5.4</td><td>Sensor tests: methodology and experimental techniques</td><td>94</td></tr><tr><td>5.5</td><td>LGAD performance before and after irradiation</td><td>95</td></tr><tr><td>5.5.1</td><td>Electrical characterisation: I-V and C-V</td><td>95</td></tr><tr><td>5.5.2</td><td>Operating bias Voltage and self-triggering</td><td>100</td></tr><tr><td>5.5.3</td><td>Collected charge and gain</td><td>102</td></tr><tr><td>5.5.4</td><td>Efficiency</td><td>104</td></tr><tr><td>5.5.5</td><td>Time resolution</td><td>105</td></tr><tr><td>5.5.6</td><td>Uniformity, inter-pad gap and edge region</td><td>107</td></tr><tr><td>5.5.7</td><td>Long term and stability tests</td><td>109</td></tr><tr><td>5.5.8</td><td>Leakage current and power after irradiation</td><td>112</td></tr><tr><td>5.6</td><td>Operational aspects and bias voltage evolution in HGTD</td><td>114</td></tr><tr><td>5.7</td><td>Summary of present sensor design</td><td>114</td></tr><tr><td>5.8</td><td>Roadmap for future sensor productions and activities</td><td>116</td></tr></tbody></table>
<table><tr><td>6</td><td>Front-end Electronics</td><td>119</td></tr><tr><td>6.1</td><td>General requirements</td><td>120</td></tr><tr><td>6.2</td><td>ASIC architecture</td><td>122</td></tr><tr><td>6.2.1</td><td>Channel architecture</td><td>123</td></tr><tr><td>6.2.2</td><td>Readout architecture</td><td>125</td></tr><tr><td>6.3</td><td>Single-channel readout electronics</td><td>127</td></tr><tr><td>6.3.1</td><td>Preamplifier</td><td>127</td></tr><tr><td>6.3.2</td><td>Discriminator</td><td>129</td></tr><tr><td>6.3.3</td><td>TDC</td><td>130</td></tr><tr><td>6.3.4</td><td>Internal pulser</td><td>132</td></tr><tr><td>6.3.5</td><td>Hit processor</td><td>133</td></tr><tr><td>6.3.6</td><td>Luminosity processing unit</td><td>135</td></tr><tr><td>6.4</td><td>End of Column logic and digital blocks</td><td>136</td></tr><tr><td>6.4.1</td><td>Clock generation unit</td><td>136</td></tr><tr><td>6.4.2</td><td>Matrix readout process</td><td>138</td></tr><tr><td>6.4.3</td><td>Slow control</td><td>141</td></tr><tr><td>6.5</td><td>Radiation tolerance</td><td>142</td></tr><tr><td>6.6</td><td>Power distribution and grounding</td><td>143</td></tr><tr><td>6.7</td><td>Prototype performance</td><td>144</td></tr><tr><td>6.7.1</td><td>Test bench measurements</td><td>144</td></tr><tr><td>6.7.2</td><td>Test beam measurements</td><td>146</td></tr><tr><td>6.7.3</td><td>Irradiation tests</td><td>148</td></tr><tr><td>6.8</td><td>Monitoring</td><td>149</td></tr><tr><td>6.8.1</td><td>Temperature monitoring</td><td>149</td></tr><tr><td>6.8.2</td><td>Supply voltages monitoring</td><td>150</td></tr><tr><td>6.8.3</td><td>Complete monitoring system</td><td>151</td></tr><tr><td>6.9</td><td>Roadmap towards production</td><td>152</td></tr><tr><td>7</td><td>Module Assembly and Loading</td><td>155</td></tr><tr><td>7.1</td><td>Introduction</td><td>155</td></tr><tr><td>7.2</td><td>The bare module</td><td>155</td></tr><tr><td>7.2.1</td><td>Bare module assembly</td><td>155</td></tr><tr><td>7.2.2</td><td>First bare module prototypes: process and results</td><td>156</td></tr><tr><td>7.2.3</td><td>Hybridization specifications</td><td>160</td></tr><tr><td>7.2.4</td><td>Quality assurance / quality control</td><td>162</td></tr><tr><td>7.2.5</td><td>Production hybridization strategy</td><td>162</td></tr><tr><td>7.3</td><td>Module design and assembly</td><td>163</td></tr><tr><td>7.3.1</td><td>General description</td><td>163</td></tr><tr><td>7.3.2</td><td>Voltage distribution and signal readout: flex cables</td><td>164</td></tr><tr><td>7.3.3</td><td>Gluing and wire-bonding</td><td>173</td></tr><tr><td>7.3.4</td><td>Specifications, quality assurance / quality control</td><td>174</td></tr><tr><td>7.3.5</td><td>Production strategy for flex cables and module assembly</td><td>176</td></tr></table>
Contents

<table><tbody><tr><td>7.4</td><td>Module loading</td><td>177</td></tr><tr><td>7.4.1</td><td>General description</td><td>177</td></tr><tr><td>7.4.2</td><td>Support units and detector units</td><td>177</td></tr><tr><td>7.4.3</td><td>Gluing studies</td><td>180</td></tr><tr><td>7.4.4</td><td>Procedure for loading and qualification</td><td>181</td></tr><tr><td>7.4.5</td><td>Detector unit assembly strategy</td><td>182</td></tr><tr><td>7.5</td><td>Thermal Simulations</td><td>182</td></tr><tr><td>7.6</td><td>Roadmap towards production</td><td>189</td></tr><tr><td>8</td><td>Power distribution, Grounding and Shielding</td><td>191</td></tr><tr><td>8.1</td><td>High voltage</td><td>191</td></tr><tr><td>8.2</td><td>Low voltage</td><td>192</td></tr><tr><td>8.3</td><td>Grounding/shielding</td><td>193</td></tr><tr><td>8.4</td><td>Roadmap for power system</td><td>194</td></tr><tr><td>9</td><td>Peripheral Electronics</td><td>195</td></tr><tr><td>9.1</td><td>Data transmission</td><td>196</td></tr><tr><td>9.1.1</td><td>LpGBT</td><td>200</td></tr><tr><td>9.1.2</td><td>Optical links</td><td>202</td></tr><tr><td>9.2</td><td>DC-DC converters</td><td>202</td></tr><tr><td>9.3</td><td>Control and monitoring</td><td>203</td></tr><tr><td>9.4</td><td>Connectors</td><td>204</td></tr><tr><td>9.5</td><td>Peripheral boards</td><td>204</td></tr><tr><td>9.5.1</td><td>Physical limitations</td><td>204</td></tr><tr><td>9.5.2</td><td>Layout considerations</td><td>205</td></tr><tr><td>9.5.3</td><td>Layout</td><td>206</td></tr><tr><td>9.6</td><td>Power dissipation</td><td>208</td></tr><tr><td>9.7</td><td>Roadmap towards PEB production</td><td>208</td></tr><tr><td>10</td><td>DAQ, calibration, luminosity and control</td><td>211</td></tr><tr><td>10.1</td><td>DAQ interface</td><td>211</td></tr><tr><td>10.1.1</td><td>Off-detector electronics</td><td>211</td></tr><tr><td>10.1.2</td><td>Calibration and timing</td><td>213</td></tr><tr><td>10.2</td><td>Timing correction</td><td>215</td></tr><tr><td>10.2.1</td><td>Sources of clock jitter</td><td>216</td></tr><tr><td>10.2.2</td><td>Timing correction procedure</td><td>218</td></tr><tr><td>10.3</td><td>Luminosity</td><td>220</td></tr><tr><td>10.3.1</td><td>HGTD as a luminometer</td><td>221</td></tr><tr><td>10.3.2</td><td>Linearity of the luminosity determination</td><td>222</td></tr><tr><td>10.3.3</td><td>Statistical precision of the luminosity determination</td><td>223</td></tr><tr><td>10.3.4</td><td>Noise and afterglow subtraction</td><td>224</td></tr><tr><td>10.3.5</td><td>Systematic uncertainties affecting the luminosity determination</td><td>225</td></tr></tbody></table>
Contents

<table><tbody><tr><td>10.3.6 Occupancy readout at 40 MHz</td><td>228</td></tr><tr><td>10.3.7 Luminosity back-end electronics</td><td>231</td></tr><tr><td>10.3.8 Processing of the occupancy data in the Luminosity Software</td><td>232</td></tr><tr><td>10.3.9 Per-event luminosity information stored in the ATLAS raw data</td><td>232</td></tr><tr><td>10.3.10 Operation in non-Stable Beams conditions</td><td>233</td></tr><tr><td>10.3.11 Minimum-bias trigger at Level-0</td><td>234</td></tr><tr><td>10.4 Detector Control System</td><td>234</td></tr><tr><td>10.4.1 High Voltage</td><td>235</td></tr><tr><td>10.4.2 Low voltage</td><td>235</td></tr><tr><td>10.4.3 Environmental monitoring</td><td>236</td></tr><tr><td>10.4.4 Peripheral electronics</td><td>238</td></tr><tr><td>10.4.5 Configuration</td><td>239</td></tr><tr><td>10.4.6 DCS software</td><td>240</td></tr><tr><td>10.4.7 External systems</td><td>241</td></tr><tr><td>10.4.8 Interlock system</td><td>242</td></tr><tr><td>10.5 Roadmap for DAQ, luminosity and control system</td><td>243</td></tr><tr><td><b>11 Detector Mechanics</b></td><td><b>245</b></td></tr><tr><td>11.1 Engineering design overview</td><td>245</td></tr><tr><td>11.2 Detector overall layout</td><td>246</td></tr><tr><td>11.3 CO<sub>2</sub> cooling system</td><td>248</td></tr><tr><td>11.3.1 Requirements</td><td>249</td></tr><tr><td>11.3.2 Cooling design</td><td>251</td></tr><tr><td>11.3.3 Cooling plant demonstrator</td><td>255</td></tr><tr><td>11.4 Moderator</td><td>256</td></tr><tr><td>11.5 Hermetic vessel</td><td>257</td></tr><tr><td>11.5.1 Requirements</td><td>257</td></tr><tr><td>11.5.2 Front cover</td><td>258</td></tr><tr><td>11.5.3 Back cover</td><td>260</td></tr><tr><td>11.5.4 Inner ring design</td><td>261</td></tr><tr><td>11.5.5 Outer ring design</td><td>262</td></tr><tr><td>11.6 Support and cooling disks</td><td>264</td></tr><tr><td>11.6.1 Requirements</td><td>265</td></tr><tr><td>11.6.2 Geometry and design</td><td>265</td></tr><tr><td>11.6.3 Assembly criteria</td><td>266</td></tr><tr><td><b>12 Detector Infrastructure</b></td><td><b>267</b></td></tr><tr><td>12.1 Specifications</td><td>267</td></tr><tr><td>12.2 Services layout</td><td>269</td></tr><tr><td>12.3 Patch panels in PP-EC area</td><td>271</td></tr><tr><td>12.4 Services routing on the calorimeter front wall</td><td>272</td></tr><tr><td>12.5 Services connection to outer ring and inside the vessel</td><td>274</td></tr></tbody></table>
Contents

<table><tbody><tr><td>12.6</td><td>Services installation</td><td>275</td></tr><tr><td>13</td><td>Detector Assembly, Installation, and Commissioning</td><td>279</td></tr><tr><td>13.1</td><td>Assembly and commissioning on surface</td><td>279</td></tr><tr><td>13.1.1</td><td>Half disks instrumentation</td><td>279</td></tr><tr><td>13.1.2</td><td>Detector assembly on hermetic vessel</td><td>280</td></tr><tr><td>13.1.3</td><td>Quality Assurance after assembly</td><td>280</td></tr><tr><td>13.2</td><td>Installation in the cavern and commissioning</td><td>281</td></tr><tr><td>13.2.1</td><td>Access and maintenance scenarios</td><td>281</td></tr><tr><td>13.2.2</td><td>Transport and installation the HGTD in the cavern</td><td>282</td></tr><tr><td>13.2.3</td><td>Services connection and commissioning</td><td>284</td></tr><tr><td>13.2.4</td><td>Radiation environment, and radio protection</td><td>285</td></tr><tr><td>14</td><td>Demonstrator</td><td>289</td></tr><tr><td>14.1</td><td>Introduction</td><td>289</td></tr><tr><td>14.2</td><td>Heater demonstrator</td><td>289</td></tr><tr><td>14.3</td><td>Peripheral and back-end electronics, data acquisition</td><td>293</td></tr><tr><td>14.3.1</td><td>Peripheral electronics demonstrator</td><td>293</td></tr><tr><td>14.3.2</td><td>DAQ demonstrator</td><td>294</td></tr><tr><td>14.3.3</td><td>HGTD module</td><td>295</td></tr><tr><td>14.4</td><td>Full demonstrator</td><td>296</td></tr><tr><td>14.5</td><td>Full demonstrator tests</td><td>296</td></tr><tr><td>14.6</td><td>Schedule and organisation</td><td>297</td></tr><tr><td>15</td><td>Project Organization, Costs, and Schedule</td><td>299</td></tr><tr><td>15.1</td><td>Organization and management</td><td>299</td></tr><tr><td>15.1.1</td><td>Upgrade organisation in ATLAS</td><td>299</td></tr><tr><td>15.1.2</td><td>HGTD project organisation</td><td>300</td></tr><tr><td>15.1.3</td><td>Technical milestones</td><td>303</td></tr><tr><td>15.1.4</td><td>Deliverables and WBS</td><td>305</td></tr><tr><td>15.2</td><td>Schedule and main milestones</td><td>307</td></tr><tr><td>15.3</td><td>Resources</td><td>323</td></tr><tr><td>15.3.1</td><td>CORE costs</td><td>325</td></tr><tr><td>15.3.2</td><td>Required Labour Effort</td><td>327</td></tr><tr><td>15.4</td><td>Risk Analysis and Risk Mitigation</td><td>329</td></tr><tr><td>15.4.1</td><td>Risk Management Process and Plan</td><td>330</td></tr><tr><td>15.4.2</td><td>Major risks and mitigation strategies</td><td>331</td></tr><tr><td>A</td><td>Expected Energy Spectra</td><td>337</td></tr><tr><td>B</td><td>Monte Carlo samples</td><td>339</td></tr><tr><td>C</td><td>Two-ring Layout Used in Simulation</td><td>341</td></tr></tbody></table>
Contents

D Technical Drawings 343

Bibliography 353

The ATLAS Collaboration 361
<figure><img src="image_9.png" /></figure>
# 1 Introduction

The high-luminosity (HL) phase of the Large Hadron Collider (LHC) at CERN [1] aims to deliver an integrated luminosity of up to 4000 fb⁻¹. The instantaneous luminosity of the HL-LHC will reach up to $7.5 \times 10^{34} \text{ cm}^{-2} \text{ s}^{-1}$, a large increase from the $2.1 \times 10^{34} \text{ cm}^{-2} \text{ s}^{-1}$ obtained during Run 2 of the LHC. Two extended periods without physics operation are anticipated prior to the HL-LHC operation during which upgrades will be made to the ATLAS experiment. Long Shutdown 2 (LS2) which began in 2019 facilitates the Phase-I upgrades, and Long Shutdown 3 (LS3) which is currently planned to last from 2025 until mid 2027 will be used for the extensive Phase-II upgrades, which will allow ATLAS to cope with the higher luminosities expected at the HL-LHC, and provide new capabilities. Due to the current Covid-19 emergency, potential changes to the schedule and cost of the machine will be discussed in the next year.

This report describes the technical design of a High-Granularity Timing Detector (HGTD), a novel detector introduced to augment the new all-silicon Inner Tracker (ITk) [2] in the forward region, adding the capability to measure charged-particle trajectories in time as well as space. The HGTD will measure the times of minimum-ionising particles with an average time resolution of approximately 30 ps per track at the beginning of the operation of HL-LHC, increasing to 50 ps at the end of the operation of HL-LHC. The HGTD will provide high-precision time measurements for charged particles, enhancing the performance of physics object reconstruction, complementing the ITk in the forward region. The object-level reconstruction improvements increase the physics potential of ATLAS at the HL-LHC.

The past decade of LHC running has been highly successful, despite the challenging experimental environment, with projects such as the discovery of the Higgs boson, the continued precision measurements of physics at the electroweak scale, and the broad search programs. The legacy of the last few years of LHC studies is therefore a stronger confidence in the potential of the LHC to push the reach in both precision and sensitivity well beyond what was originally assumed possible. It can be also argued that, with new abilities to determine the times of the interactions within one bunch crossing, new techniques beyond what are elaborated in this document will be developed to exploit this new capability in Run 4.

The scope of the HL-LHC physics programme is vast, covering many important areas of active research in terms of Standard Model (SM) precision measurements, study of the Higgs boson properties, as well as continuing searches of physics signatures beyond the SM at the
# 1 Introduction

TeV scale. The experimental challenges of the HL-LHC will be more difficult than those at the LHC, and improvements in our detectors are required to meet these demands.

Many of the precision SM measurements as well as the Higgs properties measurements are already limited by systematic uncertainties using the Run-1 and Run-2 datasets. It is therefore important to improve the detector capabilities to limit the impact of systematic uncertainties related to the reconstructed physics objects as well as the modelling of backgrounds. To this end, improvements on the signal-to-background ratio, in addition to the statistical significance gains, are needed to increase the precision of these measurements. The HGTD will play a significant role in improving the reconstruction of physics objects in the forward region of ATLAS, restoring the performance achieved there to levels similar to the ones in the central detector regions. This will lead to a reduction in systematic uncertainties in this new phase space which has been largely unexplored in the first decade of the ATLAS physics programme.

Precision measurements of SM processes benefit from access to new regions of phase space, going beyond on-shell signal strength determination. Measurements of Higgs pseudo-observables as well as its couplings and production cross-sections are key measurements planned for the HL-LHC. These measurements will require well-understood detector performance in the forward region of ATLAS. Similarly, HL-LHC will allow ATLAS to measure to high precision differential distributions of SM processes, and with the HGTD, the precision and phase-space available for these measurements will be increased.

Without increasing the centre-of-mass energy of the collisions in the HL-LHC, many searches for new physics will shift from analyses in the style of bump-hunting to analyses looking for broad off-shell discrepancies in the tails of distributions and other new methods, such as long-lived particles giving rise to displaced vertices. These searches will be extremely challenging and any hope in finding new physics, just beyond the reach of the collision energies, will also require precise understanding of all reconstructed objects in the increased acceptance ($|η|$ up to 4) with the new detector.

A critical aspect of precision measurements is the precise determination of the luminosity. The HGTD is uniquely positioned to measure both the online luminosity on a bunch-by-bunch basis during HL-LHC running, and the high-precision determination of the integrated luminosity offline. The luminosity uncertainty is already one of the leading uncertainties in measurements of Higgs couplings during the first two runs of the LHC, and thus the HGTD will contribute to determine an accurate luminosity measurement for measurements of the Higgs properties with ATLAS.

This document is organised as follows. A detector overview and its requirements (e.g. expected radiation levels) are presented in Chapter 2. Chapter 3 presents simulation-based studies showing how the detector will improve ATLAS object reconstruction and physics sensitivity. The technical design of the HGTD is summarized in Chapter 4. The HGTD will consist of many silicon-based Low Gain Avalanche Detectors (LGADs), placed in front of
the end-cap and forward calorimeters at 2.4 < |η| < 4.0 and arranged such that a charged
particle traverses two or three sensors. Chapter 5 describes the LGAD sensors and their
expected performance, based on measurements of prototype devices that include irradiation
at the levels expected at the HL-LHC. Chapter 6 describes the front-end electronics, a
low-noise, radiation-hard custom ASIC called the ALTIROC, and the performance of the
analog front end. Chapter 7 discusses the hybridization of the LGAD and ALTIROC into
modules of a single LGAD sensor bump-bonded to two ALTIROC chips, their assembly
into detector units which are mounted onto cooling discs, and their connection via flex
cables to peripheral electronics boards at the outer radii. Chapter 8 describes the powering
and control of the detector. Chapter 9 describes the peripheral electronics boards, and
Chapter 10 summarizes the connection of the detector to the ATLAS data acquistion system,
the real-time inter-calibration of the arrival time within the readout path and the 40 MHz
readout of highly-granular hit multiplicity data for real-time luminosity measurement.
Chapter 11 provides the engineering design of the cooling system for the LGADs and
front-end electronics Chapter 12 presents the mechanical design of the overall detector, the
necessary services and their routing. Chapter 13 describes the assembly and commissioning
of the detector. Chapter 14 describes a set of intermediate prototypes that will integrate
elements of the full detector during the remaining R&D period into a demonstrator, in
order to validate key aspects of the design. Finally, Chapter 15 documents the organisation,
schedule and resources of the project to deliver and commission the detector for the start of
the HL-LHC operations in Run 4.
<figure><img src="image_10.png" /></figure>
# 2 Detector Requirements and Layout

## 2.1 Beam conditions at the HL-LHC

Pileup is one of the main challenges at the HL-LHC. The exact beam-spot characteristics of the HL-LHC have not yet been determined. Several scenarios are under study for the nominal operation scheme [3]. This report assumes that an average of 200 simultaneous pp interactions ($\langle\mu\rangle = 200$, Phase-2 planned maximum pileup) will occur within the same bunch crossing interval. A major challenge for the ITk is the pileup suppression in the primary vertex and in the object reconstruction in this high pileup environment, especially in the end-cap region. The luminous region will have an estimated Gaussian spread of 30 to 60 mm along the beam axis (z direction<fnref n="1" />.) The width in time could range from 175 to 260 ps. The case considered in this report is the “nominal” scenario, with Gaussian standard deviation of approximately 50 mm along the beam axis and spreads of 175 ps in time.

The spatial pileup line density, i.e. the number of collisions per length unit along the beam axis during one bunch crossing, is a key quantity for evaluating the performance of ATLAS with and without the HGTD. For $\langle\mu\rangle = 200$ an average pileup density of 1.8 vertices/mm is expected. However this average masks the effect of the local variations which are illustrated in Figure 2.1. In the same plot the distribution for $\langle\mu\rangle = 30$ is shown for comparison. The local pileup vertex density then is calculated by computing the average number of interactions per unit length in a window of $\pm 3$ mm around the signal vertex for $\langle\mu\rangle = 200$. This window is large enough to avoid quantisation effects and small enough to probe the tails of the distribution. The most probable local pileup density for this scenario is 1.44 vertices/mm for $\langle\mu\rangle = 200$.

The ITk measures the longitudinal impact parameter of a track with respect to perigee. This can be combined with the corresponding high precision time measurement of all the tracks associated to the primary vertex in order to exclude those that are not compatible with one-another. Figure 2.2 gives an illustration of this technique, showing the distribution of

<footnote n="1">¹ The ATLAS experiment uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upward. Cylindrical coordinates $(r, \phi)$ are used in the transverse plane, $\phi$ being the azimuthal angle around the z-axis. The pseudo-rapidity is defined in terms of the polar angle $\theta$ as $\eta = -\ln \tan(\theta/2)$.</footnote>
## 2 Detector Requirements and Layout

<figure><img src="image_11.png" /><figcaption>Figure 2.1: Local pileup vertex densities at generator level for two values of $\langle\mu\rangle$: $\langle\mu\rangle = 30$ and $\langle\mu\rangle = 200$.</figcaption></figure>

the truth interaction time as a function of the $z$ position, for one single Hard Scatter (HS) $t\bar{t}$ event with $\langle\mu\rangle=200$.

While the tracker resolution in $z_0$ is better than the typical distance between two vertices, the vertex reconstruction with ITk allows vertices to be separated. This is mainly the case in the central region (see Figure 2.6). When the $z_0$ resolution degrades, and becomes larger than the distance between two vertices, precision timing allows these vertices to be separated, reducing the density of vertices which are considered for a given track. The dispersion in time, for a given $z$, is visible in Figure 2.2.

<figure><img src="image_12.png" /><figcaption>Figure 2.2: Visualisation of the truth interactions in a single bunch crossing in the $z-t$ plane, showing the simulated Hard Scatter (HS) $t\bar{t}$ event interaction (red) with pileup interactions superimposed (black) for $\langle\mu\rangle = 200$.</figcaption></figure>
### 2.2 Detector overview and requirements

The HGTD is being designed for operation with $\langle\mu\rangle = 200$ and a total integrated luminosity of 4000 fb$^{-1}$. Taking into account the space constraints of the existing ATLAS Experiment, including the more advanced planning for the tracker upgrade when R&D on the HGTD began, the HGTD will be located in the gap region between the barrel and the end-cap calorimeters, at a distance in z of approximately $\pm 3.5$ m from the nominal interaction point. This region lies outside the ITk volume and in front of the end-cap and forward calorimeters, in the volume currently occupied by the Minimum-Bias Trigger Scintillators, which will be removed. The position of the two vessels for the HGTD within the ATLAS detector is shown in Figure 2.3.

<figure><img src="image_13.png" /><figcaption>Figure 2.3: Position of the HGTD within the ATLAS Detector. The HGTD acceptance is defined as the surface covered by the HGTD between a radius of 120 mm and 640 mm at a position of z = $\pm 3.5$ m along the beamline, on both sides of the detector.</figcaption></figure>

The envelope of the detector vessel has a radial extent of 110 to 1000 mm. The envelope in z is 125 mm, including the neutron moderator, supports, and front and rear vessel covers. A 50 mm-thick moderator is placed behind the HGTD to reduce the back-scattered neutrons created by the end-cap/forward calorimeters, protecting both the ITk and the HGTD. A silicon-based timing detector technology is chosen due to the space limitations. The sensors must be thin and configurable in arrays. In close collaboration with RD50 [4] and few manufacturers, an extensive R&D program is still ongoing. However baseline sensors that can provide the required timing resolution in the harsh radiation environments were already produced by three different vendors. LGAD [5] pads of 1.3 mm × 1.3 mm with an active thickness of 50 µm fulfil these requirements. This pad size ensures occupancies below 10%
## 2 Detector Requirements and Layout

at the highest expected levels of pileup, small dead areas between pads, and low sensor capacitance, which is important for the time resolution. The sensors will be operated at low temperatures (–30 °C) to mitigate the impact of irradiation.

A custom ASIC (ALTIROC), which will be bump-bonded to the sensors, is being developed to meet the requirements on time resolution and radiation hardness. The ASIC will also provide functionality to count the number of hits registered in the sensor and transmit it at 40 MHz to allow unbiased, bunch-by-bunch measurements of the luminosity and the implementation of a minimum-bias trigger. After optimising the layout for timing performance, cost and radiation tolerance, the detector described in this document is based on three active regions $120 \text{ mm} < r < 230 \text{ mm}$, $230 \text{ mm} < r < 470 \text{ mm}$, and $470 \text{ mm} < r < 640 \text{ mm}$ providing in average 2.6, 2.4 and 2.0 hits per track respectively. Beyond $r > 640 \text{ mm}$ are the peripheral electronics. The active area covers the pseudo-rapidity range $2.4 < |\eta| < 4.0$. A description of the detector layout optimisation is presented in Section 2.3.

Each HGTD end-cap is the integration of one hermetic vessel, two instrumented double-sided layers (mounted on two cooling/support disks), and two moderator pieces placed inside and outside the hermetic vessel. Each cooling/support disk is physically separated in two half circles. Furthermore, the layers are rotated in opposite directions with respect to one another by 15 to 20° in order to maximize the hit efficiency.

A global view of the various components of the detector and its main parameters are shown in Figure 2.4 and Table 2.1. The time resolution parameters have been optimised using information from the sensor (Chapter 5) and front-end electronics (Chapter 6) performance from lab and test beam measurements.

## 2.3 Detector layout and optimisation

The goal of the detector design is to provide the best possible time resolution in order to effectively suppress the effects of pileup in the forward region. The ability to associate tracks to primary vertices depends on the longitudinal impact parameter resolution of the ITk. The ITk layout is shown in Figure 2.5. Figure 2.6 shows the resolution, $\sigma_{z_0}$, of the longitudinal track impact parameter, $z_0$, measured by the ITk as a function of $\eta$, for muons with $p_T = 1$ GeV and $p_T = 10$ GeV. In this report, performance studies have been performed with an ITk layout and simulation [6] including a sensor pitch of 50×50 µm.

For good spatial separation of the HL-LHC collision vertices, $\sigma_{z_0}$, should be significantly better than the inverse of the average pileup density, 600 µm. Figure 2.6 shows that, in the central region, $\sigma_{z_0}$ is well below this limit. In the forward region, however, the resolution exceeds the limit by a large factor, reaching 3 mm for particles with low transverse momentum at $|\eta| \approx 4$, due to the combination of geometric projection and, as shown in
## 2.3 Detector layout and optimisation

<figure><img src="image_14.png" /><figcaption>Figure 2.4: Global view of the HGTD to be installed on each of two end-cap calorimeters. The various components are shown: hermetic vessel (front and rear covers, inner and outer rings), two instrumented double-sided layers (mounted in two cooling disks with sensors on the front and back of each cooling disk), two moderator pieces placed inside and outside the hermetic vessel.</figcaption></figure>

<table><caption>Table 2.1: Main parameters of the HGTD.</caption><tbody><tr><td>Pseudo-rapidity coverage</td><td>2.4 &lt; |η| &lt; 4.0</td></tr><tr><td>Thickness in z</td><td>75 mm (+50 mm moderator)</td></tr><tr><td>Position of active layers in z</td><td>±3.5 m</td></tr><tr><td>Weight per end-cap</td><td>350 kg</td></tr><tr><td>Radial extension:</td><td></td></tr><tr><td>Total</td><td>110 mm &lt; r &lt; 1000 mm</td></tr><tr><td>Active area</td><td>120 mm &lt; r &lt; 640 mm</td></tr><tr><td>Pad size</td><td>1.3 mm × 1.3 mm</td></tr><tr><td>Active sensor thickness</td><td>50 μm</td></tr><tr><td>Number of channels</td><td>3.6 M</td></tr><tr><td>Active area</td><td>6.4 m²</td></tr><tr><td>Module size</td><td>30 × 15 pads (4 cm × 2 cm)</td></tr><tr><td>Modules</td><td>8032</td></tr><tr><td>Collected charge per hit</td><td>&gt; 4.0 fC</td></tr><tr><td>Average number of hits per track</td><td></td></tr><tr><td>2.4 &lt; |η| &lt; 2.7 (640 mm &gt; r &gt; 470 mm)</td><td>≈2.0</td></tr><tr><td>2.7 &lt; |η| &lt; 3.5 (470 mm &gt; r &gt; 230 mm)</td><td>≈2.4</td></tr><tr><td>3.5 &lt; |η| &lt; 4.0 (230 mm &gt; r &gt; 120 mm)</td><td>≈2.6</td></tr><tr><td>Average time resolution per hit (start and end of operational lifetime)</td><td></td></tr><tr><td>2.4 &lt; |η| &lt; 4.0</td><td>≈ 35 ps (start), ≈ 70 ps (end)</td></tr><tr><td>Average time resolution per track (start and end of operational lifetime)</td><td>≈ 30 ps (start), ≈ 50 ps (end)</td></tr></tbody></table>
## 2 Detector Requirements and Layout

<figure><img src="image_15.png" /><figcaption>Figure 2.5: Schematic layout of the ITk for the HL-LHC phase of ATLAS. The active elements of the barrel and end-cap ITk Strip detector are shown in blue, for the ITk Pixel detector the sensors are shown in red for the barrel layers and in dark red for the end-cap rings. Here, only one quadrant and only the active detector elements are shown.</figcaption></figure>

Figure 2.7, increased material. As a result, there is increased residual pileup contamination when assigning reconstructed objects to the reconstructed vertex.

The main contributions to the time resolution of a detector element are:

$$ \sigma_{\text{total}}^2 = \sigma_L^2 + \sigma_{\text{elec}}^2 + \sigma_{\text{clock}}^2 \qquad (2.1) $$

where $\sigma_L^2$ are Landau fluctuations in the deposited charge as the charged particle traverses the sensor, $\sigma_{\text{elec}}^2$ represents the contributions from the readout electronics, and $\sigma_{\text{clock}}^2$ is the clock contribution. Beam tests and sensor simulations show that thinner silicon sensors reduce the contribution from Landau fluctuations. With a 50 µm thick LGAD sensor, this contribution amounts to approximately 25 ps. This is further discussed in Chapter 5. With fast detector signals and a high signal-to-noise ratio, the contribution from the electronics can be kept to approximately 25 ps. This is achievable only if applying corrections for the time walk induced by different signal amplitudes, using small bins in the time-to-digital conversion and applying precise in-situ inter-calibration. The details of the design of the readout electronics to achieve this are described in Chapter 6. The clock contribution should be kept below 15 ps; its distribution is discussed in more detail in Chapter 10.

For simplicity, the size used for the pads (single active pixel sensor) is the same for the entire HGTD, 1.3 mm × 1.3 mm. This pad size balances several characteristics. For smaller pad
<figure><img src="image_16.png" /><figcaption>Figure 2.6: Resolution of the longitudinal track impact parameter, $z_0$, as a function of $\eta$ for muons of $p_T = 1$ GeV and $p_T = 10$ GeV using ITk alone.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>Figure 2.7: Material budget in radiation length $X_0$ (left) and nuclear interaction length $\lambda_0$ (right) as a function of pseudo-rapidity $\eta$, broken down by sub-system and material category for the ITk Layout [6] and beam pipe.</figcaption></figure>

sizes, both electronic noise and physics occupancy are smaller, while the number of channels to be instrumented and the cumulative area of inter-pad dead zones are larger. The size was chosen to give a maximum occupancy of less than 10% in the modules exposed to the highest particle fluxes near the smallest instrumented radius. The choice also ensures a low double-hit probability for a single pad in one bunch crossing. Unifying the pad size across the entire detector also simplifies the production of sensors and assembly of the detector.

Each LGAD module contains 30 × 15 pads, for a total area of 4 × 2 cm². There are in total 8032 modules in the HGTD. The layout of modules was defined by maximising the coverage and minimising the effect of non-instrumented regions. The overlap between modules on the front and back of the disk was then optimised to give approximately uniform performance
## 2 Detector Requirements and Layout

as a function of radius.

The geometry of the detector has been optimised to approximate a flat timing resolution as a function of $\eta$. Due to radiation damage, the timing resolution of the detector will be degraded as the integrated luminosity delivered by the LHC increases. This radiation depends strongly on $r$, with higher radiation closer to the beam axis. The radiation levels expected for the full lifetime of the HL-LHC, including safety factors, are discussed in Section 2.4.

The readout rows are sets of modules whose flex cables (flexible PCB cables) are guided together towards larger radii to the peripheral on-detector electronics. They extend as a line of modules from lower to higher radii. The maximum length of the readout rows is limited by the manufacturing capabilities for the flexible circuits used for the data transmission. Their disposition for the first and second layer is shown as rectangles in Figure 2.8. The active width of a module is 39 mm which limits how well the area near the circular opening at 120 mm can be covered, however, for $r > 150$ mm the coverage is complete. The non-instrumented zone is 0.5 mm for each row edge to account for mechanical tolerances, adding up to 1 mm. Furthermore, an inactive region of 0.3 to 0.5 mm at the edge of each LGAD arrays is present. Adding up conservatively row and sensor edges, a dead region of 2 mm between rows is expected. The total effective width of a readout row is therefore 41 mm. These constraints lead to the helix structure shown in Figure 2.8. A particle transiting the detector should encounter multiple sensors as it passes through the two layers. Figure 2.8(a) shows the geometry of the first layer and Figure 2.8(b) shows the geometry of the second layer. The first and second layer are arranged to mirror the geometry of one another. Each of the layers is rotated in opposite directions by 15 to 20°. The baseline angle of 20° rotation between disks is shown in Figure 2.8(c). Any angle of rotation beyond 10° results in similar performance in terms of the number of simulated hits and dead regions. The baseline angle is chosen largely due to detector services considerations, which are further discussed in Chapter 12 and Chapter 13. Along with optimising the coverage, the rotation frees sufficient room at 640 mm to install the cooling equipment between the peripheral electronics.

Each layer of the HGTD is double-sided, i.e., the modules with sensors and on-detector electronics are mounted on the front and back sides of a common cooling disk. As illustrated in Figure 2.9, the modules on the two sides of a disk are arranged to overlap. A study using full simulation was performed to determine the optimal overlap between modules in three rings to achieve the required timing resolution via the average number of simulated hits given the expected time resolution of the pads. The maximal overlap is limited by the need for sufficient space between the modules to allow the readout of the data. For $r > 470$ mm, an overlap of 20%, for $230 mm < r < 470$ mm an overlap of 54% and for $r < 230$ mm an overlap of 70% was the result of the optimisation. The HGTD acceptance is defined as the surface covered by the HGTD between a radius of 120 mm and 640 mm. The number of simulated hits as a function of radius and transverse plane position is shown in Figure 2.10.
<figure><img src="image_18.png" /><figcaption>Figure 2.8: The orientation of the readout rows for the first and second layer encountered by a particle, separately and with the overlay of both. Each layer is rotated in alternating directions by 20°. In the figures the staves of the three rings are separated by the circular lines.</figcaption></figure>

The relative fraction of tracks as a function of simulated hits per track for each ring can be found in Figure 2.11.

<figure><img src="image_19.png" /><figcaption>Figure 2.9: The schematic drawing shows the overlap between the modules on the front and back of the cooling disk. There is a sensor overlap of 20% for $r > 470$ mm, 54% for $230$ mm $< r < 470$ mm and 70% for $r < 230$ mm.</figcaption></figure>

The material for the HGTD is highlighted in Figure 2.12, which includes the material for the moderator located behind the HGTD active sensor area.

Beyond pileup mitigation, HGTD can play an important role in the ATLAS HL-LHC physics programme as a luminometer. An accurate luminosity determination will be a critical input for precision measurements. The luminosity uncertainty can be a limiting factor to
## 2 Detector Requirements and Layout

<figure><img src="image_20.png" /><figcaption>Figure 2.10: Hit multiplicity as function of $x$, $y$ (left) and $r$ (right). The figures were made using simplified simulations, resulting in an uncertainty of roughly 10% compared to the full simulation studies of the HGTD, discussed in Section 3.1. The vertical grey dashed lines in the right plot shows the separation between the three rings.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>Figure 2.11: Fraction of tracks as a function of number of associated simulated hits, separated for tracks in the inner, middle and outer ring.</figcaption></figure>

many precision cross-section measurements, including achieving $O(1\%)$ accuracy on certain measurements of the Higgs boson production and couplings. It is therefore important to be able to determine the luminosity as accurately as in Run 2, which will be a challenge in the harsh HL-LHC environment. The HGTD provides unique and pileup-robust capabilities for measuring the luminosity at the HL-LHC and will be an essential part of the combined ATLAS luminosity measurement.

Taking advantage of the high granularity of the detector, the luminosity can be measured by counting the mean number of simulated hits in the detector, a quantity linearly proportional
<figure><img src="image_22.png" /></figure>

Figure 2.12: Radiation length $X_0$ (left) and nuclear interaction length $\lambda_0$ (right) as a function of pseudo-rapidity $\eta$, broken down by type of material for the HGTD, using the simulation of the two ring detector geometry described in Section 3.1.1. The moderator is included as it is within the hermetic vessel, although it is situated behind the active area of the HGTD. The baseline cooling pipes will be made with titanium instead of stainless steel as used in the simulation and material plots shown in this figure. The resulting radiation and nuclear interaction lengths will also be reduced with titanium cooling pipes.

to the average number of interactions per bunch crossing. The counting will be done over two time windows, one centred at the bunch crossing and with a width of 3.125 ns, the other with both width and relative position tuneable with a step of 3.125 ns. The application of these capabilities and their implementation are further discussed in Chapter 6 and Chapter 10.

The time resolution per track as a function of the radius is shown in Figure 2.13, for various integrated luminosity during the HL-LHC runs, corresponding to the replacements of the two inner rings during the lifetime of the detector. This replacement strategy is due to the expected radiation damage to the detector, described in detail in Section 2.4.

## 2.4 Radiation hardness

One of the most important parameters of the HGTD will be the radiation hardness of the sensors and electronics. Since the HGTD will be installed with a pseudo-rapidity coverage of $2.4 < |\eta| < 4.0$, it is essential that the detector can withstand the radiation levels throughout the HL-LHC operations. The neutron-equivalent fluence at a radius of 120 mm, is expected to reach $5.6 \times 10^{15} \text{ neq cm}^{-2}$ and the total ionising dose (TID) about 3.3 MGy as shown in Figure 2.14. To account for uncertainties in the simulation, a safety factor of 1.5 is applied to both estimates. An additional factor of 1.5 is applied to the TID due to uncertainties in the behaviour of the electronics after irradiation, primarily for low-doses-rate effects, which have not been fully qualified as of today. This leads to a total safety factor of 1.5 for the sensors that are most sensitive to the particle fluence, and 2.25 for the electronics which
## 2 Detector Requirements and Layout

<figure><img src="image_23.png" /></figure>

Figure 2.13: Time resolution per hit (left) and per track (right) within HGTD acceptance as a function of the radius. The time resolution is shown for various integrated luminosities. The time resolution is improved at higher luminosities corresponding to the replacements of inner-most rings during the lifetime of the detector.

are more sensitive to the TID. After applying these, the detector would need to withstand
$8.3 \times 10^{15} \text{ n}_{\text{eq}} \text{ cm}^{-2}$ and 7.5 MGy.

To achieve sufficient performance of the sensors and ASICs, the detector layout has been designed considering a replacement scenario during the HL-LHC. Through an intensive R&D campaign described further in Chapter 5 and Chapter 6, a minimum charge of 4 fC is required to obtain a high efficiency signal. This can be achieved up to a radiation damage of $2.5 \times 10^{15} \text{ n}_{\text{eq}} \text{ cm}^{-2}$ and 2.0 MGy. As a result, the sensors and electronics within the lowest-radius ($r < 230$ mm) will be replaced after each $1000 \text{ fb}^{-1}$ and the sensors and ASICs within $230 \text{ mm} < r < 470$ mm should be replaced at half of the data-taking ($2000 \text{ fb}^{-1}$) during the HL-LHC program. This corresponds to about 52% of the sensors and ASICs which will need to be replaced. The maximum fluence and total ionising dose as a function of the radial position including the replacement of the rings can be found in Figure 2.15. In the resulting three-ring layout, the maximal TID and fluence, using the Fluka estimations of September 2019, does not exceed 2 MGy and $2.5 \times 10^{15} \text{ neq/cm}^2$. In the inner ring the total Si 1MeV neq has a similar contribution from neutrons and charged particles while in the middle and outer rings the dominant effect comes from neutrons.

The exact radial transition between the three rings will be tuned for the final detector layout, once the FLUKA simulations will be updated with the final ITk layout, and the radiation hardness of the final sensors and ASICs are re-evaluated.

More details can be found in Chapter 5 to Chapter 6. The expected proton, neutron, and pion energy spectra in the HGTD front and rear layer after $4000 \text{ fb}^{-1}$ are shown in Figure A.1, Figure A.2, and Figure A.3.
<figure><img src="image_24.png" /><figcaption>(a) Nominal $Si1MeV_{neq}$ fluence for HL-LHC.</figcaption></figure>

<caption>(b) Nominal ionising dose for HL-LHC.</caption>

Figure 2.14: Expected nominal $Si1MeV_{neq}$ fluence and ionising dose as functions of the radius in the outermost sensor layer of the HGTD for 4000 fb$^{-1}$, i.e. before including safety factors. The contribution from charged hadrons is included in 'Others'. These estimations used Fluka simulations using ATLAS Fluka geometry 3.1Q7 (from December 2019).
<figure><img src="image_25.png" /><figcaption>(a) $\text{Si1MeV}_{\text{neq}}$ fluence for HL-LHC with scale factor applied and considering ring replace-factors. (b) Ionising dose for HL-LHC with scale factor applied and considering ring replace-factors.</figcaption></figure>

Figure 2.15: Expected $\text{Si1MeV}_{\text{neq}}$ radiation levels in HGTD, using Fluka simulations, as a function of the radius considering a replacement of the inner ring every $1000 \text{ fb}^{-1}$ and the middle ring replaced at $2000 \text{ fb}^{-1}$. For the radiation levels, the particle type is included and the contribution from charged hadrons is included in 'Others'. These curves included a safety factor (SF) of 1.5 to account for simulation uncertainty. An additional safety factor of 1.5 is applied to the TID to account for low dose-rate effects on the electronics, leading to a safety factor of 2.25.
# 3 Performance and Physics Benchmarks

One of the most significant ATLAS detector upgrades for HL-LHC is the replacement of the inner tracker system and its extension in pseudorapidity coverage up to $|η| = 4$. The forward extension provides object-level improvement of jets from vector boson fusion (VBF), vector boson scattering (VBS), and many other key signatures for the HL-LHC physics program. However, exploiting forward tracks is challenging. As $η$ increases beyond the acceptance of the current tracker ($|η| < 2.5$), tracks become more collinear to the beam and are subject to large multiple scattering effects due to increased material from services relative to the central barrel region. While the ATLAS Phase 2 inner detector is able to reconstruct charged particles up to $η = 4$ with very high precision, the above effects are particularly relevant for the case of soft pileup forward tracks that may contaminate the hard-scatter vertex. At very low track $p_T$, there is a large and rapid degradation of the longitudinal impact parameter $z0$ resolution as a function of $η$ to the point in which the $z0$ resolution of pileup tracks is larger than the typical separation between primary vertices. This effect significantly weakens the ability of the tracking detector to unambiguously associate low $p_T$ tracks to vertices, resulting in reduced physics performance capabilities in the forward region. In other words, for the first time, a high luminosity hadron collider will operate a forward tracker in an environment in which the pileup density is higher than its spatial resolution in $z$ for low $p_T$ tracks. HGTD has been designed primarily to overcome this challenge, ensuring that the physics performance, particularly the pileup suppression, does not degrade in the forward region. This is achieved by leveraging the time spread of the LHC beam spot with a fast timing detector that can associate time stamps to forward tracks. The capability to provide high-precision time measurements for charged particles allows the HGTD to enhance the performance of physics object reconstruction in the forward region, complementing the ITk in the forward region. Those object-level improvements can then, in turn, increase the physics potential of ATLAS.

The reconstruction of track times in the forward region, on the other hand, is also a challenging task. The two main experimental challenges of a forward timing detector are the large amount of material in front of it, and the limited $η$ acceptance of the HGTD in the space available between the ITk and the end-cap calorimeter. The former limits the rate of forward tracks that can be associated to a time with high confidence. The latter impacts the ability to determine the global event-vertex time. The hard-scatter interaction needs to produce enough particles within the HGTD acceptance, and separate them from forward activity from pileup interactions. In this section the focus is on both the event reconstruction and
physics improvements introduced by HGTD, as well as on the challenges associated to the reconstruction and use of timing information in the forward region.

This chapter is organised in four sections. In the first section, the HGTD simulation and the modeling of low-level performance are described, such as the timing distribution and detector occupancy at the level of simulated HGTD hits. The second section describes the reconstruction algorithms developed to associate HGTD hits to tracks found by the Inner Tracker (ITk) and thereby assign them times, and how those times are used to determine the times of primary *pp* vertices. Detailed studies are performed using simulated samples of single-particle events as well as from full physics events with an average of 200 additional pileup interactions overlaid. Since the ability to correctly assign times to tracks is key to the higher-level performance for physics objects, particular attention is devoted to the understanding of the hit-to-track matching efficiency, mis-tag rate and to identify the main factors that limit performance. After describing the low-level performance, the third section discusses the application of the newly available track and vertex times to improve the reconstruction of jets and leptons in the forward region. In particular, the focus is on the improvements in pileup-jet rejection, and lepton isolation efficiency, but possible additional applications are also discussed. The final section illustrates how the improvements in object-level performance can enhance the sensitivity of the ATLAS physics programme through a few example studies. Two main broad classes of physics analyses are considered, motivated by the specific physics object performance improvements studied: Vector Boson Fusion final states, which benefit from the increased pileup-jet rejection in the forward region, and the measurement of the weak mixing angle, which leverages the improved forward lepton isolation efficiency. Additional physics applications, including the potential to significantly constrain the luminosity uncertainty are also discussed.

## 3.1 Simulation and hit-level detector response

The full simulation of the HGTD is performed using a software release dedicated to the HL-LHC ATLAS upgrade programme. The production of simulated samples follows the same steps as the regular ATLAS offline software chain [7]: event generation, detector simulation, digitisation of simulated energy depositions into detector read-out data, and event reconstruction<fnref n="1" />.

The detector simulation uses a layout of the HGTD ("two-ring") which is very close to the baseline layout ("three-ring") summarized in Chapter 2 and described in more detail in the other sections of this report. The layout described in this chapter, and included in the simulations, is not identical due to the layout optimization undertaken in parallel to these simulation studies. The number of modules in the two scenarios is within 1% of each other (with slightly fewer modules in the simulation in comparison to the detector description

<footnote n="1">¹ Details about the list of samples prepared for the studies in this document can be found in Appendix B.</footnote>
in Table 2.1) with the same $\eta$ coverage. Therefore it is expected that the performance and physics potential will be similar for both layouts. Plots of the detector geometry used in the simulation will be shown in Section 3.1.1, similar to those in Section 2.2, for a direct comparison.

The moderators downstream of the active HGTD detector elements are included, with a total thickness of 50 mm. The front and back covers, as well as the heaters, are also included. The cooling plates are modeled in detail, including the cooling loops modeled as steel tubes filled with liquid CO$_2$, and the support plates for the modules.

### 3.1.1 Detector geometry

The GEANT4 toolkit [8] is used to simulate the ATLAS detector. The simulation uses dedicated *GeoModel* packages [9] to implement the detector geometry and convert it to GEANT4 volumes. As particles are propagated through this geometry, the various interactions between the particles and the detector material are simulated. In sensitive detector elements, processes ranging from energies of a few eV, such as the ionisation in gases, up to TeV energies, are simulated to provide a detector-response model that is as realistic as possible. The simulation propagates particles step-wise through the material of the volumes in the detector model and produces energy depositions at specific points in space and time.

In each HGTD end-cap, there are two cooling plates with silicon sensors mounted on both sides totaling to four individual active layers. The detector description of the HGTD has been extended to include approximate volumes representing the peripheral electronics at radii greater than 640 mm. For illustration, a simulated event is shown in Figure 3.1 visualising the placement of the individual modules along with tracks representing the trajectories of simulated charged particles.

The detector modules each consist of one sensor and two readout ASICs (see Chapter 4). These are simulated as boxes of size 22 mm x 40 mm with silicon sensors of size 20.5 mm x 40 mm placed flat in the x-y plane, corresponding closely to the actual sensor size which is discussed in Chapter 5. The modules are larger than the sensors in one dimension to provide the margin needed for wire-bonding the ASIC to the flex. The total thickness of the silicon sensor is 250 µm of which the active part makes up 50 µm and the passive part 200 µm in agreement with the chosen LGAD technology.

The flex PCB cables connecting the ASICs to the peripheral electronics beyond 640 mm have also been implemented in the simulation. As the total thickness of these cables increases as a function of radius, the contribution of the flex cables can be seen clearly in the HGTD material distribution in Figure 2.12.

As mentioned at the beginning of this section, due to the evolving detector design, the module layout used in the full simulations differs from the nominal layout described in
## 3 Performance and Physics Benchmarks

<figure><img src="image_26.png" /><figcaption>Figure 3.1: Visualization of a simulated QCD dijet event showing the trajectories of charged particles and the resulting simulated hits in the HGTD. A wedge in $\phi$ and volumes representing services and support structures have been removed to expose the individual detector modules of the HGTD. No pileup interactions were overlaid in this simulated event.</figcaption></figure>

Section 2.3. The geometry implemented in the GEANT4 detector description is a two-ring layout, Figure C.1 in Appendix C shows the readout row orientation of the two-ring layout used for the full simulations. The detector description includes 80% overlap between sensors on front and back sides of a cooling plate at $R < 320$ mm, and 20% outside, as shown in Figure C.3 in Appendix C. This can be compared with the overlap regions described in Figure 2.9 for the three-ring layout.

Figure 3.2 shows the average number of HGTD simulated hits per track in simulated events for the two-ring layout, as a function of the X and Y position as well as the radial distance from the beam axis, which is close to the one shown for the nominal layout in the previous chapter (Figure 2.10). The minor difference in the detector geometry description will only have a minor influence on the studies of physics objects and analyses, due to the nearly identical geometric coverage and the very similar numbers of simulated HGTD hits per track across different pseudorapidity regions. The three-ring layout will in the future be
## 3.1 Simulation and hit-level detector response

propagated to the GEANT4 detector description and allow simulation studies with a layout
fully consistent with the nominal design.

<figure><img src="image_27.png" /><figcaption>Figure 3.2: The average hit multiplicity as a function of the X and Y position as well as radius (and pseudorapidity) is shown for the two-ring detector layout used in the simulation, for muons with a $p_T$ of 45 GeV. The vertical grey dashed line in the right plot shows the separation between the two rings. This can be compared to Figure 2.10 for the three-ring layout.</figcaption></figure>

### 3.1.2 Sensor simulation

A pad size of 1.3 mm × 1.3 mm is used in the simulations. Two sources of inefficiency over the surface of the modules are implemented in the simulations:

* the guard ring of 0.5 mm surrounding the edge of the sensor, and

* the inter-pad dead zones of 50 µm between active pads.

As a result, around 80% of the total silicon area is active. The different zones of the sensors are illustrated in Figure 3.3 showing the positions of energy depositions from single-particle simulations in active and non-instrumented regions.

The sensor simulation, just like the digitisation and reconstruction described below, is implemented using software developed for the pixel-based tracking detectors in ATLAS, which also provides functionality for associating truth information to the simulated detector hits.
<figure><img src="image_28.png" /><figcaption>Figure 3.3: Positions of simulated energy deposits in active detector regions (red), inter-pad dead zones (black) and the guard ring surrounding the edges of a sensor (blue), given in local module coordinates x and y. This figure is made through drawing points for individual GEANT4 energy depositions from single-particle simulations and shows the level of detail implemented in the geometry model used.</figcaption></figure>

### 3.1.3 Simulation of digitised readout signals

The GEANT4 energy depositions are processed in a digitisation step in order to emulate the detector electronics and generate the detector readout signals. The LGAD sensors are described as planar n-in-p pixel sensors with electron carriers. The channel efficiency is simulated as perfect for energy depositions above threshold, and no defects from radiation damage or defective hardware are included.

During digitisation, the energy deposited for each GEANT4 step in the active silicon volume is used to evaluate the free charge and the drift time to the readout surface based on the sensor thickness, carrier mobility, depletion and bias voltages, and Lorentz shift. Given the characteristics of the sensors, the capacitive coupling to nearby pixels (i.e. cross-talk) is considered small, matching conclusions from LGAD beam tests and discussed in Section 5.5.4. Any cross-talk effects are therefore neglected for now.

In the digitisation step, each energy deposition is also used to generate a pulse following a shape extracted from beam tests of LGAD sensors, see Figure 3.4. Figure 3.4(a) shows the nominal pulse shape and Figure 3.4(b) shows the result of two particles passing through the same pad, separated by 300 ps. A convolution of a Gaussian and a Landau distribution was found to give a good description of the pulse shape. The amplitude of the simulated pulse and its location in time are determined by the magnitude and time of the GEANT4 energy depositions. On top of this pulse, the electronic noise as measured in test beam studies [10]
is added to each pulse bin, as variations randomly sampled from a Gaussian centered at zero and with a standard deviation corresponding to 1.5% of the mean pulse amplitude of a MIP. The pulse time is extracted from the leading edge of the pulse, thereby modelling one component contributing to the total timing resolution. The impact of Landau fluctuations on the overall timing resolution is modelled via an additional Gaussian smearing of the pulse shape derived after the previous steps, which contributes to a timing resolution of about 20 ps. The resolution contributed by the electronics is modelled by smearing the signal time with two Gaussian functions, one reflecting the clock jitter and time-walk contribution from the readout system ($\sigma$ = 25 ps with no irradiation) and the other for the clock distribution ($\sigma$ = 15 ps). The simulation of timing resolution is set up according to the specification detailed in Section 2.3, and the total resolution for the case of no irradiation contributed from the above sources is about 35 ps per hit. The impact due to the overlapping hits on the expected occupancy is found to be minor and illustrated later in Section 3.1.4.

<figure><img src="image_29.png" /><figcaption>Figure 3.4: The simulated pulse shape in a pad of the HGTD is shown for (a) one particle and (b) two particles passing through the same pad separated by 300 ps. The impact on the shape due to the clock jitter variations of ± 25 ps is given in (a). The particles under study are traversing the HGTD perpendicularly.</figcaption></figure>

Samples of single muons and pions with $\langle\mu\rangle = 0$ and flat $\eta$ distributions have been simulated to study the expected time distribution for HGTD hits. The distribution of the time measurements of the energy depositions from single-muon simulations in the HGTD sensors is shown in Figure 3.5, corresponding to the timing performance expected before any radiation damage. The time distribution is obtained by taking the time of the deposition, subtracting the time-of-flight (TOF) expected for a particle with $\beta = 1$ travelling from the production vertex to the sensor in a straight line, then subtracting the true time of the primary vertex. This simplified approach was taken to demonstrate the overall timing structure with the available information at the level of hit simulation. The general TOF correction used for track-hit assignment at the reconstruction level and for the later studies of objects and physics analyses is detailed in Section 3.2.1.
### 3 Performance and Physics Benchmarks

For all layers, the depositions originating from primary and secondary particles are in time for the bulk of the distribution, where primary and secondary particles are those produced from hard-scattering vertices and material interactions, respectively. However, the distribution for secondaries also features a pronounced tail in the timing distribution, arising from secondary particles with low momentum and/or longer path length.

<figure><img src="image_30.png" /><figcaption>Figure 3.5: The distribution of times of simulated energy depositions after applying corrections for the expected time-of-flight from the origin to the sensor and the time of the primary vertex ($t_0$). Simulated hits originating from primary and secondary particles are shown from a single-muon sample without pileup.</figcaption></figure>

The simulated hit-time in the first and last layer of the HGTD is shown in Figure 3.6 for single-pion events. The structure is similar in all layers, and simulated hits for the bulk of the primary and secondary particles are within a narrow time window with respect to the true arrival time. The distributions from secondary particles exhibit significant tails towards larger times, more pronounced for the pions which undergo hadronic interactions within the ITk and the material upstream of the HGTD than for the single-muon events in Figure 3.5. The secondary-hit distributions have larger magnitudes compared with those from primary hits, due to the fact that all hits were plotted without any selection. For a realistic evaluation of performance for physics objects and analyses, the impact from secondary hits can be much reduced, with a proper selection criterion (see Section 3.2).

The digitisation software may also be used to emulate the expected timing performance at any point during the HL-LHC programme. With increased integrated luminosity, the detector gradually suffers more radiation-induced damage which degrades the timing performance. To mitigate this, modules are replaced according to the replacement scheme discussed in Section 2.4. As a consequence, the per-hit and per-track timing resolution will generally vary as a function of radius and integrated luminosity in a non-trivial way, which
## 3.1 Simulation and hit-level detector response

<figure><img src="image_31.png" /><figcaption>Figure 3.6: The distribution of times of simulated energy depositions after applying corrections for the expected time-of-flight from the origin to the sensor and the time of the primary vertex ($t_0$). Simulated hits originating from primary and secondary particles are shown from a single-pion sample without pileup.</figcaption></figure>

was demonstrated in Section 2.3.

The contribution to the timing resolution due to radiation damage is taken into account as a function of the position of the sensor and the accumulated integrated luminosity with a Gaussian smearing. The doses used are those computed using FLUKA simulations in Section 2.4, then data from test bench measurements of sensors determine the corresponding gain for the sensor and the resulting degradation in per-hit timing resolution, based on measurements with ALTIROC0.

For all studies in this chapter, unless specified otherwise, the timing resolution (35 ps per hit) corresponding to the initial running condition at HL-LHC is used in the simulation, hereafter referred to as the “initial” timing scenario.

### 3.1.4 Occupancy

The hit occupancy is studied using simulated minimum-bias and $t\bar{t}$ events with a pileup of $\langle\mu\rangle = 200$. As expected from the particle flow as a function of rapidity in hadron collisions, the probability to have a hit in a pad (with fixed pad size as a function of radius) decreases as a function of the distance from the beam axis. To reduce the probability that an individual pad is traversed by several particles in the same event, a maximal occupancy of less than 10% is required (Section 2.3). This is achieved, but with the smallest margin around $R = 160$ mm, where an occupancy of 8% is observed. Figure 3.7(a) shows the hit occupancy expected for the minimum-bias events, defined as the percentage of pads in the HGTD registering a hit, for the HGTD baseline pad size of 1.3 mm × 1.3 mm. Compared to the innermost layer there is a slight increase for the outermost layer, primarily caused by the increased probability of
## 3 Performance and Physics Benchmarks

initiating showers due to hadronic interactions as more material is traversed. In Figure 3.7(b) the distribution of the number of pads in a module with signal is shown as a function of the radius for $t\bar{t}$ events. The variation of the number of pads with signal in a module has to be taken into account in the calculation of the bandwidth for the data transfer to the peripheral electronics.

<figure><img src="image_32.png" /><figcaption>Figure 3.7: The occupancy (a) and the number of fired pads (b) per module are shown as a function of the radius for a pad size 1.3 mm × 1.3 mm at a pileup of $\langle\mu\rangle = 200$.</figcaption></figure>

By studying the GEANT4 truth information it is possible to study the types of particles giving rise to hits. In $t\bar{t}$ events with $\langle\mu\rangle = 200$, pileup particles and secondaries from showers created in the upstream detector material dominate the occupancy. Figure 3.8(a) shows the breakdown of the origin of the hits measured in the HGTD within a window of $\pm 1$ ns centered around the time of the primary particles as a function of the radius.

If two particles deposit energy in the same pad, the signal of one can be missed or be deformed by a signal from another particle that arrives earlier, and this effect is referred to as “shadowing”. It is therefore important to evaluate the number of hits from primaries masked by particles arriving earlier (Figure 3.4(b)). Figure 3.8(b) shows the percentage of pads fired by secondaries and pileup particles (also consisting of primary and secondary particles from pileup) shadowing a primary particle with respect to the number of pads where at least one primary particle has deposited energy within the 2 ns window. For this high-pileup sample the percentage of shadowed pads is 4.5% at low radii where the occupancy is maximal, decreasing to 1% at larger radii. Performing the same analysis for $\langle\mu\rangle = 0$ shows that the level of 1% is due to secondary particles originating from the same hard-scatter interaction and characterised by a time of arrival compatible within the timing resolution. In this limit the shadowing effect does not bias the time measurement.
## 3.1 Simulation and hit-level detector response

<figure><img src="image_33.png" /><figcaption>Figure 3.8: (a) The origin of the hits detected in the HGTD, in the lower panel the ratio of the primaries with respect to all firing pads is shown, and (b) the percentage of shadowed pads with respect to all firing pads as a function of the radius.</figcaption></figure>

### 3.1.5 Detector-level reconstruction

Three different clustering approaches were studied:

* Geometric clustering: this approach groups adjacent fired pads to form clusters neglecting the time measurement associated to them. No timing information is exploited in this method, and it is identical to the method used in the ITk pixel reconstruction.

* Geometric clustering with time filtering: as above but also using time measurements. Adjacent pads are grouped if the time difference of the considered channels is smaller than 30 ps, corresponding to an overly tight constraint to accentuate any effect from adding timing.

* No clustering: each fired pad is converted into a cluster object.

Figure 3.9 shows the reconstructed cluster size (number of adjacent fired pads) in module-local<fnref n="2" /> $x$ and $y$ using the geometric clustering algorithm with and without time filtering for simulated $t\bar{t}$ events with a pileup of $\langle\mu\rangle = 200$. The reconstructed cluster size is compared to the “true” cluster size, defined as the size of clusters arising from the same simulated particle reconstructed with the geometric clustering with time filtering for $t\bar{t}$ events without pileup. When time consistency is required, smaller clusters are obtained with an average size close to one pad in local $x$ and $y$ coordinates. Despite the 30 ps time window corresponding to a very tight requirement, the size of the resulting clusters still deviate more from that of the true clusters than when using single-pad clusters (i.e. no clustering). Figure 3.10

<footnote n="2">² The local $x$ and $y$ coordinates represent the two coordinates along the sensor grid. Local $x$ is in the $R\phi$ plane perpendicular to the beam line while local $y$ points radially in $R$.</footnote>
## 3 Performance and Physics Benchmarks

<figure><img src="image_34.png" /><figcaption>Figure 3.9: Average cluster width (number of adjacent fired pads) in module-local (a) x and (b) y coordinates for clusters obtained with the geometric clustering algorithm with and without time filtering, in $t\bar{t}$ events with $\langle\mu\rangle = 200$. The reconstructed cluster sizes are compared to the “true” cluster sizes, defined with the clusters arising from the same simulated particle reconstructed with the geometric clustering with time filtering for $t\bar{t}$ events without pileup.</figcaption></figure>

shows the probability of merging contributions originating from multiple particles into the same cluster with the geometric clustering algorithm with and without time filtering in the same $t\bar{t}$ sample. In order to correctly associate clusters to tracks and provide good timing measurements, the rate of merging multiple contributions into one cluster should remain as low as possible. Based on these results, the no-clustering option was chosen as input to the track reconstruction in the studies for this TDR.

## 3.2 Reconstruction and detector performance

This section discusses the performance of the HGTD relating to reconstructed tracks and primary vertices. The assignment of times to tracks is discussed in Section 3.2.1, after which the methodology and performance of assigning times to primary vertices is presented in Section 3.2.2. A thorough understanding of these basic ingredients is critical for the later discussion of improvements on object performance and physics results.

### 3.2.1 Association of HGTD timing measurements to tracks

This section describes the techniques developed to assign a time stamp to reconstructed tracks. The algorithm is based on the progressive extrapolation of tracks to the active HGTD surfaces, in each surface the association to the tracks of nearby hits in the HGTD is performed.
## 3.2 Reconstruction and detector performance

<figure><img src="image_35.png" /><figcaption>Figure 3.10: Probability of merging contributions originated by multiple particles in the same cluster with the geometric clustering algorithm with and without time filtering in $t\bar{t}$ events with a pileup of $\langle\mu\rangle = 200$.</figcaption></figure>

In a second step, properties of the ITk part of the track and the associated hits in HGTD are used to remove incorrect assignments to improve the purity of correctly assigned times.

The algorithm that extrapolates the track and associates hits proceeds as follows. First, tracks reconstructed in the ITk are extrapolated to the HGTD by using the last measurement of the track in the ITk as the starting point. The tracks are extended to the HGTD surfaces using a progressive Kalman filter. In each sensor layer (two per HGTD layer since they are double sided), HGTD clusters found around the extrapolated crossing location are evaluated for compatibility with the track by attempting to add them to the track in a forward filtering step. Each hit in the active layer that is spatially compatible with the extrapolated position is considered, and the one with the lowest $\chi^2$ is accepted as an extension of the track. The extended tracks must satisfy a requirement of $\chi^2$/n.d.f of less than 5.0. In case of a successful extension, the track parameters are updated and extrapolated to the next sensor layer in the HGTD. This is done progressively for the four sensor layers of the HGTD. At each step, the track information from the last step is used as the starting point of the extension.

To compare reconstructed track times with truth track times (defined as the true times of the production vertices corresponding to the tracks under consideration), the individual hit times need to be corrected. This is achieved by a TOF correction done for each hit in the HGTD. The path length of the particle's track is assumed as a straight line between the origin of the track and the position of a given hit. This mean difference between the track's TOF and the straight line approximation has been found to be roughly 1 ps in simulation. The origin of the track is defined as $(0,0,z_0)$, where $z_0$ is the longitudinal impact parameter of the track (defined as the z coordinate of the point on the track closest to the primary vertex in the transverse plane). The TOF is then calculated by dividing the path length by the speed
### 3 Performance and Physics Benchmarks

of light<fnref n="3" /> and subtracted from the hit time. The track-time is then calculated as the arithmetic mean of the times of the individual associated HGTD hits used in the track extrapolation.

The precision of the extrapolation is affected by the material in the ITk and between the ITk and the HGTD. In Figure 3.11 the precision of the extrapolation (resolution per extrapolated HGTD hit) as a function of $η$ to the HGTD surface is shown. Single muons with transverse momenta of 1 GeV and 10 GeV were analysed. The extrapolation is performed from the last hit in the ITk associated to the track. For the majority of tracks $p_T > 1$ GeV, the precision of the extrapolation is better than the pad size used in the HGTD (1.3 mm × 1.3 mm).

<figure><img src="image_36.png" /></figure>

Figure 3.11: The extrapolation resolution in radius $r$ and in the product $r \times \phi$ for tracks with $p_T = 1$ GeV and $p_T = 10$ GeV. The resolution is plotted as a function of $η$ for the extrapolation of the track from the last hit in the ITk. The actual layers (segmentation in radius) in the ITK where the last hits are located are indicated by different colors. The resolution is better than the size of a single pad in the HGTD.

<footnote n="3">³ Further iterations of this algorithm will take into account the actual path length of the track and the measured momentum.</footnote>
The performance of track-time determination has been evaluated using single-muon and single-pion samples at $\langle\mu\rangle = 0$, generated with a flat distribution in $\eta$ and $\phi$, and the physics sample simulated for VBF $H \to Z(vv)Z(vv)$ at $\langle\mu\rangle = 200$. The choice of a VBF sample was motivated by the fact that this final state contains forward jets within the HGTD acceptance. Furthermore, VBF is a broad class of topology particularly suitable for HGTD improvements. The single-particle samples are used to compare the performance for the ideal case of high-$p_T$ muons that undergo less material interactions, and the more challenging low-$p_T$ pions with hadronic interactions. The high-pileup VBF sample is used as an example to show the more realistic performance for physics studies. All reconstructed tracks with $p_T > 1$ GeV within the HGTD acceptance are used, exactly corresponding to the set of tracks defined for the denominator in the later efficiency calculations. The detector timing resolution corresponding to the start of HL-LHC running is considered.

The overall efficiency of associating a timing measurement from the HGTD to a track is shown as function of pseudorapidity for the two single-particle samples in Figure 3.12. Given the fact that the timing measurement is available when at least one HGTD hit is associated to the ITk track, the overall efficiency is therefore identical to the efficiency of the track extrapolation. It shows the overall rate for determining a track-time (black line), with a bin-by-bin breakdown categorising the origins of the HGTD hits providing track-time measurements. The categories shaded in green to cyan represent “correct” assignments where a faction of HGTD hits genuinely originate from the same primary particle (true particle from hard scattering) as for the ITK track, with the fractions noted in the legends. The case where the primary particle giving rise to the track does not produce any HGTD hits, but timing measurements from hits caused by other particles are labelled “misassignment” and shown in magenta. Primary particles which do produce at least one hit in HGTD but get unrelated hits associated to its track constitute the category labelled “confusion” which is shown in red (but hardly visible in this figure). The impact of the upstream material on the efficiency of assigning a time is apparent for the pions, for which a small fraction of tracks are observed to get times assigned stemming from hits produced by secondary particles.

The resulting track-time resolution (shown in Figure 3.13), i.e. the difference between the measured and true track-times ($t_{reco} - t_{truth}$), is calculated for tracks extrapolated with one, two, three and four associated HGTD hits separately. Fits to the Gaussian core of each distribution yield $\sigma$ values which are consistent with the expectations, i.e. $\sigma_{hit} / \sqrt{n_{hits}}$. The pions that undergo hadronic interactions give rise to tails that are not visible for the muon events. The slight asymmetry in the tails of these distributions is caused by low-$p_T$ particles which travelled a longer path than the assumed straight line between the track origin and the hit position.

Figure 3.14 shows distributions for the same track-time residual variable, but split up into the categories indicating the number of correct and incorrect hits assigned to the tracks, showing how each category contributes to the tails. The non-Gaussian tail for tracks in which the assigned HGTD hits all originated from primary particles is due to the resolution
3 Performance and Physics Benchmarks

<figure><img src="image_37.png" /><figcaption>Figure 3.12: Overall time association rate for tracks as function of pseudorapidity for (a) single-muon and (b) single-pion events without pileup. A bin-by-bin breakdown of correct (green shades) and incorrect (red/magenta) hit associations is also shown.</figcaption></figure>

<figure><img src="image_38.png" /><figcaption>Figure 3.13: Difference between the measured and true track-time for extrapolated tracks with HGTD extensions single-particle events of (a) single-muon and (b) single-pion events without pileup. Distributions corresponding to tracks with different numbers of associated HGTD hits are shown separately. For each distribution, the fitted Gaussian $\sigma$ and the fraction of tracks outside $2\sigma$ are given in the legend.</figcaption></figure>
effect of track $z_0$ used for TOF correction, which is more profound in the cases of pion and VBF events (consistent with expectation). The fraction of tracks with misassigned hits is close to negligible for both single-particle samples, but Figure 3.14(c) shows that the VBF $H(\text{inv})$ sample suffers from dramatically increased tails due to misassignment, in addition to the Gaussian core with about a resolution of 30 ps. This misassignment occurs when a track undergoes a material interaction before reaching the HGTD such that no hits from the primary track are found in the extrapolated path of the track-hit association algorithm. When this happens in a high-pileup environment, the track-hit assignment algorithm frequently assigns a nearby hit from an unrelated particle, e.g. secondary or pileup particles, resulting in an incorrect track-time.

In order to address the challenge of misassigned hits, a hit-cleaning procedure is applied as a second step to improve the purity of the determined track-times. First, one requires the last ITk hit on the track to be on a detector layer closest to the HGTD in the longitudinal direction. This requirement suppresses (wrong) time assignment to tracks that underwent hadronic interactions earlier in the tracker volume. Second, at least two associated hits in the HGTD are required for tracks within $3.5 < |\eta| < 3.9$. This is a region with substantial material upstream of the HGTD, but that also features larger overlaps between the HGTD modules, allowing for a more stringent number of hits requirement. These two quality requirements aim at identifying tracks undergoing material interactions, for which the time assignment is likely incorrect. This of course reduces the fraction of tracks that will be assigned a time. The final cleaning step ("outlier removal") applies only to tracks that have at least two hits assigned. It consists of checking the consistency in time among all the associated hits and then removing the track under consideration if the times assigned to the HGTD hits have significant inconsistency.

The impact of the cleaning procedure on the track-time association rate is shown in Figure 3.15 as a function of track $\eta$ for the VBF $H(\text{inv})$ sample. The cleaning procedure is effective at reducing the number of tracks with incorrect times, at the expense of a slight reduction of the overall efficiency to correctly attach a time to a track. In the future, more sophisticated versions of track-hit reconstruction and cleaning can be developed and are expected to further improve efficiencies and reduce misassignments.

Based on the above studies (especially the timing resolution presented in Figure 3.14), the track-time is considered to be assigned correctly, if the number of associated HGTD hits corresponding to the same primary particle is more than 50% of the total; otherwise, it is considered as a misassignment. Figure 3.16 shows the rates of correct assignment and misassignment of track-times, after the cleaning procedure, as a function of track $\eta$ and $p_T$. The overall efficiency to correctly assign a time to a reconstructed track is around 50% at 1 GeV and plateaus at 60% for $p_T > 4$ GeV, with a misassignment rate of approximately 10%. The impact of the cleaning procedure on the track-time resolution, separately for cases with different fractions of primary hits, is shown in Figure 3.17. Comparing this figure with Figure 3.14(c) one can see how the fraction of non-Gaussian tails has been reduced
3 Performance and Physics Benchmarks

<figure><img src="image_39.png" /><figcaption>Figure 3.14: Difference between the measured and true track-time for extrapolated tracks with HGTD extensions single-particle events of (a) single-muon and (b) single-pion events without pileup, and (c) VBF $H(\text{inv})$ events with $\langle\mu\rangle = 200$. A breakdown of how correct (green shades) and incorrect (red/magenta) hit associations contribute in each bin is shown. These distribution are before hit cleaning.</figcaption></figure>
## 3.2 Reconstruction and detector performance

<figure><img src="image_40.png" /><figcaption>Figure 3.15: Rate of correctly assigned and misassigned times as a function of track $\eta$ before (left) and after (right) the cleaning procedure.</figcaption></figure>

significantly. The track and time hit requirements of the cleaning procedure help reduce the red and magenta components of the time resolution distribution due to tracks with no primary hits, whereas the outlier removal step reduces the contribution of the green components by removing out-of-time hits that degrade the time resolution.

### 3.2.2 Determination of the time of the primary vertex

Due to the large uncertainty of the longitudinal impact parameter for tracks in the forward region (Figure 2.6), the association of tracks to nearby vertices purely based on spatial information is ambiguous in high-pileup environments, especially for low transverse momentum

<figure><img src="image_41.png" /><figcaption>Figure 3.16: Rate for correct and incorrect assignment of track-times as a function of track $\eta$ (left) and $p_T$ (right). The sum of two rates gives the inclusive efficiency of track-time assignment.</figcaption></figure>
3 Performance and Physics Benchmarks

<figure><img src="image_42.png" /><figcaption>Figure 3.17: Difference between the measured and true track-time for extrapolated tracks with at least one HGTD hit for VBF $H \to Z(\nu\bar{\nu})Z(\nu\bar{\nu})$ events after the cleaning procedure, separately for cases with different fractions of primary hits that are left by true particles not originating from material interactions</figcaption></figure>

tracks. The ability to determine the time of the primary vertex of the hard-scatter process, here denoted as $t_0$, provides a new handle to enhance the capability of the ATLAS detector to remove pileup tracks contaminating physics objects originating from the hard-scatter vertex.

The experimental determination of the vertex $t_0$, however, is challenging. There are two key factors that affect the accurate determination of the hard-scatter vertex time. First, due to the limited pseudorapidity acceptance of the HGTD, the hard-scatter interaction needs to have enough high-$p_T$ tracks with $|\eta| > 2.4$. Second, the limited efficiency for correct track-time association efficiency for hadrons further reduces the number of tracks available to determine $t_0$. It will be shown that these two effects limit the availability of a global vertex time to approximately 65% of the events in a VBF $H(\text{inv})$ sample.

This section focuses on the implementation and performance of a relatively simple vertex $t_0$ technique. The algorithm proceeds as follows. First, an iterative time-clustering algorithm is used to find clusters of tracks that are within a window in $z$ around the selected hard-scatter vertex in the event and have consistent times. The window is defined using a 2-dimensional parameterisation of the track $z_0$ resolution as a function of track $p_T$ and $\eta$, as shown in Figure 2.6 for only two $p_T$ bins. To ensure tracks inside a cluster are consistent in time, the track-time of a given track must agree with that of any other track within a window of $3 \times \sigma_t$, where $\sigma_t$ is the square root sum of track-time errors of the two tracks under consideration. Next, a Boosted Decision Tree (BDT) algorithm was trained to identify the most likely hard-
scatter cluster among the various clusters, taking eight variables as input. The eight variables
are: the weighted averages (taking into account the corresponding track parameter errors)
of both the transverse impact parameter and $1/p_T$ as well as the uncertainties on these two
averages, the uncertainty on the weighted average of the longitudinal impact parameter,
the distance and significance in $z$ between the cluster's averaged $z_0$ and the position of the
primary vertex, and the total sum of $p_T^2$ of the tracks. Signal (hard-scatter-like) clusters were
defined as those clusters containing more than or equal to 50% of hard-scatter tracks in them,
as determined using truth information in VBF $H(inv)$ events. Background (pileup-like)
clusters were those with less than 50% of hard-scatter tracks.

Figure 3.18 shows the BTD output for signal and background clusters, as well as a detailed description of how often it selects the correct in-time cluster. The best cluster is determined as the one having at least three tracks, and the maximum BDT output that passes a cut of 0.2. The cut was chosen to keep the background efficiency below ~10%. In about 60% of the vertices, the BDT selects the correct cluster. Whereas approximately 25% of the cases, no cluster is selected (either because the BDT output is less than 0.2 or because the cluster has less than three tracks) and the algorithm does not provide a $t_0$ for the event. The remaining 15% of the cases correspond to mixed clusters that have various fractions of pileup and hard-scatter tracks. In particular, 5% of the time, this algorithm will calculate the time purely based on pileup tracks and therefore result in an incorrect time for the hard scattering vertex.

After a time-compatible track cluster is chosen, the vertex $t_0$ is defined as the weighted average time of all the tracks belonging to the cluster. Figure 3.19 shows the distribution of reconstructed $t_0$ minus truth $t_0$ for all vertices for which a $t_0$ was found, separated into various categories based on the fraction of hard-scatter tracks. The vertices with at least 50% HS tracks has an RMS spread of 22 ps, while the ones with some but smaller fraction of HS tracks and only pileup tracks have spreads of 70 ps and approximately 200 ps, respectively.

3.3 Physics object performance

The new capability introduced by the HGTD to provide a vertex $t_0$ as well as time information
for forward tracks can be exploited to mitigate the impact of pileup in high-level physics
object reconstruction. In this section the "initial" timing scenario was used. After a detailed
description about the ways in which timing information can be leveraged to improve the
association of tracks to vertices, this section focuses on how the HGTD can improve the
suppression of forward pileup jets and the efficiency of forward lepton isolation based on full
simulation studies. At the end of the section, a brief description of additional applications of
the HGTD left for future work is also included.
3 Performance and Physics Benchmarks

<figure><img src="image_43.png" /><figcaption>Figure 3.18: (a) BDT output distribution for in-time clusters containing more than or equal to (signal) or less than (background) 50% of hard-scatter tracks; (b) Fraction of events as a function of the fraction of hard-scatter tracks in each cluster. The first bin corresponds to the cases in which the BDT selects the correct cluster as hard-scatter. The last bin are cases in which the BDT does not select any cluster. The intermediate bins show the various ways in which the BDT picks an incorrect cluster, where “HS” (“PU”) stands for hard-scatter (pileup).</figcaption></figure>

<figure><img src="image_44.png" /><figcaption>Figure 3.19: Vertex $t_0$ resolution separately for various cases, where “HS” (“PU”) stands for hard-scatter (pileup).</figcaption></figure>
### 3.3.1 Challenges for associating tracks to vertices

The precise assignment of tracks to primary vertices (track-to-vertex association) is one of the key elements to mitigate the effects of pileup on the full suite of event reconstruction algorithms at hadron colliders. Jet reconstruction and calibration, pileup mitigation for jets, b-tagging, lepton isolation, and jet substructure measurements rely strongly on the correct assignment of tracks to primary vertices and jets.

A track is associated to a vertex if its origin is geometrically compatible in $z$ with the vertex position. The compatibility can be determined by the resolution on the track $z_0$ impact parameter such that

$$ \frac{|z_0 - z_{\text{vertex}}|}{\sigma_{z_0}} < s, \qquad (3.1) $$

where $\sigma_{z_0}$ is the per-track resolution on the longitudinal impact parameter which depends primarily on the track $\eta$ and $p_T$, and $s$ is a significance cut. Typical values for $s$ are 2.5 or 3.

While the longitudinal impact parameter resolution is relatively constant and small ($\le 30\mu m$) for $|\eta| < 1.5$, it grows rapidly with pseudorapidity, reaching several millimetres for $|\eta| \gtrsim 3.2$ for low-$p_T$ tracks. The $\eta$ dependence of the impact parameter resolution is mostly determined by the geometry of the inner detector. As $\eta$ increases, tracks become more collinear to the beam line.

Based on Figure 2.6, a 1 GeV track with $|\eta| = 3$ has a $z_0$ resolution of approximately 1 mm. With a most probable average vertex density (at $\langle \mu \rangle = 200$) of 1.8 vertices/mm at $z = 0$, this means that, on average, a low $p_T$ forward track can be compatible with up to about 9 near-by vertices on average. This means that the association of low $p_T$ tracks to vertices becomes ambiguous at large pseudorapidity and high luminosity, leading to a high level of pileup track contamination. Or, in other words, track-to-vertex association will suffer significantly from pileup contamination, reducing the efficiency of track-based pileup suppression methods.

Another way to understand this challenge is by comparing the $z_0$ resolution of a few millimetres for forward low $p_T$ tracks with the average separation between vertices, given by the inverse of the average vertex density $1/\langle \rho(z) \rangle \sim 0.6$ mm. This means that the tracker longitudinal impact parameter resolution in the forward region is significantly larger than the typical separation between vertices. This is an intrinsic challenge of forward trackers in hadron colliders.

Timing information constitutes a powerful new way to address this challenge. By requiring all tracks within a $z$ window around the primary vertex [11] to have a common time compatible with the time of the hard-scatter vertex, the additional pileup tracks from nearby interactions can be significantly reduced. The hard-scatter vertex is reconstructed from all possible tracks in the full inner detector, while its time is derived from the associated tracks within the HGTD acceptance. In this way, the use of timing information provided by the
HGTD can therefore improve the performance of physics object reconstruction, which are detailed in following sections.

### 3.3.2 Strategy of improving physics object performance

This section describes how the use of timing information can improve the reconstruction of physics objects, such as jets and leptons, by reducing the impact of forward tracks from pileup interactions that cannot be unambiguously associated to the hard-scatter vertex of the event.

There are two main approaches. In one approach, the hard-scatter vertex time $t_0$ is determined so that it can be used as a global reference to check the time compatibility of tracks associated to jets or other physics objects in the event. This is the most powerful, and intuitive, way to utilise timing information, and it is a natural extension of the track-to-vertex association in 4 dimensions (space-time). Once a vertex $t_0$ is found, tracks are required to satisfy

$$ \frac{t_{trk} - t_0}{\sigma_t} < s \qquad (3.2) $$

where $\sigma_t$ is the sum in quadrature of the vertex $t_0$ and the track-time ($t_{trk}$) errors, and $s$ is a significance cut, such as 2, or 3.

As discussed in Section 3.2.2, however, the experimental challenges associated to the determination of the vertex $t_0$ limit the full power of this approach.

A second approach, denoted self-tagging, does not require the knowledge of the hard-scatter time. The key idea is to check the consistency of the measured production time for all tracks associated to the same physics object (such as a jet) among themselves. For example, if a jet consists of four tracks but one of them has a significantly different time, then this fourth track which is incompatible in time can be filtered out. More generally, the self-tagging method consists of finding clusters of tracks within a jet that have compatible times, and splitting the jet into smaller sub-jets with consistent times. Specific algorithms can then use the sub-jets in different ways, as will be shown in the next subsections with particular examples.

The self-tagging approach is limited by several elements. First, it requires physics objects to have at least two tracks with time assigned. In the case of pileup jets, the majority of them have only one track in the acceptance of HGTD, reducing the power of this method compared to the global $t_0$ approach. In other applications, like b-tagging or particle-flow jet reconstruction, where more tracks are available, this approach can be important. Second, the self-tagging approach can only address the case of stochastic pileup contamination, as opposed to hard-QCD pileup interactions. It assumes that a jet consists of a group of tracks with a common time origin plus additional tracks out-of-time from nearby, uncorrelated, pileup interactions. In a hard-QCD pileup jet, on the other hand, all its tracks will have a
common time, making this method not applicable. As the fraction of hard-QCD pileup jets increases with jet $p_T$, the self-tagging method will work best at low jet $p_T$.

Both the global $t_0$ and the self-tagging approaches are complementary to each other, and can be combined for maximum performance across jet $p_T$. The following subsections show how these two techniques can be used to improve the rejection of pileup jets and lepton isolation. Other applications, like b-tagging, missing transverse energy, and particle flow are outside the scope of this TDR due to their complexity, but are also expected to benefit from the use of track-time information to mitigate the impact of pileup.

### 3.3.3 Suppression of pileup jets

Pileup jets can reduce the precision of Standard Model measurements and the sensitivity to discover new physics. For example, additional jets can increase the number of background events passing a selection, as well as reduce the efficacy of kinematic variables or discriminants to separate signals from backgrounds. Hence, the efficient identification and rejection of pileup jets are essential to enhance the physics potential of the HL-LHC. These pileup jets can be produced as the result of a hard QCD process (QCD jets) from a pileup vertex, or by random combinations of particles from multiple vertices. At low jet $p_T$, the latter mechanism is dominant, whereas at high jet $p_T$, the majority of pileup jets are QCD jets.

The key element to suppress pileup in jets is the accurate association of jets with tracks and primary vertices. A simple but powerful discriminant is the $R_{p_T}$ jet variable, defined as the scalar sum of the $p_T$ of all tracks that are inside the jet cone and originate from the hard-scatter vertex $PV_0$, divided by the fully calibrated jet $p_T$, i.e.

$$R_{p_T} = \frac{\Sigma p_T^{\text{trk}}(PV_0)}{p_T^{\text{jet}}}$$

The tracks used to calculate $R_{p_T}$ fulfill the quality requirements defined in Ref. [11] and are required to have $p_T > 1$ GeV. The matching criteria are defined in Ref. [12]. In this study, jets are reconstructed from clusters of calorimeter energy deposits using the anti-$k_t$ algorithm [13, 14] with radius parameter $R = 0.4$. Reconstructed hard-scatter jets are required to be within $\Delta R = \sqrt{(\Delta\eta)^2 + (\Delta\phi)^2} < 0.3$ of a truth jet with $p_T > 10$ GeV. Hard-scatter and pileup jets for simulated events are defined by their matching to truth jets, which are reconstructed from stable and interacting final state particles coming from the hard interaction. The pileup jets must be at least $\Delta R > 0.6$ away from any truth hard scattering jet with $p_T > 4$ GeV.

At moderate levels of pileup, where track impact parameter measurements can be used to assign tracks to vertices with relatively little ambiguity, small values of $R_{p_T}$ correspond to jets which have a small fraction of charged-particle $p_T$ originating from the hard-scatter vertex $PV_0$. These jets are therefore likely to be pileup jets. However, at high-pileup conditions, and
## 3 Performance and Physics Benchmarks

particularly in the forward region, the power of this discriminant is reduced, because the longitudinal impact parameter resolution becomes worse and the pileup tracks could have more chance to be incorrectly included in the numerator of $R_{p_T}$.

As described in Section 3.3.2, there are two approaches to incorporate the time information of tracks inside jets: self-tagging, and global vertex $t_0$. In the self-tagging approach, jets with at least two tracks with time information are split into sub-jets of in-time track clusters. The $R_{p_T}$ variable is then recomputed for each in-time cluster plus the additional tracks that have no time assigned. Then, the jet $R_{p_T}$ is defined as the maximum $R_{p_T}$ of all sub-jets. Since each cluster contains a subset of tracks, by construction, the self-tagging $R_{p_T}$ will have a smaller value (as expected) under the presence of pileup, improving the discrimination power of the method. When a global vertex $t_0$ is available, $R_{p_T}$ can be recomputed after removing tracks outside a $2\sigma_t$ window around the reconstructed time of the hard-scatter vertex. It is also possible to combine both approaches such that when no $t_0$ is found, the self-tagging method is used.

Figure 3.20 shows the rejection, i.e., the inverse of the mis-tag efficiency, of pileup jets as a function of the efficiency for selecting hard-scatter jets using the $R_{p_T}$ discriminant for jets with low and high $p_T$ in VBF Higgs invisible events with $\langle\mu\rangle = 200$ without and with the HGTD using the three approaches described above: self-tagging, $t_0$, and combined. The combined method improves the rejection of pileup jets with $30 < p_T < 50$ GeV in the forward region up to a factor of approximately 1.5 at a signal efficiency of 85%. The presented performance for the ITK-only case is largely consistent with that presented in Ref. [15].

Figure 3.21 shows the relative pileup-jet rate for relatively low-$p_T$ jets, as a function of pseudorapidity using the combined timing reconstruction algorithms described in this section. A significant improvement is observed at larger values of $\eta$ where the z impact parameter resolution is worse and timing information becomes more important to associate tracks to vertices.

Figure 3.22(a) shows the track time resolution as a function of the integrated luminosity after the 3-ring replacement scenario described in Section 2.4. In Figure 3.22(b), the pileup jet rejection improvements are shown for the same integrated luminosity steps. The hit simulation and reconstruction is based on the 2-ring scenario as in Figure 3.20 and Figure 3.21, however the time resolution per hit is smeared according to the 3-ring replacement scenario. This figure highlights the performance changes over the lifetime of the detector for a signal efficiency of 85%. The combined method improves the rejection of pileup jets with $30 < p_T < 50$ GeV in the forward region up to a factor of 40% at the start of the detector lifetime to 25% at the end of lifetime.
### 3.3 Physics object performance

<figure><img src="image_45.png" /><figcaption>(a) Jets with $30 \text{ GeV} < p_T < 50 \text{ GeV}$.</figcaption></figure>

<figure><img src="image_46.png" /><figcaption>(b) Jets with $p_T > 50 \text{ GeV}$.</figcaption></figure>

Figure 3.20: Pileup jet rejection as a function of hard-scatter jet efficiency in the $2.4 < |\eta| < 4.0$ region at the beginning of the lifetime of the detector, VBF H to invisible sample, for the ITk-only and combined ITk + HGTD reconstruction.

<figure><img src="image_47.png" /></figure>

Figure 3.21: Relative pileup jet rate as a function of jet pseudorapidity, for jets with $30 \text{ GeV} < p_T < 50 \text{ GeV}$.
### 3 Performance and Physics Benchmarks

<figure><img src="image_48.png" /><figcaption>Figure 3.22: (a) Track time resolution as a function of the integrated luminosity taking into account the 3-ring replacement scenarios described in Section 2.4. (b) Pileup jet rejection as a function of integrated luminosity in the $2.4 < |η| < 4.0$ region, VBF H to invisible sample, for a signal efficiency of 85%. The pileup jet rejection is not shown at the replacement of 3000 fb$^{-1}$ for jets > 50 GeV due to a lack of statistics in the MC sample.</figcaption></figure>

#### 3.3.4 Lepton track isolation

The ability to assign a time to leptons can be exploited to reduce the impact of pileup in the case of applying track-isolation criteria to leptons in the forward region. The efficiency of the “track-based” lepton isolation is defined as the probability that no additional tracks with $p_T > 1$ GeV are reconstructed within $\Delta R < 0.2$ of the lepton track. In the forward region, the relatively large $z$ window required to associate tracks to the primary vertex results in increased pileup track contamination, which consequently degrades the isolation efficiency. The association of a time to the lepton track can be utilised to reject tracks within the isolation cone which come from pileup interactions spatially close to the hard-scatter vertex.

As an example, this is studied using electrons from Z boson events. Similar results are expected for tau leptons decays in acceptance. Forward electrons with $p_T > 20$ GeV passing the standard ATLAS “medium” identification criteria are selected [16]. The electron track is defined as the track closest to the calorimeter cluster of the electron, out of those that have a ratio of track $p_T$ to transverse cluster energy greater than 0.1.

In order to improve the lepton isolation definition, the time of all tracks with $p_T > 1$ GeV which are within the $\Delta R < 0.2$ isolation cone are compared with the time of the electron track. If the time difference between the two is larger than twice the quadratic sum of the timing resolution of both tracks, or if the surrounding track fails to obtain a time, the track is discarded. This procedure allows the recovery of the cases in which a nearby pileup track will cause the lepton isolation to fail.

The isolation efficiency as a function of the pileup density is shown in Figure 3.23 for the
ITk-only and HGTD scenarios, where all electrons no matter whether a timing measurement
is available or not are included in the denominator. The isolation efficiency is shown for
both the initial time resolution of the detector as well as the time resolution at the end of
lifetime as shown in Figure 2.13.

<figure><img src="image_49.png" /><figcaption>Figure 3.23: The efficiency for electrons to pass track-isolation criteria, denoted as $\epsilon(p_T^{\text{iso}})$, as function of the local vertex density, for the ITk-only and ITk+HGTD scenarios. The isolation efficiency is shown for both the “initial” time resolution of the detector as well as the “final” time resolution at the end of lifetime as shown in Figure 2.13.</figcaption></figure>

While the efficiency drops with increased pileup vertex density when using only the ITk, the addition of the HGTD timing information reduces this drop, keeping an efficiency above 85% even at high pileup density, i.e. with up to three additional vertices per mm around the hard-scatter vertex on average. For a local pileup density of the order of 1.6 vertices/mm the electron isolation efficiency is improved by about 10%, which corresponds to a factor of two reduction of the inefficiency. These results show that the expected HGTD performance is sufficient to achieve a forward lepton track isolation efficiency essentially independent of the pileup vertex density and at a level similar to that achieved in the central region. The study of the impact on the isolation efficiency for background electrons produced inside jets or from misidentification is beyond the scope of the study in this document. The result from this study is later applied in the study of the sensitivity improvement in the weak mixing angle measurement.

**3.3.5 Additional applications**

While improvements in the performance of jets and forward leptons have been demonstrated
in the previous sections, the incorporation of timing information into the full suite of ATLAS
physics object event reconstruction is expected to bring additional improvements in other areas not yet considered in this document. In particular, the HGTD is expected to enhance the performance of particle-flow jet energy reconstruction, transverse missing energy, and forward b-jet tagging. Discussions about potential improvements in the understanding of the pileup activity and the dimension of beam spots are given at the end.

## Particle-flow jet reconstruction

Particle-flow jet reconstruction relies on the ability to match charged particle tracks with calorimeter signals and primary vertices. In particular, a key component of this approach, leading to the improved jet energy resolution, is the removal of calorimeter energy deposited by tracks originating from pileup vertices. The ambiguity to accurately associate forward tracks to nearby vertices is expected to limit the capability of particle-flow algorithms to reduce the impact of energy fluctuations due to pileup within jets in the forward region. This effect can be addressed by the use of timing information to correctly identify hard-scatter and pileup tracks within the jet. For jets with low track-multiplicities, on the other hand, one may take advantage of the vertex $t_0$ identification. Improved jet energy resolution can lead to further improvements of sensitivity in many key physics channels, such as Vector Boson Fusion analyses. The full integration of HGTD into the particle-flow reconstruction chain, however, is a long-term goal, involving many steps at the level of calorimeter reconstruction and calibration that are still under development.

## Missing $E_T$

There are three ways in which the HGTD can be utilised to potentially enhance the resolution of the missing $E_T$. The first means is by leveraging the improved jet energy resolution from particle-flow reconstruction using HGTD. Second, by reducing the (forward) pileup contamination in the track-based *soft-term* of the missing ET. The soft-term is defined by all charged tracks associated to the primary vertex that do not belong to hard physics objects. The knowledge of the track-time will enable a more pure selection of forward tracks in the soft-term component of the missing $E_T$. Third, the improved forward pileup jet suppression will directly translate into improvements in the missing $E_T$ resolution, by the rejection of pileup jets that appear to come from the primary vertex but do not belong to the hard-interaction. A full propagation of the pileup jet suppression and the incorporation of timing information to the soft-term reconstruction will be pursued in the future.

## b-tagging

The HGTD can be particularly useful to mitigate the impact of pileup track contamination on b-tagging. The presence of pileup tracks with relatively large $z$ impact parameter with respect to the hard-scatter vertex can create fake secondary vertices leading to a reduction in light-quark jet rejection. A combination of self-tagging (for high multiplicity track jets) and vertex $t_0$ could potentially enhance the rejection of pileup tracks to compensate for the lost b-tagging performance at high vertex densities. The full incorporation of timing information
within the software framework for heavy-flavour tagging requires major infrastructure
changes and is left for a future study.

Additional pileup applications

Section 3.3.3 discussed how HGTD can address the challenge of pileup by mitigating the impact of pileup jets in the forward region. But the HGTD can also help control pileup activities in different ways. For example, the ability to access the time of charged tracks can serve as a robust way to isolate and estimate pileup contributions in data and constrain systematic uncertainties related to pileup itself. Timing information can also be used to create dedicated (orthogonal) control regions to increase the understanding of pileup effects on track reconstruction in dense environments, possibly leading to reduced systematic uncertainties in track-jet observables for physics. These are some of the most difficult experimental uncertainties limiting jet shape measurements and tagging techniques which will be a major element of the Run 4/5 physics programme. Furthermore, the HGTD adds robustness and redundancy, as well as complementarity to ITk, to ensure the full exploitation of the forward region for physics.

Four-dimensional beam spot

Knowledge about the shape and characteristics of the luminous regions at the interaction
points of the experiments is valuable information. With the timing capabilities of the HGTD,
the beam spot can be determined in four dimensions, adding a time profile in addition to
the distributions of where the interactions happen along the three spatial directions. This
provides an extra handle for understanding the beams. Accurate determination of the beam
spot is also of high importance for several ATLAS applications, e.g. tracking and flavor-
tagging in the online trigger system, the offline reconstruction and calibration processes,
and etc. Adding a fourth dimension to the determination of the beam spot can result in
improvements for all of these uses.

**3.4 Physics**

This section describes the impact of the HGTD on a set of selected physics analyses. Each of
these were chosen as representative examples of broader classes of analyses in final states of
particular interest, such as Vector Boson Fusion (VBF) and Vector Boson Scattering (VBS)
processes, and precision measurements with leptons in the forward region.

There are three main ways in which the HGTD will enhance the physics capabilities of ATLAS by exploiting the new dimension of timing information that is orthogonal to any other detector measurement:

* by improving the reconstruction of physics objects such as forward jets and leptons, key in VBF, VBS, and lepton-based forward-backward asymmetry measurements;
## 3 Performance and Physics Benchmarks

* by providing new features on the data from the use of timing information uncorrelated with other detector measurements;

* and by providing a new, powerful capability for precise online and offline luminosity measurements at ATLAS to help achieve the goal of 1% luminosity uncertainty for the Higgs precision physics programme of the HL-LHC.

The broad class of physics analyses benefiting from improved jet and lepton reconstruction are exemplified by a search for VBF-produced Higgs bosons decaying invisibly, and with Standard Model (SM) measurements of a VBS process and the weak mixing angle $\sin^2 \theta_{\text{eff}}$. VBF final states constitute a major component of the HL-LHC physics programme, both in terms of precision measurements and new physics searches. In the specific case of Higgs decaying invisibly, the Higgs boson could be the portal to dark matter, or, in the context of Hidden Valley models, a rich dark sector beyond the SM [17, 18]. This particular decay mode, however, is meant to provide an example of how the HGTD can improve the relevant VBF analyses. The primary way in which the HGTD can enhance VBF physics event reconstruction is by reducing the impact of pileup. VBF final states are characterised by two tagged jets with a large rapidity gap such that most of the time at least one jet is within the HGTD acceptance. One of the dominant backgrounds is due to QCD $Z^+$ jet production, where the final state often contains a hard-scatter jet plus at least one additional forward pileup jet produced in a different interaction close to the hard-scatter vertex. Utilising the improved pileup jet rejection provided by HGTD, it will be shown that the signal-over-background ratio can increase by 7-15%, depending on the event selection categories considered. Additionally, the impact of forward pileup jets and the potential impact of HGTD on a VBS WZjj analysis is discussed. The measurement of the weak mixing angle $\sin^2 \theta_{\text{eff}}$ exemplifies the potential of the HGTD to improve the broader class of precision measurements containing at least one forward lepton. As it will be shown, the improved lepton isolation efficiency, allowed by better pileup track rejection, enables the signal acceptance increasing for this analysis resulting in a 13% increase on the $\sin^2 \theta_{\text{eff}}$ sensitivity in the dominant central-forward category.

As introduced beforehand the power of the HGTD as a new luminometer can significantly improve the luminosity measurement uncertainties. A reduced luminosity uncertainty is considered to be one of the keystones to enable precision measurements at the HL-LHC. In fact, it is known that in order to achieve the HL-LHC goals for Higgs coupling precision (percentage level for the main couplings), significant improvements in the precision of the luminosity measurement (with a target of 1%) are required [19]. The HGTD provides several unique capabilities to reach this goal: very high granularity and low occupancy, timing information to enable afterglow background removal, and additional redundancy complementing the primary ATLAS luminosity detector for Run 4 (LUCID).

The results presented here are only meant to provide a few representative examples of how timing information and the HGTD can impact the physics potential at the LHC. There are more opportunities for HGTD to improve final states containing low-$p_T$ objects in the
forward region which are particularly sensitive to the impact of pileup, as well as completely new possibilities. One example in which the HGTD could provide entirely new, future, opportunities that can expand the scope of the HL-LHC physics programme at ATLAS is the search for magnetic monopoles, discussed at the end of this section (although it requires ALTIROC modification, so it's not part of the baseline).

In addition it has to be pointed out that precision timing information is a completely new feature at hadron collider experiments, different and uncorrelated to any existing measurement. It is expected that the use of more sophisticated machine learning algorithms and physics analyses using timing variables will result in both further improvements and new applications. Moreover, many potential improvements from improved particle-flow jet and missing transverse energy, jet vetos, forward b-tagging, etc. have not yet been considered in time for this TDR.

### 3.4.1 Vector boson fusion Higgs production

The analysis of Vector Boson Fusion (VBF) Higgs production is a major component of the HL-LHC physics programme. This production mechanism has the highest cross section after gluon-gluon fusion and provides key features in the trigger and offline to separate the signal from backgrounds. The main characteristic of VBF events is the presence of two jets with a large rapidity gap. Since most of the time at least one of those jets is within the HGTD acceptance, this final state can benefit from the improved jet reconstruction and pileup jet suppression provided by the HGTD. There are several ways in which the HGTD can increase the sensitivity to VBF topologies. First, the HGTD can reduce the impact of pileup. Depending on the decay final states of the Higgs boson, the major backgrounds usually originate from the production of one or two bosons in association with two jets, where one of the two could be a forward pileup jet. While tracking-based pileup jet suppression algorithms are powerful at removing pileup jets, this task is more challenging in the forward region and timing information can overcome this limitation. In addition to reducing the impact of pileup, improved jet and transverse missing momentum reconstruction can lead to improvements in the signal to background ratio (S/B).

The search for invisible decays of the Higgs produced through VBF was chosen as a representative analysis to illustrate the impact of the HGTD on VBF topologies. This analysis is particularly challenging because of the lack of high $p_T$ features in the central region [20]. However, it is likely that the conclusions from this specific study are relevant for the broader set of VBF and vector-boson-scattering physics analyses planned for the HL-LHC. The dominant backgrounds in this case are the production of W/Z+jet, where the resulting final states often contain one hard-scatter jet plus an additional forward pileup jet, or two forward pileup jets. The relative improvement on the sensitivity is demonstrated by showing the gain on S/B, which is particularly relevant for an analysis dominated by background systematic uncertainties.
This study was performed using a full simulation based on GEANT4 [7, 8] with the goal of accounting for all pileup effects in a more detailed and complete way than in a fast simulation approach. The signal VBF $H \to \text{invisible and dominant QCD } Z(\to \nu\bar{\nu})+\text{jets backgrounds were simulated with POWHEG-BOX [21–25]}$ (v1_r2856) interfaced with PYTHIA8 [26, 27] (v8.186). This study only considers QCD $Z+\text{jet background for simplicity, but } Z+\text{jet and } W+\text{jet have the same jet structure, so it is likely that the conclusions obtained for the pileup jets in } Z+\text{jets will be relevant also for } W+\text{jets. Other considerations such as lost leptons in } W+\text{jets will scale differently than } Z(\to \nu\bar{\nu})+\text{jets with the extended tracking coverage of the ITk, but that is not considered further here. Further details of the analysis strategy can be found in Ref. [28].}$

Due to the challenges of Monte Carlo generation at $\langle\mu\rangle = 200$, the number of signal and background events is limited. This required a loosening of some of the selection criteria typically used in VBF analyses. Therefore, the conclusions of this study apply to a VBF preselection instead of a fully emulated Run 4-5 VBF Higgs to invisible analysis. This will illustrate potential gains that could be achieved until a more sophisticated analysis with larger Monte Carlo statistics is available.

Events are required to have at least two jets with leading and second-leading jet with $p_T^1 > 75$ GeV and $p_T^2 > 50$ GeV, respectively. Furthermore, the two leading jets are required to have $\Delta\eta(j_1, j_2) > 3$. All jets are required to pass an ITk-only $R_{p_T}$ pileup jet tagger [29] operating at 85% hard-scatter efficiency. The looser selection requirements on $\Delta\eta$ and the lack of $m_{jj}$ cut results in topologies with less forward activity than what is expected with a realistic (tighter) selection on these variables. Hence, it is expected that timing information will lead to larger improvements than what is reported in this study.

In the Run-2 VBF Higgs to invisible analysis, an additional selection is made requiring that the $\Delta\phi$ angle between the two leading jets is less than 2. This cut helps to reduce the impact of background events consisting of forward dijet pileup interactions. The effect of this requirement was checked and found to be insignificant within the statistical precision of this study. This is likely due to the fact that the pileup jet structure at high luminosity is different from that in Run 2 such that simple extrapolations from Run 2 pileup expectations are not necessarily accurate. For example, the relative fraction of stochastic vs QCD pileup jets depends on the luminosity, with the former being larger at high $\mu$, and the $\Delta\phi$ angle requirement is mostly useful for rejecting the case with back-to-back QCD jets. The Run 2 analysis additionally applies selections on the scalar and vector sum of event momenta (missing $H_T$ and missing $E_T$, respectively). These selections have been shown to suppress events with two forward jets in the Run 2 selection. Further studies are required to see if a similar benefit is possible in the higher pileup environment at the HL-LHC.

There are two main ways in which the HGTD can be used to enhance the suppression of $Z+\text{jet pileup background and increase the signal acceptance, depending on the number of jets within the HGTD acceptance. First, by the use of the jet-by-jet pileup suppression technique described in Section 3.3.3. This means finding the event vertex time, and using}$
it as a reference when comparing it with the times of tracks within each jet. As studied using the signal events and presented in Figure 3.20(b), the rejection of forward pileup jets with $p_T > 50$ GeV is improved by approximately a factor of 1.2 with the HGTD, assuming a hard-scatter jet efficiency of 85%. The performance improvement is largely limited by the ability to find the correct vertex time. For events in which both jets are forward (FF), however, the knowledge of the vertex time is not so critical. This is because it is enough to compare the relative time of both forward jets to determine if they are compatible with each other (i.e. both jets originate from the same interaction vertex) or not (each jet comes from a different vertex). In this context, HGTD is expected to provide higher levels of improvements in the FF category, compared to the simpler approach consisting of applying the pileup jet tagging algorithm to both jets independently. The use of a dedicated pileup event tagging algorithm for the FF category, however, was not considered in this document due to lack of time. Such method is expected to be developed as a next step. The relative fraction of CF and FF events for signal and Z+jet background event as a function of $m_{jj}$ is shown in Figure 3.24. At low and moderate values of $m_{jj}$, where $S/B$ is low, the majority of the events are in the central-forward category, followed by forward-forward, and central-central. As $m_{jj}$ (and, as result, $S/B$) increases, the relative fraction of events with two forward jets within the HGTD acceptance also increases. This increase is more prominent for background events and, as a result, of larger pileup-jet contributions.

Whereas this analysis is based on full ATLAS detector simulation, the impact of HGTD was estimated in a parametrised way, taking as reference the ROC curves of pileup jet suppression obtained from full simulation. Assuming a fixed ITk-based hard-scatter selection efficiency of 85%, events were reweighted as a function of the pileup jet rejection efficiency gain relative to the ITk-only scenario.

Figure 3.25 shows the expected gain in $S/B$ as a function of the improvement in pileup jet suppression efficiency, normalized to the ITk-only performance ($S/B = 1$ when the x-axis is unity, by construction). For a particular pileup jet efficiency gain from the application of HGTD relative to ITk, the dotted blue line shows the corresponding gain in $S/B$. For example, a 20% increase in forward pileup rejection for jets above 50 GeV (without any loss in hard-scatter efficiency), would correspond to a $S/B$ gain of approximately 15% (corresponding to the y-axis when the horizontal value is 0.80). Figure 3.25 includes two additional curves that are useful to understand the contribution of the CF and FF topologies separately. The black (red) curve corresponds to the case where HGTD is only used in CF (FF) events. For the particular event selection cuts used in this analysis, and for a jet-by-jet pileup suppression improvement of 20%, the $S/B$ gain obtained from using HGTD on FF events only is comparable to that of CF events only. Figure 3.25 and the relevant conclusions were made for the loose VBF selection, where the $m(jj)$ threshold is small. Higher $m(jj)$ requirements are expected to further enhance the FF contribution.
<figure><img src="image_50.png" /><figcaption>Figure 3.24: The dashed line shows the fraction of signal VBF $H \to$ invisible and Z+jet background events as a function of a $m_{jj}$ threshold after a loose VBF preselection. Forward jets are those with $|\eta| > 2.4$. Solid (dotted) lines correspond to VBF $H \to$ invisible (Z+jet) events. The fraction of central-central, central-forward, and forward-forward events are shown in black, red, and blue colors respectively.</figcaption></figure>

### 3.4.2 Vector boson scattering

The study of VBS diboson production is a salient piece in the physics programme for the HL-LHC, due to the sensitivity it provides to probe the nature of electroweak symmetry breaking [30–32]. At the LHC, the electroweak (EW) production of diboson and two jets is the main channel used to study VBS, where the irreducible background typically originates from the QCD production of the same final state. In this section, the potential improvement which the HGTD could bring is discussed using the example of VBS WZjj. The relevant measurements of EW WZjj production are currently limited by the data statistics [33, 34], and a more precise measurement is foreseen at the HL-LHC [35], due to the larger integrated luminosity and the upgraded detector capabilities. Improvements to VBS analyses could increase the reach to higher $q^2$ (higher $m_{jj}$) and potentially give access to longitudinally polarised diboson production which is of particular interest for studying electroweak symmetry breaking. The HGTD can help improve the measurement by further rejecting pileup jets in the forward region, and this is particularly important for certain phase spaces in the charac-
<figure><img src="image_51.png" /></figure>

Figure 3.25: Normalized signal over background gain relative to ITk-only pileup jet suppression performance, as a function of the additional pileup jet rejection from HGTD. The solid black (dotted red) line represents the HGTD improvement from the CF (FF) event topologies separately. The dotted blue line shows the total improvement when the combined HGTD+ITk pileup suppression algorithm is applied to all jets in the event.

teristic distributions which are largely contaminated by background events with forward
pileup jets. The studies in this section are limited to showing the fraction of background due
to pileup, thereby illustrating the areas where HGTD can provide improvement.

The study in this section was performed using a fast simulation of the ATLAS detector [36]. The trigger, reconstruction and identification efficiencies, the energy and transverse momentum resolutions of leptons and jets are computed (as a function of η and p_T) from tabulated values that were evaluated using full simulation. The signal sample generation and event selections outlined below follow closely the study done for 2019 CERN Yellow Report which was part of the 2019 CERN Yellow Report documenting the expected performance of the ATLAS and CMS experiments at the HL-LHC [35, 37]. The signal EW WZjj was simulated using Sherpa 2.2.2 [38], while the irreducible background from QCD WZjj production was simulated using Sherpa 2.2.1. Other small background contributions are not considered in this study. Pileup interactions are generated with PYTHIA8 and with an average of 200 interactions per bunch crossing.
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Events with exactly three leptons (e or μ) are selected, where e (μ) must have $p_T$ > 15 GeV, $|η|$ < 4 (2.7), and pass the loose (tight) identification criteria. At least one lepton candidate is required to have $p_T$ > 25 GeV. The event must have at least one same-flavour opposite-sign lepton pair, with an invariant mass that is consistent within 10 GeV of PDG $m_Z$, and the Z boson candidate is formed by the pair which gives the invariant mass closest to $m_Z$. The third lepton is assigned to the W boson and its $p_T$ is required to be greater than 20 GeV. Finally, the transverse mass of the W candidate, computed using the $E_T^{miss}$ and the $p_T$ of the third lepton, is required to be above 30 GeV. At least two jets with $p_T$ > 30 GeV in opposite hemisphere and with $|η|$ < 3.8 are required, with an invariant dijet mass $m_{jj} > 500$ GeV.

The opportunity for improvement by using information from the HGTD is investigated by removing the contribution of forward pileup jets. The focus is on two different aspects. First, the purity of the sum of the EW WZjj and QCD WZjj processes which interfere and cannot be computed separately at higher orders. Second, two differential distributions are studied, selected for their ability to probe the theoretical modelling, to discriminate between EW WZjj and QCD WZjj, and their sensitivity to anomalous quartic gauge couplings (QGC) [39].

For the first case, one example is the $\Delta\eta_{jj}$ distribution shown in Figure 3.26. The contamination originating from forward pileup jets constitutes about 50% of the selected events for $\Delta\eta_{jj} > 5$. If completely suppressed, the purity (Figure 3.26(b)) of the sum of EW WZjj and QCD WZjj would approach 100% over the entire kinematic range, providing increased sensitivity to new physics at large momentum transfer.

For the second case, a variable considered for its discriminating power between EW and QCD WZ production is the centrality<fnref n="4" /> shown in Figure 3.27(a). The pileup component of the EW and QCD WZjj distributions mainly concentrates under the EW distribution (not shown here), at slightly higher value of the centrality, while the QCD distribution is centered around zero. By removing the forward pileup jets contribution the EW WZjj purity increases by 30% for the values of centrality over 2, so that the EW WZjj signal becomes larger than that contaminated by pileup (Figure 3.27(b)). The high centrality region is more EW WZjj enriched and is also expected to be more sensitive to new physics effects. Therefore a higher purity in this region is beneficial as it isolates a pileup free EW WZjj set of events.

The differential distributions shown here illustrate how improved rejection of forward pileup jets can improve the purity of the sum of EW+QCD WZjj as well as the separation power between the EW WZjj and QCD WZjj processes. The improved purity allows for more sensitive tests of WZjj production in spite of the high-pileup environment.

In summary, the above studies illustrate the importance of background from pileup jets in forward VBS topologies. The extended tracker acceptance of the ITk together with the HGTD timing information will help identify and remove such backgrounds and increase the purity of the event selection in crucial regimes for the study electroweak scattering processes.

<footnote n="4">⁴ The centrality is here defined as min($\Delta\eta^{\text{min}}$, $\Delta\eta^{\text{max}}$), where $\Delta\eta^{\text{min}} = \eta_{\ell}^{\text{min}} - \eta_{j}^{\text{min}}$ and $\Delta\eta^{\text{max}} = \eta_{\ell}^{\text{max}} - \eta_{j}^{\text{max}}$ are calculated using the minimum and maximum lepton and jet pseudorapidities.</footnote>
<figure><img src="image_52.png" /><figcaption>(a) $\Delta\eta_{jj}$ with breakdown of pileup backgrounds.</figcaption></figure>

<caption>(b) Impact of removing forward pileup jets.</caption>

Figure 3.26: Distribution of $\Delta\eta_{jj}$ for (a) EW WZjj plus QCD WZjj where backgrounds with at least one pileup jet are highlighted. FF, CF and CC refer to the two jets being either both forward ($|\eta| > 2.4$), one central and one forward, or both central. (b) is the ratio of EW+QCD WZjj events divided by all selected events vs $\Delta\eta_{jj}$ with and without events of CF/FC and FF jets with at least a forward pileup jet.

<figure><img src="image_53.png" /><figcaption>(a) Pileup contributions for QCD WZ.</figcaption></figure>

<caption>(b) Purity of EW WZ with and without backgrounds with forward pileup jets.</caption>

Figure 3.27: Centrality distributions for (a) QCD WZjj with shown fractional contributions from pileup jets, and (b) is the ratio of EW WZjj divided by all selected events in bins of centrality
### 3.4.3 Measurement of $sin^2 \theta_{eff}$

In the Standard Model, the Z boson couplings differ for left- and right-handed fermions due to the mixing between the neutral states associated to the $U(1)$ and $SU(2)$ gauge groups. The difference leads to an asymmetry in the angular distribution of positively and negatively charged leptons produced in Z boson decays and depends on the weak mixing angle, $sin^2 \theta_{eff}$ [40]. Experimentally, this asymmetry can be expressed by

$$A_{FB} = \frac{N(\cos \theta^* > 0) - N(\cos \theta^* < 0)}{N(\cos \theta^* > 0) + N(\cos \theta^* < 0)},$$

where $\theta^*$ is the angle between the negative lepton and the quark in the Collins-Soper frame [41] of the dilepton system. In this formalism, the quark is always assumed to move in the direction of the boost of the dilepton system. This asymmetry is enhanced by $Z/\gamma^*$ interference and exhibits significant dependence on the dilepton mass.

The weak mixing angle is one of the fundamental parameters of the SM. Several measurements of $sin^2 \theta_{eff}$ have been made at previous and current colliders, and the current world average of $sin^2 \theta_{eff} = 0.23153 \pm 16 \times 10^{-5}$ is dominated by the combination of measurements at LEP and at SLD, which, however, exhibit a tension. At LHC, the best sensitivity to $sin^2 \theta_{eff}$ is at high Z rapidity when at least one lepton is present in the forward region [42]. Only Z bosons decaying to electrons are considered in this analysis since this final state provides the best experimental precision within the largest acceptance.

Simulated $Z/\gamma^* \to ee$ signal samples at $\sqrt{s} = 14$ TeV are smeared to match the expected detector response. The performances of the upgraded ATLAS detector [43] in the high pileup environment of the HL-LHC are emulated using the physics object performance recommendations in Ref. [44]. The fiducial acceptance of $Z/\gamma^* \to ee$ events is split into three independent channels depending on the electron $|\eta|$: CC, CF, FF when C represents electron reconstructed in the central region ($|\eta| < 2.47$) and F represents electron reconstructed in the forward region ($2.5 < |\eta| < 4.2$). Both electrons are required to have $p_T > 25$ GeV. The invariant mass of the electron pair is required to be loosely consistent with the Z boson mass, $60 < m_{ee} < 200$ GeV, and the events are further categorised in 10 equal-size bins in absolute dilepton rapidity up to $|y_{ee}| = 4.0$.

The contribution of jets misidentified as electrons is suppressed using a tight electron identification and a track isolation requirement. The use of the calorimeter-based isolation and its potential improvements at HL-LHC is not considered in this study. In the forward region, the timing information provided by the HGTD is used to improve the electron isolation by rejecting additional tracks from interactions close in space, but separated in time from the hard-scatter vertex. The purity of the candidate sample is determined with simulation, and is found to be greater than 99% in the CC channel, between 90 and 98% in the CF, and between 60 and 90% in the FF channel. In the FF channel, there is a possibility that both electrons can get their charges measured wrongly, which will introduce ambiguity
to the determination of $A_{\text{FB}}$. This effect is not considered in this study, and is not expected to affect the conclusion drawn in this study, which is expressed as the relative improvement due to the inclusion of the HGTD. The signal-over-background ratio with HGTD is up to 20% higher with respect to the case of ITk only in the CF channel.

$A_{\text{FB}}$ is calculated from the selected electron pairs, and unfolded to correct for detector effects and migrations in $m_{\ell\ell}$ and $|y_{ee}|$ bins. In the CF and FF channels migrations in the $m_{\ell\ell}$ are up to 50% and 60% respectively. Various sources of uncertainty are considered. Those associated with backgrounds are mostly relevant in CF and FF channel and are estimated to be 5% on the background yield and considered uncorrelated among the $m_{\ell\ell}$ and $|y_{ee}|$ bin.

Significant uncertainties arise from knowledge of the momentum scale and resolution for the electrons. Following Reference [45] a systematic of 0.5% (0.7%) is considered to account for possible non-linearity in the energy scale of electron reconstructed in the central (forward) region with $E_{\text{T}} < 55$ GeV and up to 1.5% (2.1%) for central (forward) electron with $E_{\text{T}} > 100$ GeV.

The expected sensitivity to particle level $A_{\text{FB}}$ as a function of $m_{ee}$, for an integrated luminosity of 3000 $fb^{-1}$, is shown in green in Figure 3.28 for each channel for the chosen rapidity bin. As expected the largest asymmetry is observed in the CF channel. The extraction of $\sin^2 \theta_{\text{eff}}$ is done by minimising the $\chi^2$ value between particle-level $A_{\text{FB}}$ distributions with different weak mixing angle hypotheses, at LO in QCD, with the NNLO CT14 parton distribution function (PDF). As shown in Figure 3.28, the imperfect knowledge of the PDF results in sizeable uncertainties on $A_{\text{FB}}$, in particular in regions where the absolute values of the asymmetry is large, i.e. at high and low $m_{\ell\ell}$. On the contrary, near the Z boson mass peak, the effect of varying $\sin^2 \theta_{\text{eff}}$ is maximal, while being significantly smaller at high and low masses. Thus, in this projection a global fit is performed where $\sin^2 \theta_{\text{eff}}$ is extracted while constraining at the same time the PDF uncertainties [42]. With this analysis, the expected sensitivity of the extraction of $\sin^2 \theta_{\text{eff}}$ are respectively 25 × 10⁻⁵, 21 × 10⁻⁵ and 40 × 10⁻⁵ for the CC, CF and FF channel. The uncertainty of the results is dominated by the currently limited knowledge of the PDFs. If looking purely at the experimental uncertainties, including the HGTD in the ATLAS forward region brings a 13% improvement on the $\sin^2 \theta_{\text{eff}}$ sensitivity in the CF channel. Combining the three channels together the expected sensitivity reaches a precision of $\Delta \sin^2 \theta_{\text{eff}} = 18 \times 10^{-5}$ (±16 × 10⁻⁵ (PDF) ± 9 × 10⁻⁵ (exp.)) which exceeds the precision achieved in all previous single-experiment results so far.

### 3.4.4 Impact of the luminosity uncertainty

Many high-precision cross section measurements at the HL-LHC will be limited by the uncertainty in the integrated luminosity. That uncertainty affects not only the normalisation of the signal, but also that of any background not determined from data, thus enters cross-section measurements in a twofold way. At the ECFA HL-LHC Experiments Workshop in
3 Performance and Physics Benchmarks

<figure><img src="image_54.png" /><figcaption>Figure 3.28: Distribution of $\Delta A_{FB}$ as a function of mass for the CC, CF and FF channels. The filled bands correspond to the experimental sensitivity with and without the HGTD. The solid red lines correspond to a variations of $\sin^2 \theta_{\text{eff}}$ corresponding to $40 \times 10^{-5}$. The dashed blue lines illustrate the total error from CT14 NNLO PDF. Overlaid green line shows the particle-level $A_{FB}$ distribution.</figcaption></figure>
Aix-Les-Bains in 2016, it was stated that “Experimental progress on luminosity determination may be the keystone for precision physics at the HL-LHC”. This applies to the Higgs boson physics programme, where the luminosity uncertainty could be the dominant source of systematic uncertainty unless the error is reduced to approximately 1% (compared to the best measurement of 1.7% for ATLAS in Run-2 [46]), despite the much harsher environment for the luminosity measurement at the HL-LHC. The percentage precision of the luminosity measurement is also critical for measuring important SM processes, such as W and Z boson production, and single and pair production of top quarks. Further information about the expected performance of the luminosity determination at the HL-LHC can be found in Ref. [36].

The HGTD has been designed with luminosity determination capabilities in mind from the beginning, and a few unique capabilities will provide important information that can help constrain the total luminosity uncertainty to a low level. With its relatively low occupancy even at the highest anticipated luminosities, the detector response is nearly perfectly linear as a function of $\langle\mu\rangle$ (see Section 10.3). This characteristic, combined with being able to operate both at the low interaction rates during a van der Meer scan and at $\langle\mu\rangle = 200$, can help constrain the significant uncertainty component otherwise incurred when extrapolating from low to high $\langle\mu\rangle$. Secondly, the timing resolution of the HGTD allows measuring and subtracting difficult transient backgrounds in the high-radiation environment. The uncertainties of such backgrounds (e.g. so-called *afterglow*) can otherwise limit the precision of methods relying on hit- or track-counting techniques. Finally, the HGTD will have a dedicated readout path for sending occupancy data for each module at 40 MHz, allowing bunch-by-bunch luminosity measurements online without trigger bias. This is important for promptly feeding back luminosity information to the machine for luminosity-levelling purposes which are of increased importance at the HL-LHC. The technical details of the implementation of the luminosity capabilities, including the method and treatment of systematic uncertainties, are given in Section 10.3. The description of the occupancy readout in the ASIC is given in Chapter 6.

As input to the update to the European Strategy for Particle Physics in 2020, the expected performance for many analyses at the HL-LHC was studied both in ATLAS and CMS [47]. Unfortunately, there is no breakdown of the impact of individual sources of systematic uncertainties for any of the ATLAS combined Higgs boson measurements. Such breakdowns exist however for some of the single-channel measurements. Since the Higgs boson analyses cannot constrain the uncertainty on the luminosity, it is straightforward to compare any value for the luminosity uncertainty to the magnitude of the other uncertainties affecting these analyses.

Table 3.1 lists the largest sources of uncertainty, aside from integrated luminosity, affecting three important Higgs boson cross section measurements; gluon-fusion ($ggH$) production of Higgs bosons with decays to $\gamma\gamma$ and $ZZ^*$, and combined gluon-fusion and vector boson fusion (VBF) production of Higgs bosons with decay to $\tau\tau$. For all these measurements,
### 3 Performance and Physics Benchmarks

an uncertainty of 2% on the integrated luminosity would be the single largest source of uncertainty on the results.

<table><caption>Table 3.1: List of dominant uncertainties (excluding the uncertainty on the integrated luminosity) affecting various expected Higgs boson cross section results at the HL-LHC using 3000 fb⁻¹ of data. An uncertainty on the luminosity measurement of 2% would be the dominant source of uncertainty for all these measurements.</caption><thead><tr><td>Analysis channel</td><td>Largest uncertainty</td><td>Δσ/σ<sub>SM</sub></td></tr></thead><tbody><tr><td>Cross section for ggH(→ γγ)</td><td>Photon isolation efficiency</td><td>1.9%</td></tr><tr><td>Cross section for ggH(→ ZZ*)</td><td>Electron eff. reco. total</td><td>1.5%</td></tr><tr><td>Cross section for ggH + VBF, H → ττ</td><td>QCD scale ggH, p<sub>T</sub><sup>H</sup> ≥ 120 GeV</td><td>1.7%</td></tr></tbody></table>

The above considerations illustrate the importance of a precise luminosity measurement for the Higgs boson physics programme at the HL-LHC. The same concerns apply to any measurement of processes with similar, or larger, cross sections compared to the Higgs boson.

Finally, it is important to stress that precision in the luminosity programme can only be achieved by having several independent luminosity detectors, and that any single detector will not be able to achieve the precision goals. With readout at 40 MHz, and with occupancy determination in a dedicated sideband time window (further described in Section 6.2.1), the HGTD has unique capabilities compared to other silicon detectors. These are aimed at constraining the sources of systematic uncertainties affecting the luminosity determination to the percent level or better.

### 3.4.5 Trigger for magnetic monopole searches

Magnetic monopoles (single pole of magnetic charge) are hypothetical elementary particles which appear in several models beyond the Standard Model [48–51]. Monopoles would appear as long-lived particles which would give dramatic ionisation since a monopole with one Dirac unit of magnetic charge charge, DC 1, is ionisation-wise equivalent to an electric charge of 68.5e. Searches for monopoles have been conducted with the ATLAS detector for central signature in the electromagnetic calorimeter [52–54], and with the dedicated MoEDAL experiment at LHCb [55].

However, according to a recent review, the exclusion limits presented in the previous sentence do not apply for scenarios with monopoles with $m < 200$ GeV [56]. The HGTD could enhance the monopoles discovery capability of ATLAS in HL-LHC by providing an online trigger to highly ionising particle. The HGTD response to single monopoles with a mass of 200 GeV and magnetic charges of 1 DC and 2 DC was simulated. The distribution of simulated hit energies in the HGTD for a single monopole event is shown in Figure 3.29(a). Single high-energy HGTD hits from monopoles are clearly separated from the deposits from
<figure><img src="image_55.png" /><figcaption>Figure 3.29: (a) Energies of simulated hits in HGTD in one single monopole event. (b) Distributions of hit energies in simulated events of minimum bias interactions and single-particle samples with pions and monopoles.</figcaption></figure>

MIPs as seen in Figure 3.29(b). This can provide a clear and unique signature that can be exploited by HGTD electronics to recognise candidate Monopole events at trigger level. The HGTD will send hit summary data at 40 MHz to a dedicated luminosity processing system (Section 10.3) so a special bit can be added to flag high-energy depositions in a single pad. If one channel reports such a high-energy deposit, the corresponding readout ASIC will report a reserved word in place of the luminosity hit counts. If the off-detector luminosity processing electronics receives such a signal, it will send a special trigger signal to the Central Trigger Processor, and dedicated algorithms implemented in software in the Event Filter can investigate the event further. The detection of very high-energy hits requires modifications to the ALTIROC (Chapter 6) readout chip (addition of a second very high threshold discriminator, Section 6.2), and is not included in the current baseline design. If not realised for the nominal ALTIROC, the proposed functionality could be implemented in future versions of the HGTD readout and be installed with the scheduled module-ring replacements.

### 3.4.6 Limitations in the Monte Carlo modeling

Finally, two aspects of the simulated Monte Carlo samples used for these studies are worth discussing.

Modeling the jet activity in the forward region is challenging as the current trackers in ATLAS and CMS only extend to $|η| < 2.5$. Charged-particle multiplicities in inelastic proton–proton collisions have been measured in this region using the *Minimum-Bias Trigger Scintillator* detector [57], and transverse energy flow using calorimeter measurements [58], both indicating the shortcomings of the standard ATLAS PYTHIA tunes when it comes to describing
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forward activity. Studies in high-pileup data in Run 2 show significant discrepancies with more forward jet activity than predicted by the simulations tuned to data recorded at low $\mu$. Several mechanisms could contribute to this discrepancy, ranging from poor modeling of the particle-level process to effects of calorimeter calibration affecting seeding of energy clusters in the forward region during reconstruction. While it is likely that several factors conspire to give rise to this discrepancy, which grows rapidly with $\mu$, it cannot be excluded that the minimum-bias events used to simulate pileup interactions in the samples used for the studies in this document severely underestimate the forward jet activity expected at the HL-LHC. This would imply more background, and a stronger need for the HGTD.

In addition, the samples used for the studies in this chapter have a spatial beam-spot spread of $\sigma_z \approx 50$ mm. In the scenarios under discussion for HL-LHC operation, the beam spot extension in z would plateau at slightly lower values around 40 mm, yielding ~10% higher vertex densities. A beam spot that is more spatially compressed makes it more challenging to do pileup suppression with the ITk alone, and the relative improvement from HGTD would likely be larger.
# 4 Technical Overview

## 4.1 Introduction

This chapter summarizes the fundamental aspects of the design of the HGTD. The main requirements that drive the design and the proposed technical solutions are discussed in this chapter. Measurements from the on-going R&D program are presented, especially on sensors and electronics, that demonstrate the achieved performance.

## 4.2 Detector overview and key requirements

The detector has been designed for operation with 200 proton-proton collisions per bunch crossing and a total integrated luminosity of 4000 fb⁻¹. The HGTD will be located in the gap region between the end of the ITK and the end-cap calorimeter, at a distance of approximately ±3.5 m from the interaction point. Figure 4.1 shows a transverse view of the detector, without the front cover of the vessel, where the front layer of the first double-sided active layer (in blue) and the peripheral electronics boards (PEBs) location(in green) can be seen. The envelope of the detector vessel has a radial extent of 110 to 1000 mm. The envelope in z, including the moderator, supports and front and rear vessel covers is 125 mm. This includes the moderator that is placed behind the HGTD with a total thickness of 50 mm, to reduce the back-scattered neutrons created in the end-cap/forward calorimeters, protecting both the ITk and the HGTD. Each end-cap is made of one hermetic vessel, two instrumented double-sided layers (mounted in two cooling/support disks), and two moderator pieces placed inside and outside the hermetic vessel. The weight of an end-cap is approximately 350 kg. The moderator, whose mass is equally distributed between the pieces located inside and outside the vessel, contributes to 150 kg.

The front vessel cover and each cooling/support disk are physically separated in two half circular disks to enable the opening of the detector in the presence of the beam pipe.

The active detector element is made of Low-Gain Avalanche Silicon Detectors (LGADs) read-out by dedicated front-end electronics ASICs (ALTIROC). It covers the pseudo-rapidity range $2.4 < |η| < 4.0$ (120 mm $< R < 640$ mm). The active area is divided into three rings (inner, middle and outer ring). The inner ring covering the region $3.5 < |η| < 4.0$ (120 mm $< R < 230$ mm) is equipped with modules mounted on the front and back sides of a given
cooling plate, with 70 % overlap along the readout row direction, in order to provide on average 2.7 hits per track in the most irradiated and highest occupancy region.

The middle ring covering the region $2.7 < |η| < 3.5$ (230 mm $< R < 470$ mm) is equipped with modules overlapping 54% providing on average 2.5 hits per track. The outer ring covering the region $2.4 < |η| < 2.7$ (470 mm $< R < 640$ mm) is equipped with modules overlapping only 20% providing on average 2.1 hits per track.

<figure><img src="image_56.png" /><figcaption>Figure 4.1: Front view of the detector. The active detector region is defined by the three rings and is surrounded by a green area where the PEBs are located, except in two areas needed for the CO₂ cooling manifolds.</figcaption></figure>

### 4.2.1 Expected Radiation levels

As discussed in Chapter 2, the radiation levels in the forward region exceed the radiation hardness of both the sensors and the front-end electronics, especially at low radius. In order to assure high performance operation during the full life time of the HL-LHC, the
plan is to replace the innermost ring after each $1000 \text{ fb}^{-1}$ (3 times in total) and the middle ring after $2000 \text{ fb}^{-1}$ (once), during long shutdowns. It is expected that improvement of the LGAD performance with respect to radiation hardness is possible and the plan would be to target slightly more demanding specifications for the inner ring replacement detector to be delivered during LS5. Figure 4.2(a) and Figure 4.2(b) show respectively the expected 1 MeV neutron-equivalent fluence and TID as a function of the detector radius with the most updated simulation of the ATLAS detector. A safety factor of 1.5 is applied to account for uncertainties in the simulation$^1$. An additional safety factor of 1.5 is applied to the total ionising dose (TID) to account for low-dose rate effects on the ASICs. In the inner ring the total Si 1MeV neq has a similar contribution from neutrons and charged particles while in the middle and outer rings the dominant effect comes from neutrons, as seen in Figure 2.14.

<figure><img src="image_57.png" /><figcaption>Figure 4.2: Expected Si1MeV$_{neq}$ radiation levels in HGTD, using Fluka simulations, as a function of the radius considering a replacement of the inner ring every $1000 \text{ fb}^{-1}$ and the middle ring replaced at $2000 \text{ fb}^{-1}$. These curves included a safety factor (SF) of 1.5 to account for simulation uncertainty. An additional safety factor of 1.5 is applied to the TID to account for low dose-rate effects on the electronics, leading to a safety factor of 2.25.</figcaption></figure>

The exact radial transition between the three rings will be optimised for the final detector layout, once the FLUKA simulations will be updated with the final ITk layout, and the radiation hardness of the final sensors and ASICs are re-evaluated. The requirement is a maximal fluence and TID not exceeding 2 MGy and $2.5 \times 10^{15} \text{ n}_{\text{eq}} / \text{cm}^2$ respectively.

<footnote>$^1$This safety factor takes into account the comparison between the Run-1 and Run-2 fluences and the simulation, as well as a possible inaccurate detector description used by FLUKA/GEANT4</footnote>
### 4.2.2 Key requirements

A high intrinsic single hit efficiency is essential throughout the lifetime of the HGTD. This puts stringent constraints on the smallest charge to be delivered after irradiation. Taking into account the lowest expected threshold of the electronics discriminator, a minimal charge of 4 fC is required to be delivered by the sensors after irradiation. In addition, a signal-over-noise (S/N) larger than 7 (from testbeam studies), while keeping a low rate of fake hits induced by the electronics noise (< 0.1 %), is needed. As measured with testbeam, in these conditions an efficiency larger than 95% can be obtained.

The target time resolution per track, combining multiple hits, is from 30 ps at the start of lifetime to 50 ps after 4000 fb⁻¹. To achieve this performance, the time resolution per hit should be about 35 ps at the start of lifetime and not worse than 70 ps at the end of lifetime over the full surface of the detector.

The main contributions to the time resolution of a hit are given by:

$$ \sigma_{\text{hit}}^2 = \sigma_{\text{Landau}}^2 + \sigma_{\text{elec}}^2 + \sigma_{\text{clock}}^2 \quad (4.1) $$

* where $\sigma_{\text{Landau}}$ is the time resolution contribution induced by the Landau fluctuations in the deposited charge as the charged particle traverses the sensor

* $\sigma_{\text{elec}}$ is the contribution from the electronics read-out (jitter and time-walk). It is required to be about 25 ps for a particle at its minimum of ionisation (MIP) with a LGAD gain of 20 (corresponding to a charge of 10 fC) at the start of the HL-LHC, and at most 70 ps after 4000 fb⁻¹ for a charge of 4 fC. The TDC contribution is expected to be negligible;

* $\sigma_{\text{clock}}$ is the non-deterministic jitter contribution from the clock distribution, expected to be smaller than 15 ps after calibration.

In addition, the detector should be able to distinguish hits in the same pad that come from consecutive bunch crossings and should provide the sum of the number of hits per ASIC for each bunch crossing. The latter is used in the luminosity measurement.

### 4.2.3 Read-out bandwidth

With the baseline ATLAS architecture, the ATLAS detector is read-out with a single Level-0 (L0) trigger at an maximum rate of 1 MHz, with a maximum latency of 10 µs [59]. The time information of the HGTD hit cells will be read out on reception of this L0 trigger signal. In the evolved scheme considered by ATLAS, called L0-L1, the HGTD will be read-out on the reception of a L1 trigger signal with a maximum frequency of 800 kHz and a maximum latency of 35 µs. The time information from each ASIC is read-out by only one data e-link to the lpGBT [60] (Section 9.1.1). Therefore the maximal bandwidth is limited to 1.28 Gbit s⁻¹.
The luminosity data is transmitted at each bunch crossing to dedicated lpGBTs, requiring a 640 Mbit s⁻¹ e-link bandwidth (Table 6.1).

<figure><img src="image_58.png" /><figcaption>Figure 4.3: View of an HGTD hybrid module equipped with its read-out flex cable tail. The bare module, glued on the flex cable, is made of a 4 × 2 cm² sensor with two bump bonded ASICs. The signal lines of the ASIC are wire bonded on one side of the module flex, while the bias voltage of the sensor is provided to the back-side of the sensor through a hole in the module flex.</figcaption></figure>

## 4.3 Hybrid HGTD module

Figure 4.3 shows a view of a hybrid module made of two parts: a LGAD sensor and two ASICs, called a bare module, and the flexible printed circuit board (flex cables). The flex is made of two pieces, a small flex board permanently glued to the bare module and a long flex tail whose length, of up to about 60 cm, depends on the module position in the detector. The sensor and the ASICs are connected through a flip-chip bump bonding process called hybridization. All connections between the ASIC and the peripheral electronics are routed through the flex cable. The bare module is glued on the back side of the sensor to the flex module small piece, and all the signals are wire bonded between the ASIC and the flex cable and for the high voltage between the sensor and the flex.

The characteristics of the bare modules are:

* The size of the bare modules, all identical, is approximately 2 × 4 cm² and each bare module contains 450 pads (15x30). Its size has been defined to optimize the coverage
at the inner radius and to provide a good yield for the hybridization process. The nominal total number of bare modules is 8032.

* The size of the pad, 1.3 × 1.3 mm², is the result of a compromise between smaller pads, leading to lower occupancy and smaller capacitance and thus low electronics jitter, and larger pads, which provide better geometric coverage with large fill factors and less power dissipation from the ASIC.

* The sensor is connected to two ASICs, each of them reading a matrix of 225 (15x15) pads. The size of the ASIC is about 20 × 22 mm².

The status of the R&D of key components is discussed briefly below, with more technical details in subsequent chapters.

### 4.3.1 Sensors

The sensors are based on LGAD technology, pioneered six years ago by the Centro Nacional de Microelectrónica (CNM) Barcelona [5] in close collaboration with the RD50 collaboration.

LGADs are n-on-p silicon detectors containing an extra highly-doped p-layer below the n-p junction to create a high field which causes internal amplification as displayed in Figure 4.4(a). When a charged particle crosses the detector, an initial current is created by the drift of the electrons and holes in the silicon. When the electrons reach the amplification region, new electron/hole pairs are created and the holes drift towards the $p^+$ region and generate a large current. This charge amplification is referred as the gain of the LGAD. This current, much larger than in a standard diode, is the key ingredient to get an excellent time resolution for energy deposited by Minimum Ionizing Particles (MIP). The expected currents for different irradiation levels (therefore different gains) are presented in Figure 4.4(b). For large gain, the rise time is about 500 ps and the signal duration is approximately 1 ns. When the irradiation neutron fluence increases, the charge is smaller and the rise time and the signal duration are shorter.

After amplification in the gain layer, the height of the LGAD signal is proportional to the gain. On the other hand, the slope $dV/dt$ depends on the thickness of the sensor, favouring thin sensors since the electronics jitter scales as the inverse of the slope. However, the jitter also depends linearly on the detector pad capacitance, therefore limiting the potential use of very thin sensors. Consequently, the optimal thickness relies strongly on the performance of the read-out ASIC. The baseline active thickness has been chosen to be 50 µm while the total thickness is 250 µm. The pad size is 1.3 × 1.3 mm² which resulted from an optimization discussed in the previous section.

Over the last five years LGAD sensors have been produced by CNM/Spain, HPK/Japan, FBK/Italy and recently NDL/China with different doping level, active thickness, pad size,
<figure><img src="image_59.png" /><figcaption>Figure 4.4: Cross section of an LGAD (a) and simulated signal current in LGADs at start and after full integrated neutron fluence (b).</figcaption></figure>

and inter-pad gaps. These detectors have been exposed to protons, neutrons and X-rays up to the expected maximum radiation levels (including the safety factors) and intensively characterized in the laboratory (with probe station, $\beta$ source, laser) or in beam tests (at CERN, DESY, FERMILAB).

Under irradiation, the expected decrease of the charge yield can be mitigated by increasing the bias voltage (up to 750 V operation voltage) and operating at low temperature (–30 °C). Figure 4.5 summarizes results obtained in the laboratory, with dedicated electronics, for sensors from different producers exposed to a neutron fluence up to $2.5 \times 10^{15} \text{ n}_{\text{eq}} \text{ cm}^{-2}$. A charge of 4 fC can be reached up to a fluence of $3 \times 10^{15} \text{ n}_{\text{eq}} \text{ cm}^{-2}$ (Section 5.5.3), providing a time resolution smaller than 70 ps per hit (Section 5.5.5). The performance of sensors from all manufacturers is similar, even if before irradiation the optimal operating bias voltage might be different because the doping profile is different. With a minimal charge of about 4 fC and a discriminator threshold of about 2 fC, a hit efficiency of at least 95% is expected. For the largest fluence, the Boron doping in the gain region has been mostly inactivated and half of the remaining reduced gain is supplied by the bulk diode, due only to the large high bias voltage applied. The time resolution in this domain is fully dominated by the electronics jitter, thus dominated by the ASIC performance at low charge.

Intense R&D is still ongoing to improve the radiation hardness with deep narrow doping implantation and carbon (C) implantation. Depending on the results of these studies, discussed in detail in Chapter 5, the exact radius of the inner and middle rings might be optimized. The operating voltage ($V_{op}$) needs to be adjusted with respect to the radiation flux.