Looking inside jets: an introduction to jet substructure and boosted-object phenomenology Simone Marzani1, Gregory Soyez2, and Michael Spannowsky3 1Dipartimento di Fisica, Universit`adi Genova and INFN, Sezione di Genova, Via Dodecaneso 33, 16146, Italy 2IPhT, CNRS, CEA Saclay, Universit´eParis-Saclay, F-91191 Gif-sur-Yvette, France 3Institute of Particle Physics Phenomenology, Physics Department, Durham University, Durham DH1 3LE, UK arXiv:1901.10342v3 [hep-ph] 17 Feb 2020 Preface The study of the internal structure of hadronic jets has become in recent years a very active area of research in particle physics. Jet substructure techniques are increasingly used in experimental analyses by the Large Hadron Collider collaborations, both in the context of searching for new physics and for Standard Model measurements. On the theory side, the quest for a deeper understanding of jet substructure algorithms has contributed to a renewed interest in all-order calculations in Quantum Chromodynamics (QCD). This has resulted in new ideas about how to design better observables and how to provide a solid theoretical description for them. In the last years, jet substructure has seen its scope extended, for example, with an increasing impact in the study of heavy-ion collisions, or with the exploration of deep-learning techniques. Furthermore, jet physics is an area in which experimental and theoretical approaches meet together, where cross-pollination and collaboration between the two communities often bear the fruits of innovative techniques. The vivacity of the field is testified, for instance, by the very successful series of BOOST conferences together with their workshop reports, which constitute a valuable picture of the status of the field at any given time. However, despite the wealth of literature on this topic, we feel that a comprehen- sive and, at the same time, pedagogical introduction to jet substructure is still missing. This makes the endeavour of approaching the field particularly hard, as newcomers have to digest an increasing number of substructure algorithms and techniques, too often characterised by opaque terminology and jargon. Furthermore, while first-principle cal- culations in QCD have successfully been applied in order to understand and characterise the substructure of jets, they often make use of calculational techniques, such as resum- mation, which are not the usual textbook material. This seeded the idea of combining our experience in different aspects of jet substructure phenomenology to put together this set of lecture notes, which we hope could help and guide someone who moves their first steps in the physics of jet substructure. 1 2 Acknowledgements Most of (if not all) the material collected in this book comes from years of col- laboration and discussions with excellent colleagues that helped us and influenced us tremendously. In strict alphabetical order, we wish to thank Jon Butterworth, Mat- teo Cacciari, Mrinal Dasgupta, Frederic Dreyer, Danilo Ferreira de Lima, Steve Ellis, Deepak Kar, Roman Kogler, Phil Harris, Andrew Larkoski, Peter Loch, David Miller, Ian Moult, Ben Nachman, Tilman Plehn, Sal Rappoccio, Gavin Salam, Lais Schunk, Dave Soper, Michihisa Takeuchi, Jesse Thaler, and Nhan Tran. We would also like to thank Frederic Dreyer, Andrew Lifson, Ben Nachman, Davide Napoletano, Gavin Salam and Jesse Thaler for helpful suggestions and comments on the manuscript. Contents 1 Introduction and motivation5 2 Introduction to QCD at Colliders 11 2.1 The theory of strong interactions . 11 2.2 Generalities on perturbative calculations . 16 2.3 Factorisation in the soft and collinear limits . 18 2.4 Infra-red and collinear safety . 22 2.5 Hadron collider kinematics . 24 3 Jets and jet algorithms 26 3.1 The concept of jets . 26 3.2 Sequential recombination algorithms . 28 3.3 Cone algorithms . 30 3.4 Experimental aspects . 33 3.5 Implementation . 37 4 Calculations for jets: the jet mass distribution 39 4.1 The one-loop calculation . 40 4.2 Going to all orders . 43 4.3 From e+e− to hadron-hadron collisions . 57 5 Jet substructure: concepts and tools 63 5.1 General guiding principles . 63 5.2 Assessing performance . 64 5.3 Prong-finders and groomers . 67 5.4 Radiation constraints . 72 5.5 Combinations of tools . 78 5.6 Other important tools . 81 5.7 Code Availability . 87 6 Calculations for the jet mass with grooming 88 6.1 mMDT/ SoftDrop mass . 88 3 CONTENTS 4 6.2 Other examples: trimming and pruning . 93 6.3 Comparison to Monte Carlo . 101 6.4 Calculations for signal jets . 106 7 Quark/gluon discrimination 113 7.1 Angularities, ECFs and Casimir scaling . 114 7.2 Beyond Casimir scaling with Iterated SoftDrop . 120 7.3 Performance and robustness . 124 8 Two-prong tagging with jet shapes 129 8.1 A dive into analytic properties . 129 8.2 Comparison to Monte Carlo simulations . 144 8.3 Performance and robustness . 148 9 Curiosities: Sudakov Safety 154 9.1 The groomed jet radius distribution θg ................... 155 9.2 The zg distribution . 157 10 Searches and Measurements 163 10.1 Tagging performance studies . 163 10.2 Measurements of jet observables . 168 10.3 Search for boosted Higgs boson in the SM . 172 10.4 Searches for new physics . 172 11 Take-home messages and perspectives 180 A Details of analytic calculations 183 B Details of Monte Carlo simulations 188 Bibliography 189 Chapter 1 Introduction and motivation The Large Hadron Collider (LHC) at CERN is the largest and most sophisticated ma- chine to study the elementary building blocks of nature ever built. At the LHC protons are brought into collision with a large centre-of-mass energy | 7 and 8 TeV for Run I (2010-13), 13 TeV for Run II (2015-18) and 14 TeV from Run III (starting in 2021) on- wards | to resolve the smallest structures in a controlled and reproducible environment. As protons are not elementary particles themselves, but rather consist of quarks and gluons, their interactions result in highly complex scattering processes, often with final state populated with hundreds of particles, which are measured via their interactions with particle detectors. Jets are collimated sprays of hadrons, ubiquitous in collider experiments, usually associated with the production of an elementary particle that carries colour charge, e.g. quarks and gluons. Their evolution is governed by the strong force, which within the Standard Model of particle physics is described by Quantum Chromodynamics (QCD). The parton (i.e. quark or gluon) that initiates a jet may radiate further partons and produce a (collimated) shower of quarks and gluons, a so-called parton shower, that eventually turn into the hadrons (π, K, p, n,...) observed in the detector. The vast majority of LHC events (that one is interested in) contain jets. They are the most frequently produced and most complex objects measured at the LHC multipurpose experiments, ATLAS and CMS. When protons collide inelastically with a large energy transfer between them, one can formally isolate a hard process at the core of the collision, which involves one highly- energetic parton from each of the two protons. These two partons interact and produce a few elementary particles, like two partons, a Higgs boson associated with a gluon, a top{ anti-top pair, new particles, ... Since the energy of this hard process is large, typically between 100 GeV and several TeV, there is a large gap between the incoming proton scale and the hard process on one hand, and between the hard process and the hadron scale on the other. This leaves a large phase-space for parton showers to develop both in the initial and final state of the collision. This picture is clearly a simplification because we can imagine that secondary parton-parton interactions might take place. These multi- 5 CHAPTER 1. INTRODUCTION AND MOTIVATION 6 parton interactions constitute what is usually referred to as the Underlying Event. To complicate things further, the LHC does not collide individual protons, but bunches of (1011) protons. During one bunch crossing it is very likely that several of the protons scatterO off each other. While only one proton pair might result in an event interesting enough to trigger the storage of the event on tape, other proton pairs typically interact to give rise to hadronic activity in the detectors. This additional hadronic activity from multiple proton interactions is called pileup. On average, radiation from pileup is much softer than the jets produced from the hard interaction, but for jet (and jet substructure) studies it can have a significant impact by distorting the kinematic relation of the jet with the hard process. In recent years the detailed study of the internal structure of jets has gained a lot of attention. At LHC collision energy electroweak (EW) scale resonances, such as the top quark, W/Z bosons and the Higgs boson, are frequently produced beyond threshold, i.e. their energy (transverse momentum) can significantly exceed their mass. Therefore, analyses and searching strategies developed for earlier colliders, in which EW- scale particles were produced with small velocity, have to be fundamentally reconsidered. Because EW resonances decay dominantly into quarks, when they are boosted, their decay products can become collimated in the lab-frame and result in one large and massive jet, often referred to as a fat jet. Initially such a configuration was considered disadvantageous in separating processes of interest (i.e. processes which included EW resonances) from the large QCD backgrounds (where jets are abundantly produced from high-energy quarks and gluons). However, with the popularisation of sequential jet clustering algorithms retaining the full information of the jet's recombination history, it transpired that one can use the internal structure of jets to tell apart jets that were induced by a decaying boosted EW resonance or by a QCD parton.