We introduce the energy flow polynomials: a complete set of jet substructure observables which form a discrete linear basis for all infrared- and collinear-safe observables. Energy flow polynomials are multiparticle energy correlators with specific angular structures that are a direct consequence of infrared and collinear safety. We establish a powerful graph-theoretic representation of the energy flow polynomials which allows us to design efficient algorithms for their computation. Many common jet observables are exact linear combinations of energy flow polynomials, and we demonstrate the linear spanning nature of the energy flow basis by performing regression for several common jet observables. Using linear classification with energy flow polynomials, we achieve excellent performance on three representative jet tagging problems: quark/gluon discrimination, boosted W tagging, and boosted top tagging. The energy flow basis provides a systematic framework for complete investigations of jet substructure using linear methods.
This study used the recent ATLAS jet substructure measurements to see if any improvements can be made to the commonly used Pythia8 Monash and A14 tunes.
In this paper we introduce a new approach to study jet substructure in the center-of-mass frame of the jet. We demonstrate that it can be used to discriminate the boosted heavy particles from the QCD jets and the method is complimentary to the existing other jet substructure algorithms. Applications to searches for hadronically decaying W/Z+jets and heavy resonance that decays to a WW final state are also discussed.
A number of recent applications of jet substructure, in particular searches for light new particles, require substructure observables that are decorrelated with the jet mass. In this paper we introduce the Convolved SubStructure (CSS) approach, which uses a theoretical understanding of the observable to decorrelate the complete shape of its distribution. This decorrelation is performed by convolution with a shape function whose parameters and mass dependence are derived analytically. We consider in detail the case of the $D_2$ observable and perform an illustrative case study using a search fo…
Even though jet substructure was not an original design consideration for the Large Hadron Collider (LHC) experiments, it has emerged as an essential tool for the current physics program. We examine the role of jet substructure on the motivation for and design of future energy frontier colliders. In particular, we discuss the need for a vibrant theory and experimental research and development program to extend jet substructure physics into the new regimes probed by future colliders. Jet substructure has organically evolved with a close connection between theorists and experimentalists and has …
We present an alternative approach to identifying and characterizing jet substructure. An angular correlation function is introduced that can be used to extract angular and mass scales within a jet without reference to a clustering algorithm. This procedure gives rise to a number of useful jet observables. As an application, we construct a top quark tagging algorithm that is competitive with existing methods.
We present a new tagger which aims at identifying partially reconstructed objects, in which only some of the constituents are collected in a single jet. As an example, we focus on top decays in which either part of the hadronically decaying W or the b jet is soft or falls outside of the top jet cone. We construct an observable to identify remnant substructure from the decay and employ aggressive jet grooming to reject QCD backgrounds. The tagger is complementary to existing ones and works well in the intermediate boost regime where jet substructure techniques usually fail. It is anticipated th…
QCD is often the dominant background to new physics searches for which jet substructure provides a useful handle. Due to the challenges associated with modeling this background, data-driven approaches are necessary. This paper presents a novel method for determining QCD predictions using templates -- probability distribution functions for jet substructure properties as a function of kinematic inputs. Templates can be extracted from a control region and then used to compute background distributions in the signal region. Using Monte Carlo, we illustrate the procedure with two case studies and sh…
Semi-visible jets arise in strongly interacting dark sectors, where parton evolution includes dark sector emissions, resulting in jets overlapping with missing transverse momentum. The implementation of semi-visible jets is done using the Pythia Hidden valley module to duplicate the QCD sector showering. In this work, several jet substructure observables have been examined to compare semi-visible jets and light quark/gluon jets. These comparisons were performed using different dark hadron fraction in the semi-visible jets (signal). The extreme scenarios where signal consists either of entirely…
We explore the scale-dependence and correlations of jet substructure observables to improve upon existing techniques in the identification of highly Lorentz-boosted objects. Modified observables are designed to remove correlations from existing theoretically well-understood observables, providing practical advantages for experimental measurements and searches for new phenomena. We study such observables in $W$ jet tagging and provide recommendations for observables based on considerations beyond signal and background efficiencies.
We present an investigation of the dependence of searches for boosted Higgs bosons using jet substructure on the perturbative and non-perturbative parameters of the Herwig++ Monte Carlo event generator. Values are presented for a new tune of the parameters of the event generator, together with the an estimate of the uncertainties based on varying the parameters around the best-fit values.
We use public data from the CMS experiment to study the 2-prong substructure of jets. The CMS Open Data is based on 31.8/pb of 7 TeV proton-proton collisions recorded at the Large Hadron Collider in 2010, yielding a sample of 768,687 events containing a high-quality central jet with transverse momentum larger than 85 GeV. Using CMS's particle flow reconstruction algorithm to obtain jet constituents, we extract the 2-prong substructure of the leading jet using soft drop declustering. We find good agreement between results obtained from the CMS Open Data and those obtained from parton shower gen…
We investigate a potential of measuring properties of a heavy resonance X, exploiting jet substructure techniques. Motivated by heavy higgs boson searches, we focus on the decays of X into a pair of (massive) electroweak gauge bosons. More specifically, we consider a hadronic Z boson, which makes it possible to determine properties of X at an earlier stage. For $m_X$ of O(1) TeV, two quarks from a Z boson would be captured as a "merged jet" in a significant fraction of events. The use of the merged jet enables us to consider a Z-induced jet as a reconstructed object without any combinatorial a…
In this paper we study the identification of boosted hadronically decaying top quarks using jet substructure in the center-of-mass frame of the jet. We demonstrate that the method can greatly reduce the QCD jet background while maintaining high identification efficiency of the boosted top quark even in a very high pileup condition. Applications to searches for heavy resonances that decay to a $t\bar{t}$ final state are also discussed.
We present a perturbative QCD factorization formula for substructures of an energetic Higgs jet, taking the energy profile resulting from the $H\to b\bar b$ decay as an example. The formula is written as a convolution of a hard Higgs decay kernel with two $b$-quark jet functions and a soft function that links the colors of the two $b$ quarks. We derive an analytical expression to approximate the energy profile within a boosted Higgs jet, which significantly differs from those of ordinary QCD jets. This formalism also extends to boosted $W$ and $Z$ bosons in their hadronic decay modes, allowing…
Future experiments beyond the LHC era will measure high-momentum bosons ($W$, $Z$, $H$) and top quarks with strongly collimated decay products that form hadronic jets. This paper describes the studies of the performance of jet substructure variables using the Geant4 simulation of a detector designed for high energy $pp$ collisions at a 100 TeV collider. The two-prong jets from $Z' \rightarrow WW$ and three-prong jets from $Z' \rightarrow t\bar{t}$ are compared with the background from light quark jets, assuming $Z'$ masses in the range 5 -- 40 TeV. Our results indicate that the performance of …
It is a challenge for the theoretical particle physicists to perform the phenomenology of the Beyond Standard Model (BSM) theories using advanced simulations which can mimic the experimental environment at the colliders as closely as possible. In collider phenomenology jet substructure is a concept that is used frequently to analyse the properties of the jets, characterised as a cluster of hadrons, which is often the end result of particle collisions at the colliders, such as Large Hadron Collider (LHC). A vast literature on jet substructure exists both from the theory and experimental point o…
We initiate the study of the time substructure of jets, motivated by the fact that the next generation of detectors at particle colliders will resolve the time scale over which jet constituents arrive. This effect is directly related to hadronization, which transforms partons into massive hadrons with a distribution of velocities. We review the basic predictions for the velocity distribution of jet hadrons, and suggest an application for this information in the context of boosted object tagging. By noting that the velocity distribution is determined by the properties of the color string which …
Looking inside jets: an introduction to jet substructure and boosted-object phenomenology
Università di Genova（热那亚大学）；INFN, Sezione di Genova（意大利国家核物理研究所热那亚分部）；IPhT, CNRS, CEA Saclay, Université Paris-Saclay（巴黎萨克雷大学）；Institute of Particle Physics Phenomenology, Physics Department, Durham University（杜伦大学）
Precision Jet Substructure of Boosted Boson Decays with Energy Correlators
Massachusetts Institute of Technology（麻省理工学院）；SLAC National Accelerator Laboratory, Stanford University（斯坦福大学斯坦福直线加速器中心）；Yale University（耶鲁大学）；Harvard University（哈佛大学）
We carry out simple analytical calculations and Monte Carlo studies to better understand the impact of QCD radiation on some well-known jet substructure methods for jets arising from the decay of boosted Higgs bosons. Understanding differences between taggers for these signal jets assumes particular significance in situations where they perform similarly on QCD background jets. As an explicit example of this we compare the Y-splitter method to the more recently proposed Y-pruning technique. We demonstrate how the insight we gain can be used to significantly improve the performance of Y-splitte…
We apply techniques from Bayesian generative statistical modeling to uncover hidden features in jet substructure observables that discriminate between different a priori unknown underlying short distance physical processes in multi-jet events. In particular, we use a mixed membership model known as Latent Dirichlet Allocation to build a data-driven unsupervised top-quark tagger and $t\bar t$ event classifier. We compare our proposal to existing traditional and machine learning approaches to top jet tagging. Finally, employing a toy vector-scalar boson model as a benchmark, we demonstrate the p…
In this paper we study the identification of the b quark inside a boosted hadronically decaying top quark in the center-of-mass frame of the jet. We demonstrate that the method can be used to greatly reduce the QCD jet background even in a very high pileup condition. The method has a much smaller fake rate for QCD jets compared to typical b quark identification algorithms in jets at the same signal efficiency. When combining the b quark identification in the center-of-mass frame of the jet with jet substructure information, we can improve the rejection rate of QCD jet background by almost an o…
Jet substructure observables play a central role at the Large Hadron Collider for identifying the boosted hadronic decay products of electroweak scale resonances. The complete description of these observables requires understanding both the limit in which hard substructure is resolved, as well as the limit of a jet with a single hard core. In this paper we study in detail the perturbative structure of two prominent jet substructure observables, $N$-subjettiness and the energy correlation functions, as measured on background QCD jets. In particular, we focus on the distinction between the limit…
TemplateTagger is a C++ package for jet substructure analysis with Template Overlap Method. The code operates with arbitrary models within fixed-order perturbation theory and arbitrary kinematics. Specialized template generation classes allow the user to implement any model for a decay of a boosted heavy object. In addition to template overlap, the code provides ability to calculate other template shape and energy flow observables. We describe in detail the structure of the package, as well as provide examples of its usage.
We introduce a novel jet substructure method which exploits the variation of observables with respect to a sampling of phase-space boundaries quantified by the variability. We apply this technique to identify boosted W boson and top quark jets using telescoping subjets which utilizes information coming from subjet topology and that coming from subjet substructure. We find excellent performance of the variability, in particular its robustness against finite detector resolution. The extension to telescoping jet grooming and other telescoping jet substructure observables is also straightforward. …
We present the first anti-k$_{T}$ jet spectrum and substructure measurements using the archived ALEPH $e^+e^-$ data taken in 1994 at a center of mass energy of $\sqrt{s} = 91.2$ GeV. Jets are reconstructed with the anti-k$_{T}$ algorithm with a resolution parameter of 0.4. It is the cleanest test of jets and QCD without the complication of hadronic initial states. The fixed center-of-mass energy also allows the first direct test of pQCD calculation. We present both the inclusive jet energy spectrum and the leading dijet energy spectra, together with a number of substructure observables. They a…
We introduce a new approach for jet physics studies using subtracted cumulants of jet substructure observables, which are shown to be insensitive to contributions from soft-particle emissions uncorrelated with the hard process. Therefore subtracted cumulants allow comparisons between theoretical calculations and experimental measurements without the complication of large background contaminations such as underlying and pile-up events in hadron collisions. We test our method using subtracted jet mass cumulants by comparing Monte Carlo simulations to analytic calculations performed using soft-co…
We describe a method to measure and subtract the incoherent component of energy flow arising from multiple interactions from jet shape/substructure observables of ultra-massive jets. The amount subtracted is a function of the jet shape variable of interest and not a universal property. Such a correction is expected to significantly reduce any bias in the corresponding distributions generated by the presence of multiple interactions, and to improve measurement resolution. Since in our method the correction is obtained from the data, it is not subject to uncertainties coming from the use of theo…
Improving sensitivity of vectorlike top partner searches with jet substructure
Indian Institute of Technology Guwahati（印度理工学院古瓦哈提分校）；Indian Institute of Science Education and Research Kolkata（印度科学教育研究所加尔各答分校）；Indian Institute of Science Education and Research, Knowledge City, Sector 81, S. A. S. Nagar, Manauli PO 140306, Punjab, India（印度科学教育研究所旁遮普邦分校）；The Institute of Mathematical Sciences（数学科学研究所）
It is widely considered that, for Higgs boson searches at the Large Hadron Collider, WH and ZH production where the Higgs boson decays to b anti-b are poor search channels due to large backgrounds. We show that at high transverse momenta, employing state-of-the-art jet reconstruction and decomposition techniques, these processes can be recovered as promising search channels for the standard model Higgs boson around 120 GeV in mass.
We introduce soft drop isolation, a new photon isolation criterion inspired by jet substructure techniques. Soft drop isolation is collinear safe and is equivalent to Frixione isolation at leading non-trivial order in the small R limit. However, soft drop isolation has the interesting feature of being democratic, meaning that photons can be treated equivalently to hadrons for initial jet clustering. Taking advantage of this democratic property, we define an isolated photon subjet: a photon that is not isolated from its parent jet but is isolated within its parent subjet after soft drop declust…
We study high-pt jets from QCD and from highly-boosted massive particles such as tops, W, Z and Higgs, and argue that infrared-safe observables can help reduce QCD backgrounds. Jets from QCD are characterized by different patterns of energy flow compared to the products of highly-boosted heavy particle decays, and we employ a variety of jet shapes, observables restricted to energy flow within a jet, to explore this difference. Results from Monte Carlo generators and arguments based on perturbation theory support the discriminating power of the shapes we refer to as planar flow and angularities…
Distinguishing quark-initiated jets from gluon-initiated jets has the potential to significantly improve the reach of many beyond-the-standard model searches at the Large Hadron Collider and to provide additional tests of QCD. To explore whether quark and gluon jets could possibly be distinguished on an event-by-event basis, we perform a comprehensive simulation-based study. We explore a variety of motivated and unmotivated variables with a semi-automated multivariate approach. General conclusions are that at 50% quark jet acceptance efficiency, around 80%-90% of gluon jets can be rejected. So…
Collider signals of dark photons are an exciting probe for new gauge forces and are characterized by events with boosted lepton jets. Existing techniques are efficient in searching for muonic lepton jets but due to substantial backgrounds have difficulty constraining lepton jets containing only electrons. This is unfortunate since upcoming intensity frontier experiments are sensitive to dark photon masses which only allow electron decays. Analyzing a recently proposed model of kinetic mixing, with new scalar particles decaying into dark photons, we find that existing techniques for electron je…
Vectorlike quarks have been shown to resolve certain long-standing discrepancies pertaining to the bottom sector. We investigate, here, the prospects of identifying the existence of a topless vectorlike doublet $(B,~Y)$, as is preferred by the electroweak precision measurements. Concentrating on single production, $viz.$ $B \bar b$ with $B \to b + Z/H$ subsequently, we find that the fully hadronic decay-channel is susceptible to discovery provided jet substructure observables are used. At the 13 TeV LHC with an integrated luminosity of 300 fb$^{-1}$, a modest value of the chromomagnetic transi…
We explicitly study how jet substructure taggers act on a set of signal and background events. We focus on two-pronged hadronic decay of a boosted Z boson. The background to this process comes from QCD jets with masses of the order of m_Z. We find a way to compare various taggers within a single framework by applying them to the most relevant splitting in a jet. We develop a tool, TOY-TAG, which allows one to get insight into what happens when a particular tagger is applied to a set of signal or background events. It also provides estimates for significance and purity. We use our tool to analy…
The CP-violating version of the Minimal Supersymmetric Standard Model (MSSM) is an example of a model where experimental data do not preclude the presence of light Higgs bosons in the range around 10 -- 110 GeV. Such light Higgs bosons, decaying almost wholly to b-bbar pairs, may be copiously produced at the LHC, but would remain inaccessible to conventional Higgs searches because of intractable QCD backgrounds. We demonstrate that a significant number of these light Higgs bosons would be boosted strongly enough for the pair of daughter $b$-jet pairs to appear as a single `fat' jet with substr…
The mass of heavy quarks, such as charm and bottom, plays an important role in the formation of parton showers. This effect is apparently not well understood when parton showers evolve in a strongly interacting quark-gluon plasma. We propose a new experimental measurement in relativistic heavy ion collisions, based on a two-prong subjet structure inside a reconstructed heavy flavor jet, which can place stringent constraints on the mass dependence of in-medium splitting functions. We identify the region of jet transverse momenta where parton mass effects are leading and predict a unique reversa…
Studies on jet substructure have evolved significantly in recent years. Jet substructure is essentially determined by QCD radiations and non-perturbative effects. Predictions of jet substructure are usually different among Monte Carlo event generators, and are governed by the parton shower algorithm implemented. For leading logarithmic parton shower, even though one of the core variables is the evolution variable, its choice is not unique. We examine evolution variable dependence of the jet substructure by developing a parton shower generator that interpolates between different evolution varia…
Study of polarization of heavy particles is an important branch of research in today's collider studies. The massive $W$ boson has two types of polarization states, which usually are studied via the angular distribution of its decay products. We have studied polarization of hadronic and boosted $W$ boson using jet substructure technique at 14 TeV LHC. Two different methods, viz. N-subjettiness and Soft Drop, were used to find the subjets, which are approximately considered to be the two hadronic decay products of $W$, inside boosted $W$ jets. These subjets were then used to find the distributi…
Jet substructure is typically studied using clustering algorithms, such as kT, which arrange the jets' constituents into trees. Instead of considering a single tree per jet, we propose that multiple trees should be considered, weighted by an appropriate metric. Then each jet in each event produces a distribution for an observable, rather than a single value. Advantages of this approach include: 1) observables have significantly increased statistical stability; and, 2) new observables, such as the variance of the distribution, provide new handles for signal and background discrimination. For ex…
Top polarization is an important probe of new physics that couples to the top sector, and which may be discovered at the 14 TeV LHC. Taking the example of the MSSM, we argue that top polarization measurements can put a constraint on the soft supersymmetry breaking parameter A_t. In light of the recent discovery of a Higgs-like boson of mass ~125 GeV, a large A_t is a prediction of many supersymmetric models. To this end, we develop a *detector level* analysis methodology for extracting polarization information from hadronic tops using boosted jet substructure. We show that with 100 fb^(-1) of …
Jet substructure techniques are playing an essential role in exploring the TeV scale at the Large Hadron Collider (LHC), since they facilitate the efficient reconstruction and identification of highly-boosted objects. Both for the LHC and for future colliders, there is a growing interest in using jet substructure methods based only on charged-particle information. The reason is that silicon-based tracking detectors offer excellent granularity and precise vertexing, which can improve the angular resolution on highly-collimated jets and mitigate the impact of pileup. In this paper, we assess how…
We study the phenomenon of jet quenching utilizing quark and gluon jet substructures as independent probes of heavy ion collisions. We exploit jet and subjet features to highlight differences between quark and gluon jets in vacuum and in a medium with the jet-quenching model implemented in JEWEL. We begin with a physics-motivated, multivariate analysis of jet substructure observables including the jet mass, the radial moments, the $p_T^D$ and the pixel multiplicity. In comparison, we employ state-of-the-art image-recognition techniques by training a deep convolutional neutral network on jet im…
In the first talk I discuss the usefulness of jet grooming for testing jet quenching mechanisms, and I present a calculation of soft-drop jet mass distribution in proton-proton and heavy ion collisions. In the second talk I discuss the comprehensive studies of quark and gluon jet substructure as a way to search for qualitatively new jet modification signatures. I emphasize the importance of precise understanding of jet substructure as well as powerful analysis tools in future heavy ion jet physics studies, with direct applications to hard probes using heavy flavors and hadronically-decaying el…
We discuss jet substructure in recombination algorithms for QCD jets and single jets from heavy particle decays. We demonstrate that the jet algorithm can introduce significant systematic effects into the substructure. By characterizing these systematic effects and the substructure from QCD, splash-in, and heavy particle decays, we identify a technique, pruning, to better identify heavy particle decays into single jets and distinguish them from QCD jets. Pruning removes protojets typical of soft, wide angle radiation, improves the mass resolution of jets reconstructing a heavy particle decay, …
We study the effectiveness of theoretically-motivated high-level jet observables in the extreme context of jets with a large number of hard sub-jets (up to $N=8$). Previous studies indicate that high-level observables are powerful, interpretable tools to probe jet substructure for $N\le 3$ hard sub-jets, but that deep neural networks trained on low-level jet constituents match or slightly exceed their performance. We extend this work for up to $N=8$ hard sub-jets, using deep particle-flow networks (PFNs) and Transformer based networks to estimate a loose upper bound on the classification perfo…
We consider the mass distribution of QCD jets after the application of jet substructure methods, specifically the mass-drop tagger, pruning, trimming and their variants. In contrast to most current studies employing Monte Carlo methods, we carry out analytical calculations at the next-to-leading order level, which are sufficient to extract the dominant logarithmic behaviour for each technique, and compare our findings to exact fixed-order results. Our results should ultimately lead to a better understanding of these jet substructure methods which in turn will influence the development of futur…
Jet physics is a rich and rapidly evolving field, with many applications to physics in and beyond the Standard Model. These notes, based on lectures delivered at the June 2012 Theoretical Advanced Study Institute, provide an introduction to jets at the Large Hadron Collider. Topics covered include sequential jet algorithms, jet shapes, jet grooming, and boosted Higgs and top tagging.
The physics beyond the Standard Model with parameters of the compressed spectrum is well motivated both in a theory side and with phenomenological reasons, especially related to dark matter phenomenology. In this letter, we propose a method to tag soft final state particles from a decaying process of a new particle in this parameter space. By taking a supersymmetric gluino search as an example, we demonstrate how the Large Hadron Collider experimental collaborations can improve a sensitivity in these non-trivial search regions.
The LHC searches for the CP-odd Higgs boson is studied (with masses from 300 GeV to 1 TeV) in the context of the general two-Higgs-doublet model. With the discovery of the 125 GeV Higgs boson at the LHC, we highlight one promising discovery channel of the hZ. This channel can become significant after the global signal fitting to the 125 GeV Higgs boson in the general two-Higgs-doublet model. It is particularly important in the scenario where two CP-even Higgs bosons in the two-Higgs-doublet model have the common mass of 125 GeV. Since the final states involve a Standard-Model-like Higgs boson,…
New jet observables are defined which characterize both fractal and scale-dependent contributions to the distribution of hadrons in a jet. These infrared safe observables, named Extended Fractal Observables (EFOs), have been applied to quark-gluon discrimination to demonstrate their potential utility. The EFOs are found to be individually discriminating and only weakly correlated to variables used in existing discriminators. Consequently, their inclusion improves discriminator performance, as here demonstrated with particle level simulation from the parton shower.
This report of the BOOST2012 workshop presents the results of four working groups that studied key aspects of jet substructure. We discuss the potential of the description of jet substructure in first-principle QCD calculations and study the accuracy of state-of-the-art Monte Carlo tools. Experimental limitations of the ability to resolve substructure are evaluated, with a focus on the impact of additional proton proton collisions on jet substructure performance in future LHC operating scenarios. A final section summarizes the lessons learnt during the deployment of substructure analyses in se…
Jet substructure has emerged to play a central role at the Large Hadron Collider (LHC), where it has provided numerous innovative new ways to search for new physics and to probe the Standard Model in extreme regions of phase space. In this article we provide a comprehensive review of state of the art theoretical and machine learning developments in jet substructure. This article is meant both as a pedagogical introduction, covering the key physical principles underlying the calculation of jet substructure observables, the development of new observables, and cutting edge machine learning techni…
At the extreme energies of the Large Hadron Collider, massive particles can be produced at such high velocities that their hadronic decays are collimated and the resulting jets overlap. Deducing whether the substructure of an observed jet is due to a low-mass single particle or due to multiple decay objects of a massive particle is an important problem in the analysis of collider data. Traditional approaches have relied on expert features designed to detect energy deposition patterns in the calorimeter, but the complexity of the data make this task an excellent candidate for the application of…
Factorization underpins our ability to make predictions at the LHC, both in Monte Carlo simulations and direct calculations. An improved theoretical understanding of jet substructure can lead to calculations that can confront data and validate the Monte Carlo description of jets. We derive constraints on jet substructure algorithms from factorization, focusing on the broad class of jet observables where the soft and collinear dynamics of QCD dominate. A necessary condition for factorization is that the phase space constraints on soft and collinear dynamics for a given observable are independen…
