Annie Y. Wei, Preksha Naik, Aram W. Harrow, Jesse Thaler
备注：
21 pages, 1 table, 6 figures. v2: correction to doubling trick and additional discussion of resource requirements; approximate version to appear in PRD
Identifying jets formed in high-energy particle collisions requires solving optimization problems over potentially large numbers of final-state particles. In this work, we consider the possibility of using quantum computers to speed up jet clustering algorithms. Focusing on the case of electron-positron collisions, we consider a well-known event shape called thrust whose optimum corresponds to the most jet-like separating plane among a set of particles, thereby defining two hemisphere jets. We show how to formulate thrust both as a quantum annealing problem and as a Grover search problem. A key component of our analysis is the consideration of realistic models for interfacing classical data with a quantum algorithm. With a sequential computing model, we show how to speed up the well-known O(N^3) classical algorithm to an O(N^2) quantum algorithm, including the O(N) overhead of loading classical data from N final-state particles. Along the way, we also identify a way to speed up the classical algorithm to O(N^2 log N) using a sorting strategy inspired by the SISCone jet algorithm, which has no natural quantum counterpart. With a parallel computing model, we achieve O(N log N) scaling in both the classical and quantum cases. Finally, we consider the generalization of these quantum methods to other jet algorithms more closely related to those used for proton-proton collisions at the Large Hadron Collider.
We study the case where quantum computing could improve jet clustering by considering two new quantum algorithms that might speed up classical jet clustering algorithms. The first one is a quantum subroutine to compute a Minkowski-based distance between two data points, while the second one consists of a quantum circuit to track the rough maximum into a list of unsorted data. When one or both algorithms are implemented in classical versions of well-known clustering algorithms (K-means, Affinity Propagation and $k_T$-jet) we obtain efficiencies comparable to those of their classical counterpart…
Jets with a large radius $R\gtrsim 1$ and grooming algorithms are widely used to fully capture the decay products of boosted heavy particles at the Large Hadron Collider (LHC). Unlike most discriminating variables used in such studies, the jet radius is usually not optimized for specific physics scenarios. This is because every jet configuration must be calibrated, insitu, to account for detector response and other experimental effects. One solution to enhance the availability of large-$R$ jet configurations used by the LHC experiments is {\it jet re-clustering}. Jet re-clustering introduces a…
Quantum computing holds the promise of substantially speeding up computationally expensive tasks, such as solving optimization problems over a large number of elements. In high-energy collider physics, quantum-assisted algorithms might accelerate the clustering of particles into jets. In this study, we benchmark quantum annealing strategies for jet clustering based on optimizing a quantity called "thrust" in electron-positron collision events. We find that quantum annealing yields similar performance to exact classical approaches and classical heuristics, but only after tuning the annealing pa…
I describe a class of iterative jet algorithms that are based on maximizing a fixed function of the total 4-momentum rather than clustering of pairs of jets. I describe some of the properties of the simplest examples of this class, appropriate for jets at an $e^+e^-$ machine. These examples are sufficiently simple that many features of the jets that they define can be determined analytically with ease. The jets constructed in this way have some potentially useful properties, including a strong form of infrared safety.
Clustering is one of the most frequent problems in many domains, in particular, in particle physics where jet reconstruction is central in experimental analyses. Jet clustering at the CERN's Large Hadron Collider (LHC) is computationally expensive and the difficulty of this task will increase with the upcoming High-Luminosity LHC (HL-LHC). In this paper, we study the case in which quantum computing algorithms might improve jet clustering by considering two novel quantum algorithms which may speed up the classical jet clustering algorithms. The first one is a quantum subroutine to compute a Min…
A jet algorithm based on the k-means clustering procedure is proposed which can be used for the invariant-mass reconstruction of heavy states decaying to hadronic jets. The proposed algorithm was tested by reconstructing E+ E- to ttbar to 6 jets and E+ E- to W+W- to 4 jets processes at \sqrt{s}=500 GeV using a Monte Carlo simulation. It was shown that the algorithm has a reconstruction efficiency similar to traditional jet-finding algorithms, and leads to 25% and 40% reduction of reconstruction width for top quarks and W bosons, respectively, compared to the kT (Durham) algorithm. In addition,…
A new class of jet clustering algorithms is introduced. A criterion inspired by successful mass-drop taggers is applied that prevents the recombination of two hard prongs if their combined jet mass is substantially larger than the masses of the separate prongs. This "mass jump" veto effectively results in jets with variable radii in dense environments. Differences to existing methods are investigated. It is shown for boosted top quarks that the new algorithm has beneficial properties which can lead to improved tagging purity.
There has recently been much interest in analytical computations of jet mass distributions with and without vetos on additional jet activity [1-6]. An important issue affecting such calculations, particularly at next-to-leading logarithmic (NLL) accuracy, is that of non-global logarithms as well as logarithms induced by jet definition, as we pointed out in an earlier work [3]. In this paper, we extend our previous calculations by independently deriving the full jet-radius analytical form of non-global logarithms, in the anti-$\kt$ jet algorithm. Employing the small-jet radius approximation, we…
Recent work in inter-jet energy flow has identified a class of leading logarithms previously not considered in the literature. These so-called non-global logarithms have been shown to have significant numerical impact on gaps-between-jets calculations at the energies of current particle colliders. Here we calculate, at fixed order and to all orders, the effect of applying clustering to the gluonic final state responsible for these logarithms for a trivial colour flow 2 jet system. Such a clustering algorithm has already been used for experimental measurements at HERA. We find that the impact o…
Many experimental analyses separate events into exclusive jet bins, using a jet algorithm to cluster the final state and then veto on jets. Jet clustering induces logarithmic dependence on the jet radius R in the cross section for exclusive jet bins, a dependence that is poorly controlled due to the non-global nature of the clustering. At jet radii of experimental interest, the leading order (LO) clustering effects are numerically significant, but the higher order effects are currently unknown. We rectify this situation by calculating the most important part of the next-to-leading order (NLO) …
We show that a general purpose clusterization algorithm, Deterministic Annealing, can be adapted to the problem of jet identification in particle production by high energy collisions. In particular we consider the problem of jet searching in events generated at hadronic colliders. Deterministic Annealing is able to reproduce the results obtained by traditional jet algorithms and to exhibit a higher degree of flexibility.
Precise predictions for Higgs production via vector-boson fusion play an important role when testing the properties of the Higgs boson and probing new-physics effects. While the inclusive cross section changes little when including NNLO and N3LO QCD corrections, a differential NNLO calculation with typical VBF cuts shows large corrections of up to 10% in distributions. In this article, we investigate the dependence of the differential NNLO QCD calculation on the jet definition. Starting from the known results at a fixed jet clustering choice, we use the electroweak H+3 jets production cross se…
We investigate modifications to the $k_\perp$-clustering jet algorithm which preserve the advantages of the original Durham algorithm while reducing non-perturbative corrections and providing better resolution of jet substructure. We find that a simple change in the sequence of clustering (combining smaller-angle pairs first), together with the `freezing' of soft resolved jets, has beneficial effects.
Jet clustering algorithms are widely used to analyse hadronic events in high energy collisions. Recently a new clustering method, known as `Cambridge', has been introduced. In this article we present an algorithm to determine the transition values of y_cut for this clustering scheme, which allows to resolve any event to a definite number of jets in the final state. We discuss some particularities of the Cambridge clustering method and compare its performance to the Durham clustering scheme for Monte Carlo generated e+e- annihilation events.
Clustering algorithms build jets though the iterative application of single particle and pairwise metrics. This leads to phase space constraints that are extremely complicated beyond the lowest orders in perturbation theory, and in practice they must be implemented numerically. This complication presents a significant barrier to gaining an analytic understanding of the perturbative structure of jet cross sections. We present a novel framework to express the jet algorithm's phase space constraints as a function of clustered groups of particles, which are the possible outcomes of the algorithm. …
We present analytical calculations of the distribution of non-global jet shapes in Higgs/vector boson + jet production at hadron colliders. Within the eikonal-limit framework and implementing various jet algorithms, we compute the full distribution of the particular jet mass shape observable at 2-loops, including the large single-logarithms known as non-global logs and clustering logs. We compare our next-to-leading-log analytical resummation to parton showers and, after matching and including non-perturbative effects, to experimental data. A good agreement is shown for all comparisons.
We address the issues of clustering and non-global logarithms for jet shapes in the process of production of a Higgs/vector boson associated with a single hard jet at hadron colliders. We perform an analytical fixed-order calculation up to second order in the coupling as well as an all-orders estimation for the specific invariant mass distribution of the highest-$p_t$ jet, for various jet algorithms. Our results are derived in the eikonal (soft) limit and are valid up to next-to-leading logarithmic accuracy. We perform a matching of the resummed distribution to next-to-leading order results fr…
We assess the performance of different jet-clustering algorithms, in the presence of different resolution parameters and reconstruction procedures, in resolving fully hadronic final states emerging from the chain decay of the discovered Higgs boson into pairs of new identical Higgs states, the latter in turn decaying into bottom-antibottom quark pairs. We show that, at the Large Hadron Collider (LHC), both the efficiency of selecting the multi-jet final state and the ability to reconstruct from it the masses of the Higgs bosons (potentially) present in an event sample depend strongly on the ch…
We extend our framework for the automated calculation of dijet soft functions to observables that do not obey the non-Abelian exponentiation theorem, like jet-veto or grooming soft functions that are sensitive to clustering effects of the jet algorithm. Although the matrix element for uncorrelated double emissions has a simpler structure than the one for correlated emissions, we argue that its singularity structure poses more stringent constraints on the required phase-space parametrisation. Our algorithm applies to both SCET-1 and SCET-2 soft functions and it is implemented in the novel progr…
Over the years, many jet clustering algorithms have been proposed for the analysis of hadronic final states in $e^+e^-$ annihilations. These have somewhat different emphasis and are therefore more or less suited for various applications. We here review some of the most used and compare them from a theoretical and experimental point of view.
We reveal the direct link between the jet clustering algorithms recently proposed by Howard Georgi and parton shower kinematics, providing firm foundation from the theoretical side. The kinematics of this class of elegant algorithms is explored systematically for partons with arbitrary masses and the jet function is generalized to $J^{(n)}_β$ with a jet function index $n$ in order to achieve more degrees of freedom. Based on three basic requirements that, the result of jet clustering is process-independent and hence logically consistent, for softer subjets the inclusion cone is larger to confo…
We investigate a new sequential recombination algorithm which effectively subtracts background as it reconstructs the jet. We examine the new algorithm's behavior in light of existing algorithms, and we find that in Monte Carlo comparisons, the new algorithm's robustness against collision backgrounds is comparable to that of other jet algorithms when the latter have been augmented by further background subtraction techniques.
We present a resummation valid to next-to leading logarithmic accuracy of the non-global and clustering effects in groomed (with modified mass drop tagger) multi-pronged observables. These effects are universal in the sense that they depend only on the flavor structure of the $1\to 2$ splitting forming the multi-pronged subjets and the opening angle of the splitting, being insensitive to the underlying hard process or underlying event. The differential spectra with and without the non-global and clustering effects are presented, and the change in the spectra is found to be small.
Most recombination-style jet algorithms cluster soft gluons in a complex way. This leads to correlations in the soft gluon phase space and introduces logarithmic corrections to jet cross sections. The leading Abelian clustering logarithms occur at least at next-to leading logarithm (NLL) in the exponent of the distribution, and we show that new clustering effects contributing at NLL likely arise at each order. Therefore we find that it is unlikely that clustering logs can be resummed to NLL. Clustering logarithms make the anti-kT algorithm theoretically preferred, for which they are power supp…
We propose a new jet algorithm for deep-inelastic scattering (DIS) that accounts for the forward-backward asymmetry in the Breit frame. The Centauro algorithm is longitudinally invariant and can cluster jets with Born kinematics, which enables novel studies of transverse-momentum-dependent observables. Furthermore, we show that spherically-invariant algorithms in the Breit frame give access to low-energy jets from current fragmentation. We propose novel studies in unpolarized, polarized, and nuclear DIS at the future Electron-Ion Collider.
Under which conditions does a jet appear as a particle--like signal from the hidden realm of quarks and gluons? Motivated by this question jet clustering conditions are formulated, in order to characterize jet clustering algorithms, which can be used for a determination of particle--like jets. Jets are understood as particle--like, if they behave like free particles. The simplest solution to the jet clustering conditions leads to a new jet algorithm: a Lorentz invariant generalization of the JADE algorithm. It is found that this generalization amplifies hadronization effects in certain phase s…
We investigate a modification of the $k_\perp$-clustering jet algorithm for hadron-hadron collisions, analogous to the ``Cambridge'' algorithm recently proposed for $e^+e^-$ annihilation, in which pairs of objects that are close in angle are combined preferentially. This has the effect of building jets from the inside out, with the aim of reducing the amount of the underlying event incorporated into them. We also investigate a second modification that involves using a new separation measure. Monte Carlo studies suggest that the standard $k_\perp$ algorithm performs as well as either of these m…
We revisit the impact of the jet algorithm on predictions of energy flow into gaps between hard jets, defined using the kt clustering procedure. The resulting prediction has two distinct components: a primary emission piece that is related to independent emission of soft gluons by the hard jets and a correlated emission (non-global) piece known only in the large N_c limit. We analytically compute the dependence of the primary emission term on the jet algorithm, which gives significantly more insight than our previous numerical study of the same. We also point out that the non-global component …
Jet clustering is traditionally an unsupervised learning task because there is no unique way to associate hadronic final states with the quark and gluon degrees of freedom that generated them. However, for uncolored particles like $W$, $Z$, and Higgs bosons, it is possible to approximately (though not exactly) associate final state hadrons to their ancestor. By labeling simulated final state hadrons as descending from an uncolored particle, it is possible to train a supervised learning method to create boson jets. Such a method much operates on individual particles and identifies connections b…
We present an algorithm for deriving partonic flavour labels to be applied to truth particle jets in Monte Carlo event simulations. The inputs to this approach are final pre-hadronization partons, to remove dependence on unphysical details such as the order of matrix element calculation and shower generator frame recoil treatment. These are clustered using standard jet algorithms, modified to restrict the allowed pseudojet combinations to those in which tracked flavour labels are consistent with QCD and QED Feynman rules. The resulting algorithm is shown to be portable between the major famili…
Collimated streams of particles produced in high energy physics experiments are organized using clustering algorithms to form jets. To construct jets, the experimental collaborations based at the Large Hadron Collider (LHC) primarily use agglomerative hierarchical clustering schemes known as sequential recombination. We propose a new class of algorithms for clustering jets that use infrared and collinear safe mixture models. These new algorithms, known as fuzzy jets, are clustered using maximum likelihood techniques and can dynamically determine various properties of jets like their size. We s…
The k_t and Cambridge/Aachen inclusive jet finding algorithms for hadron-hadron collisions can be seen as belonging to a broader class of sequential recombination jet algorithms, parametrised by the power of the energy scale in the distance measure. We examine some properties of a new member of this class, for which the power is negative. This ``anti-k_t'' algorithm essentially behaves like an idealised cone algorithm, in that jets with only soft fragmentation are conical, active and passive areas are equal, the area anomalous dimensions are zero, the non-global logarithms are those of a rigid…
Clustering logs have been the subject of much study in recent literature. They are a class of large logs which arise for non-global jet-shape observables where final-state particles are clustered by a non-cone--like jet algorithm. Their resummation to all orders is highly non--trivial due to the non-trivial role of clustering amongst soft gluons which results in the phase-space being non-factorisable. This may therefore significantly impact the accuracy of analytical estimations of many of such observables. Nonetheless, in this paper we address this very issue for jet shapes defined using the …
We present a new approach to jet definition alternative to clustering methods, such as the anti-$k_T$ scheme, that exploit kinematic data directly. Instead the new method uses kinematic information to represent the particles in a multidimensional space, as in spectral clustering. After confirming its Infra-Red (IR) safety, we compare its performance in analysing $gg \rightarrow H_{125~\rm GeV} \rightarrow H_{40~\rm GeV}H_{40~\rm GeV} \rightarrow b\bar{b}b\bar{b}$, $gg \rightarrow H_{500~\rm GeV} \rightarrow H_{125~\rm GeV}H_{125~\rm GeV} \rightarrow b\bar{b}b\bar{b}$ and $gg, q\bar{q} \rightar…
We present a new approach to jet definition alternative to clustering methods, such as the anti-$k_T$ scheme, that exploit kinematic data directly. Instead the new method uses kinematic information to represent the particles in a multidimensional space, as in spectral clustering. After confirming its Infra-Red (IR) safety, we compare its performance in analysing $qq\to H_{125\,\text{GeV}} \rightarrow H_{40\,\text{GeV}} H_{40\,\text{GeV}} \rightarrow b \bar{b} b \bar{b}$, $qq\to H_{500\,\text{GeV}} \rightarrow H_{125\,\text{GeV}} H_{125\,\text{GeV}} \rightarrow b \bar{b} b \bar{b}$ and $gg,q\ba…
We consider the energy flow into gaps between hard jets. It was previously believed that the accuracy of resummed predictions for such observables can be improved by employing the $k_t$ clustering procedure to define the gap energy in terms of a sum of energies of soft jets (rather than individual hadrons) in the gap. This significantly reduces the sensitivity to correlated soft large-angle radiation (non-global leading logs), numerically calculable only in the large $N_c$ limit. While this is the case, as we demonstrate here, the use of $k_t$ clustering spoils the straightforward single-gluon…
Jet vetoes play an important role at the LHC in the search for the Higgs and ultimately in precise measurements of its properties. Many Higgs analyses divide the cross section into exclusive jet bins to maximize the sensitivity in different production and decay channels. For a given jet category, the veto on additional jets introduces sensitivity to soft and collinear emissions, which causes logarithms in the perturbative expansion that need to be resummed to obtain precise predictions. We study the higher-order resummation properties of several conceptually distinct kinematic variables that c…
We reframe common tasks in jet physics in probabilistic terms, including jet reconstruction, Monte Carlo tuning, matrix element - parton shower matching for large jet multiplicity, and efficient event generation of jets in complex, signal-like regions of phase space. We also introduce Ginkgo, a simplified, generative model for jets, that facilitates research into these tasks with techniques from statistics, machine learning, and combinatorial optimization. We review some of the recent research in this direction that has been enabled with Ginkgo. We show how probabilistic programming can be use…
We address the problem of resumming leading clustering logs in QCD jet observables defined using the k_t, CA and SISCone algorithms. We specifically choose the jet mass distribution as an example and calculate up to order(alpha_s^4) clustering-log terms in the series expansion at single-log accuracy. These terms are found to exhibit a pattern of exponentiation and we are thus able to perform an all-orders analytical resummation for the clustering logs. We also numerically calculate the non-global logs at large N_c. We show that our result for the resummation of clustering logs is a very good a…
Generalised Dynamic Radius Jets for Robust Collider Analyses
Jožef Stefan Institute（约瑟夫·斯特凡研究所）；The Institute of Mathematical Sciences（数学科学研究所）；Indian Institute of Science Education and Research Kolkata（印度教育研究科学院加尔各答分校）
We review recent developments related to jet clustering algorithms and jet finding. These include fast implementations of sequential recombination algorithms, new IRC safe algorithms, quantitative determination of jet areas and quality measures for jet finding, among many others. We also briefly discuss the status of jet finding in heavy ion collisions, where full QCD jets have been measured for the first time at RHIC.
An infrared and collinear (IRC) safe definition of the partonic flavour of a jet is vital for precision predictions of quantum chromodynamics at colliders. Jet flavour definitions have been presented in the literature, but they are typically defined through modification of the jet algorithm to be sensitive to partonic flavour at every stage of the clustering. While this does ensure that the sum of flavours in a jet is IRC safe, a flavour-sensitive clustering procedure is difficult to apply to realistic data. We introduce a distinct and novel approach to jet flavour that can be applied to any c…
Jets constructed via clustering algorithms (e.g., anti-$k_T$, soft-drop) have been proposed for many precision measurements, such as the strong coupling $α_s$ and the nucleon intrinsic dynamics. However, the theoretical accuracy is affected by missing QCD corrections at higher orders for the jet functions in the associated factorization theorems. Their calculation is complicated by the jet clustering procedure. In this work, we propose a method to evaluate jet functions at higher orders in QCD. The calculation involves the phase space sector decomposition with suitable soft subtractions. As a …
We revisit the azimuthal decorrelation $δϕ$ between a jet and a $Z$ boson produced at hadron colliders. Employing different recombination schemes for the jets leads to significantly different NLL-resummed predictions for the distribution of this quantity. Specifically when the jets are reconstructed with the $E$-scheme (i.e., four-momentum addition) in the $k_t$ or anti-$k_t$ clustering algorithms, then the resummation becomes highly non-trivial due to the presence of non-global and/or clustering logarithms. We evaluate these logarithms analytically at two loops and numerically to all orders i…
We introduce a new class of event shapes to characterize the jet-like structure of an event. Like traditional event shapes, our observables are infrared/collinear safe and involve a sum over all hadrons in an event, but like a jet clustering algorithm, they incorporate a jet radius parameter and a transverse momentum cut. Three of the ubiquitous jet-based observables---jet multiplicity, summed scalar transverse momentum, and missing transverse momentum---have event shape counterparts that are closely correlated with their jet-based cousins. Due to their "local" computational structure, these j…
The SISCone jet algorithm is a seedless infrared-safe cone jet algorithm. There exists an implementation which is highly optimised for a large number of final state particles. However, in fixed-order perturbative calculations with a small number of final state particles, it turns out that the computer time needed for the jet clustering of this implementation is comparable to the computer time of the matrix elements. This article reports on an implementation of the SISCone algorithm optimised for low particle multiplicities.
Recent developments in jet clustering are reviewed. We present a list of fast and infrared and collinear safe algorithms, and also describe new tools like jet areas. We show how these techniques can be applied to the study of underlying event or, more generally, of any background which can be considered distributed in a sufficiently uniform way.
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 study the possibility to employ neural networks to simulate jet clustering procedures in high energy hadron-hadron collisions. We concentrate our analysis on the Fermilab Tevatron energy and on the $k_\bot$ algorithm. We consider both supervised multilayer feed-forward network trained by the backpropagation algorithm and unsupervised learning, where the neural network autonomously organizes the events in clusters.
The next-to-leading order three-jet cross section in hadron collisions is calculated in the simplified case when the matrix elements of all QCD subprocesses are approximated by the pure gluon matrix element. The longitudinally-invariant $k_\perp$ jet-clustering algorithm is used. The important property of reduced renormalization and factorization scale dependence of the next-to-leading order physical cross section as compared to the Born cross section is demonstrated.
