Hadronic Top Quark Polarimetry with ParticleNet
Not Available
Dong, Zhongtian (ORCID:0000000210003454)↗
Engineering topics
Larkoski, Andrew J.
Publications and source records attributed to Larkoski, Andrew J..
The phase space distance between collider events
How can one fully harness the power of physics encoded in relativistic N-body phase space? Topologically, phase space is isomorphic to the product space of a simplex and a hypersphere and can be equipped with explicit coordinates and a Riemannian metric. This natural structure that scaffolds the space on which all collider physics events live opens up new directions for machine learning applications and implementation. Here we present a detailed construction of the phase space manifold and its differential line element, identifying particle ordering prescriptions that ensure that the metric satisfies necessary properties. We apply the phase space metric to several binary classification tasks, including discrimination of high-multiplicity resonance decays or boosted hadronic decays of electroweak bosons from QCD processes, and demonstrate powerful performance on simulated data. Our work demonstrates the many benefits of promoting phase space from merely a background on which calculations take place to being geometrically entwined with a theory’s dynamics.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Is infrared-collinear safe information all you need for jet classification?
Machine learning-based jet classifiers are able to achieve impressive tagging performance in a variety of applications in high-energy and nuclear physics. However, it remains unclear in many cases which aspects of jets give rise to this discriminating power, and whether jet observables that are tractable in perturbative QCD such as those obeying infrared-collinear (IRC) safety serve as sufficient inputs. In this article, we introduce a new classifier, Jet Flow Networks (JFNs), in an effort to address the question of whether IRC unsafe information provides additional discriminating power in jet classification. JFNs are permutation-invariant neural networks (deep sets) that take as input the kinematic information of reconstructed subjets. The subjet radius and a cut on the subjet’s transverse momenta serve as tunable hyperparameters enabling a controllable sensitivity to soft emissions and nonperturbative effects. We demonstrate the performance of JFNs for quark vs. gluon and Z vs. QCD jet tagging. For small subjet radii and transverse momentum cuts, the performance of JFNs is equivalent to the IRC-unsafe Particle Flow Networks (PFNs), demonstrating that infrared-collinear unsafe information is not necessary to achieve strong discrimination for both cases. As the subjet radius is increased, the performance of the JFNs remains essentially unchanged until physical thresholds that we identify are crossed. For relatively large subjet radii, we show that the JFNs may offer an increased model independence with a modest tradeoff in performance compared to classifiers that use the full particle information of the jet. These results shed new light on how machines learn patterns in high-energy physics data.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Flavor fragmentation function factorization
A definition of partonic jet flavor that is both theoretically well-defined and experimentally robust would have profound implications for measurements and predictions especially for heavy flavor applications. Recently, a definition of jet flavor was introduced as the net flavor flowing along the direction of the Winner-Take-All axis of a jet which is soft safe to all orders, but not collinear safe. Here, we exploit the lack of collinear safety and propose a factorization theorem of perturbative flavor fragmentation functions that resum collinear divergences and describe the evolution of flavor from the short distance of jet production to the long distance at which hadronization occurs. Collinear flavor evolution is governed by a small modification of the DGLAP equations. We present a detailed all-orders analysis and identify exact relations that must hold amongst the various anomalous dimensions by probability conservation and the existence of fixed points of the renormalization group flow. We explicitly validate the factorization theorem at one-loop order, and demonstrate its consistency at two loops in particular flavor channels. Starting at two-loops, constraints on phase space imposed by flavor measurements potentially allow for non-trivial soft contributions, but we demonstrate that they are scaleless and so explicitly vanish, ensuring that soft particles are summed inclusively and all divergences are exclusively collinear in nature. This factorization theorem opens the door to precision calculations with identified flavor in the infrared.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Flavor Fragmentation Function Factorization
A definition of partonic jet flavor that is both theoretically well-defined and experimentally robust would have profound implications for measurements and predictions especially for heavy flavor applications. Recently, a definition of jet flavor was introduced as the net flavor flowing along the direction of the Winner-Take-All axis of a jet which is soft safe to all orders, but not collinear safe. Here, we exploit the lack of collinear safety and propose a factorization theorem of perturbative flavor fragmentation functions that resum collinear divergences and describe the evolution of flavor from the short distance of jet production to the long distance at which hadronization occurs. Collinear flavor evolution is governed by a small modification of the DGLAP equations. We present a detailed all-orders analysis and identify exact relations that must hold amongst the various anomalous dimensions by probability conservation and the existence of fixed points of the renormalization group flow. We explicitly validate the factorization theorem at one-loop order, and demonstrate its consistency at two loops in particular flavor channels. Starting at two-loops, constraints on phase space imposed by flavor measurements potentially allow for non-trivial soft contributions, but we demonstrate that they are scaleless and so explicitly vanish, ensuring that soft particles are summed inclusively and all divergences are exclusively collinear in nature. This factorization theorem opens the door to precision calculations with identified flavor in the infrared.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A spectral metric for collider geometry
By quantifying the distance between two collider events, one can triangulate a metric space and reframe collider data analysis as computational geometry. One popular geometric approach is to first represent events as an energy flow on an idealized celestial sphere and then define the metric in terms of optimal transport in two dimensions. In this paper, we advocate for representing events in terms of a spectral function that encodes pairwise particle angles and products of particle energies, which enables a metric distance defined in terms of one-dimensional optimal transport. This approach has the advantage of automatically incorporating obvious isometries of the data, like rotations about the colliding beam axis. It also facilitates first-principles calculations, since there are simple closed-form expressions for optimal transport in one dimension. Up to isometries and event sets of measure zero, the spectral representation is unique, so the metric on the space of spectral functions is a metric on the space of events. At lowest order in perturbation theory in electron-positron collisions, our metric is simply the summed squared invariant masses of the two event hemispheres. Going to higher orders, we present predictions for the distribution of metric distances between jets in fixed-order and resummed perturbation theory as well as in parton-shower generators. Finally, we speculate on whether the spectral approach could furnish a useful metric on the space of quantum field theories.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Designing observables for quantum interference in jets at subleading color
The large-Nc or topologically planar limit of gauge theories can be considered as a classical limit because all gauge bosons are distinguishable particles and therefore cannot exhibit interference. Quantum effects due to the flow of color therefore arise starting at subleading in 1/Nc. We introduce kinematic observables explicitly sensitive to effects at subleading color formed from the ratio of interfering to squared color-ordered amplitudes. Such observables are in general not infrared and collinear safe, so we introduce angular observables defined from appropriate multi-point energy correlators motivated by the form of color-ordered amplitudes. We demonstrate that color interference effects are manifest as sinusoidal oscillation in the simplest system, a collinear jet with three particles, and show the limitations of predicting this observable in all-purpose, leading-color parton shower Monte Carlos.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
A fragmentation approach to jet flavor
An intuitive definition of the partonic flavor of a jet in quantum chromodynamics is often only well-defined in the deep ultraviolet, where the strong force becomes a free theory and a jet consists of a single parton. However, measurements are performed in the infrared, where a jet consists of numerous particles and requires an algorithmic procedure to define their phase space boundaries. To connect these two regimes, we introduce a novel and simple partonic jet flavor definition in the infrared. We define the jet flavor to be the net flavor of the partons that lie exactly along the direction of the Winner-Take-All recombination scheme axis of the jet, which is safe to all orders under emissions of soft particles, but is not collinear safe. Collinear divergences can be absorbed into a perturbative fragmentation function that describes the evolution of the jet flavor from the ultraviolet to the infrared. The evolution equations are linear and a small modification to traditional DGLAP and we solve them to leading-logarithmic accuracy. The evolution equations exhibit fixed points in the deep infrared, we demonstrate quantitative agreement with parton shower simulations, and we present various infrared and collinear safe observables that are sensitive to this flavor definition.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Practical jet flavour through NNLO
Abstract 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 a collection of partons defined by any algorithm. Our definition of jet flavour is the sum of flavours of all partons that remain after Soft Drop grooming, reclustered with the "Image missing" <#comment/> algorithm. We prove that this prescription is IRC safe through next-to-next-to-leading order (NNLO), and so can interface with the most precise fixed-order calculations for jets available at present. We validate the IRC safety of this definition with numeric fixed-order codes and further show that jet flavour with Soft Drop reclustered with a generalised $$k_T$$ k T algorithm fails to be IRC safe at NNLO.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Navigating collinear superspace
We introduce a new set of effective field theory rules for constructing Lagrangians with \( \mathcal{N} \) = 1 supersymmetry in collinear superspace. In the standard superspace treatment, superfields are functions of the coordinates \( \left({x}^{\mu },{\theta}^{\alpha },{\theta}^{\dagger \overset{\cdot }{\alpha }}\right) \) , and supersymmetry preservation is manifest at the Lagrangian level in part due to the inclusion of auxiliary F - and D -term components. By contrast, collinear superspace depends on a smaller set of coordinates ( x μ , η , η † ), where η is a complex Grassmann number without a spinor index. This provides a formulation of supersymmetric theories that depends exclusively on propagating degrees of freedom, at the expense of obscuring Lorentz invariance and introducing inverse momentum scales. After establishing the general framework, we construct collinear superspace Lagrangians for free chiral matter and non-Abelian gauge fields. For the latter construction, an important ingredient is a superfield representation that is simultaneously chiral, anti-chiral, and real; this novel object encodes residual gauge transformations on the light cone. Additionally, we discuss a fundamental obstruction to constructing inter- acting theories with chiral matter; overcoming these issues is the subject of our companion paper, where we introduce a larger set of superfields to realize the full range of interactions compatible with \( \mathcal{N} \) = 1. Along the way, we provide a novel framing of reparametrization invariance using a spinor decomposition, which provides insight into this important light-cone symmetry.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Circumnavigating collinear superspace
In this paper, we extend the collinear superspace formalism to include the full range of N = 1 supersymmetric interactions. Building on the effective field theory rules developed in a companion paper — Navigating Collinear Superspace — we construct collinear superspace Lagrangians for theories with non-trivial F- and D-term auxiliary fields. For (massless) Wess-Zumino models, the key ingredient is a novel type of Grassmann-valued supermultiplet whose lowest component is a (non-propagating) fermionic degree of freedom. For gauge theories coupled to charged chiral matter, the key ingredient is a novel type of vector superfield whose lowest component is a non-propagating gauge potential. This unique vector superfield is used to construct a gauge-covariant derivative; while such an object does not appear in the standard full superspace formalism, it is crucial for modeling gauge interactions when the theory is expres sed on a collinear slice. This brings us full circle, by showing that all types of N = 1 theories in four dimensions can beconstructed in collinear superspace from purely infrared considerations. We speculate that supersymmetric theories with N > 1 could also be implemented using similar collinear superspace constructions.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Jet substructure at the Large Hadron Collider: A review of recent advances in theory and machine learning
Not Available
Larkoski, Andrew J.↗
A theory of quark vs. gluon discrimination
Understanding jets initiated by quarks and gluons is of fundamental importance in collider physics. Efficient and robust techniques for quark versus gluon jet discrimination have consequences for new physics searches, precision αs studies, parton distribution function extractions, and many other applications. Numerous machine learning analyses have attacked the problem, demonstrating that good performance can be obtained but generally not providing an understanding for what properties of the jets are responsible for that separation power. In this paper, we provide an extensive and detailed analysis of quark versus gluon discrimination from first-principles theoretical calculations. Working in the strongly-ordered soft and collinear limits, we calculate probability distributions for fixed N-body kinematics within jets with up through three resolved emissions (O(α$3\atop{s}$)). This enables explicit calculation of quantities central to machine learning such as the likelihood ratio, the area under the receiver operating characteristic curve, and reducibility factors within a well-defined approximation scheme. Further, we relate the existence of a consistent power counting procedure for discrimination to ideas for operational flavor definitions, and we use this relationship to construct a power counting for quark versus gluon discrimination as an expansion in e C F -C A $\ll$1, the exponential of the fundamental and adjoint Casimirs. Our calculations provide insight into the discrimination performance of particle multiplicity and show how observables sensitive to all emissions in a jet are optimal. We compare our predictions to the performance of individual observables and neural networks with parton shower event generators, validating that our predictions describe the features identified by machine learning
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Factorization and resummation for groomed multi-prong jet shapes
Observables which distinguish boosted topologies from QCD jets are playing an increasingly important role at the Large Hadron Collider (LHC). These observables are often used in conjunction with jet grooming algorithms, which reduce contamination from both theoretical and experimental sources. In this paper we derive factorization formulae for groomed multi-prong substructure observables, focusing in particular on the groomed D 2 observable, which is used to identify boosted hadronic decays of electroweak bosons at the LHC. Our factorization formulae allow systematically improvable calculations of the perturbative D 2 distribution and the resummation of logarithmically enhanced terms in all regions of phase space using renormalization group evolution. They include a novel factorization for the production of a soft subjet in the presence of a grooming algorithm, in which clustering effects enter directly into the hard matching. We use these factorization formulae to draw robust conclusions of experimental relevance regarding the universality of the D 2 distribution in both e+e- and pp collisions. In particular, we show that the only process dependence is carried by the relative quark vs. gluon jet fraction in the sample, no non-global logarithms from event-wide correlations are present in the distribution, hadronization corrections are controlled by the perturbative mass of the jet, and all global color correlations are completely removed by grooming, making groomed D 2 a theoretically clean QCD observable even in the LHC environment. Lastly, we compute all ingredients to one-loop accuracy, and present numerical results at next-to-leading logarithmic accuracy for e + e - collisions, comparing with parton shower Monte Carlo simulations. Results for pp collisions, as relevant for phenomenology at the LHC, are presented in a companion paper.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Casimir meets Poisson: improved quark/gluon discrimination with counting observables
Charged track multiplicity is among the most powerful observables for discriminating quark- from gluon-initiated jets. Despite its utility, it is not infrared and collinear (IRC) safe, so perturbative calculations are limited to studying the energy evolution of multiplicity moments. While IRC-safe observables, like jet mass, are perturbatively calculable, their distributions often exhibit Casimir scaling, such that their quark/gluon discrimination power is limited by the ratio of quark to gluon color factors. In this paper, we introduce new IRC-safe counting observables whose discrimination performance exceeds that of jet mass and approaches that of track multiplicity. The key observation is that track multiplicity is approximately Poisson distributed, with more suppressed tails than the Sudakov peak structure from jet mass. By using an iterated version of the soft drop jet grooming algorithm, we can define a “soft drop multiplicity” which is Poisson distributed at leading-logarithmic accuracy. In addition, we calculate the next-to-leading-logarithmic corrections to this Poisson structure. If we allow the soft drop groomer to proceed to the end of the jet branching history, we can define a collinear-unsafe (but still infrared-safe) counting observable. Exploiting the universality of the collinear limit, we define generalized fragmentation functions to study the perturbative energy evolution of collinear-unsafe multiplicity.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Soft-collinear supersymmetry
Soft-Collinear E ective Theory (SCET) is a framework for modeling the infrared structure of theories whose long distance behavior is dominated by soft and collinear divergences. This paper demonstrates that SCET can be made compatible with supersymmetry (SUSY). Explicitly, the e ective Lagrangian for N = 1 SUSY Yang-Mills is constructed and shown to be a complete description for the infrared of this model. For contrast, we also construct the e ective Lagrangian for chiral SUSY theories with Yukawa couplings, speci cally the single avor Wess-Zumino model. Only a subset of the infrared divergences are reproduced by the Lagrangian | to account for the complete low energy description requires the inclusion of local operators. SCET is formulated by expanding elds along a light-like direction and then subsequently integrating out degrees-of-freedom that are away from the light-cone. De ning the theory with respect to a speci c frame obfuscates Lorentz invariance | given that SUSY is a space-time symmetry, this presents a possible obstruction. The cleanest language with which to expose the congruence between SUSY and SCET requires exploring two novel formalisms: collinear fermions as two-component Weyl spinors, and SCET in light-cone gauge. By expressing SUSY Yang- Mills in \collinear superspace", a slice of superspace derived by integrating out half the fermionic coordinates, the light-cone gauge SUSY SCET theory can be written in terms of super elds. As a byproduct, bootstrapping up to the full theory yields the rst algorithmic approach for determining the SUSY Yang-Mills on-shell superspace action. As a result, this work paves the way toward discovering the e ective theory for the collinear limit of N = 4 SUSY Yang-Mills.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
The analytic structure of non-global logarithms: Convergence of the dressed gluon expansion
Non-global logarithms (NGLs) are the leading manifestation of correlations between distinct phase space regions in QCD and gauge theories and have proven a challenge to understand using traditional resummation techniques. Recently, the dressed gluon ex-pansion was introduced that enables an expansion of the NGL series in terms of a “dressed gluon” building block, defined by an all-orders factorization theorem. Here, we clarify the nature of the dressed gluon expansion, and prove that it has an infinite radius of convergence as a solution to the leading logarithmic and large-N c master equation for NGLs, the Banfi-Marchesini-Smye (BMS) equation. The dressed gluon expansion therefore provides an expansion of the NGL series that can be truncated at any order, with reliable uncertainty estimates. In contrast, manifest in the results of the fixed-order expansion of the BMS equation up to 12-loops is a breakdown of convergence at a finite value of α s log. We explain this finite radius of convergence using the dressed gluon expansion, showing how the dynamics of the buffer region, a region of phase space near the boundary of the jet that was identified in early studies of NGLs, leads to large contributions to the fixed order expansion. We also use the dressed gluon expansion to discuss the convergence of the next-to-leading NGL series, and the role of collinear logarithms that appear at this order. Finally, we show how an understanding of the analytic behavior obtained from the dressed gluon expansion allows us to improve the fixed order NGL series using conformal transformations to extend the domain of analyticity. Furthermore, this allows us to calculate the NGL distribution for all values of α s log from the coefficients of the fixed order expansion.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗