arXiv subjects

Andrew J. Larkoski

Publications and source records attributed to Andrew J. Larkoski.

At least 55 records · Page 3Linked to original sources

arXiv2020

Circumnavigating Collinear Superspace

In this paper, we extend the collinear superspace formalism to include the full range of $\mathcal{N} = 1$ 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 expressed on a collinear slice. This brings us full circle, by showing that all types of $\mathcal{N} = 1$ theories in four dimensions can be constructed in collinear superspace from purely infrared considerations. We speculate that supersymmetric theories with $\mathcal{N} > 1$ could also be implemented using similar collinear superspace constructions.

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arXiv2019

Calculating Pull for Non-Singlet Jets

The pull vector is a jet observable sensitive to the distribution of soft radiation controlled by the color flow in a collider event. We present calculations to leading order in the soft and collinear limits for the pull vector measured between pairs of jets that do not form a color-singlet dipole. Our calculations are presented within the context of $e^+e^-\to$ three jets events, on which pull is measured between the two subleading jets. A subset of these calculations can be re-interpreted as a bottom--anti-bottom quark jet pair in a color octet configuration, which can be a background to Higgs production at large boost. We also present a universal expression for the pull distribution in the high-boost and small jet radius limit. This distribution is controlled by color SU(3) quadratic Casimirs that arise from product representations of pairs of QCD jets.

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arXiv2019

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 $α_s$ 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 (${\cal O}(α_s^3)$). 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 $e^{C_F-C_A}\ll1$, 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.

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arXiv2019

Jet Substructure at the Large Hadron Collider: A Review of Recent Advances in Theory and Machine Learning

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 techniques for jet substructure, as well as a comprehensive reference for experts. We hope that it will prove a useful introduction to the exciting and rapidly developing field of jet substructure at the LHC.

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arXiv2019

Theory Predictions for the Pull Angle

Pull is a jet observable that is sensitive to color flow between dipoles. It has seen wide use for discrimination of particles with similar decay topologies but carrying different color representations and has been measured on W bosons from top quark decays by the D$\emptyset$ and ATLAS experiments. In this paper, we present the first theoretical predictions of pull, focusing on a color-singlet decaying in two jets. The pull angle observable is particularly sensitive to color flow, but is not infrared and collinear safe and so cannot be calculated in fixed-order perturbation theory. Nevertheless, all-orders resummation renders its distribution finite, a property referred to as Sudakov safety. In our prediction of the pull angle we also include an estimation of the effects from hadronization, and directly compare our results to simulation and experimental data.

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arXiv2019

New Insights on an Old Problem: Resummation of the D-parameter

The $D$-parameter is one of the oldest and most experimentally well-studied hadronic observables for $e^+e^-$ collisions. Nevertheless, unlike other classic observables like the $C$-parameter or thrust, the $D$-parameter has never been resummed throughout its entire singular phase space. Using insights and techniques motivated by modern multi-differential jet substructure calculations, we are able to predict the $D$-parameter distribution with no additional phase space cuts. Our approach is to measure both the $C$- and $D$-parameters on hadronic final states in $e^+e^-$ collisions. We can tune the value of the $C$-parameter with respect to the $D$-parameter to specify simple, physical configurations of final state particles in which to perform calculations. There are three parametric regions that exist: $D \ll C^2\sim 1$, $D\ll C^2\ll 1$, and $D\sim C^2\ll1$, and we calculate the $D$-parameter in each region separately. In the first two of these three regions, we present all-orders factorization theorems and explicitly demonstrate resummation to next-to-leading logarithmic accuracy. The region in which $D\sim C^2\ll1$ corresponds to the dijet limit and where the $D$-parameter loses the property of additivity. In this region we introduce a systematically-improvable procedure exploiting properties of conditional probabilities and resum to approximate next-to-leading logarithmic accuracy. The contributions from these regions can be consistently combined, and the value of the $C$-parameter integrated over to produce the cross section for the $D$-parameter. With these results, we match to leading fixed order as proof of principle and compare our resummed and matched prediction to data from LEP.

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arXiv2019

An Unorthodox Introduction to QCD

These are lecture notes presented at the 2017 CTEQ Summer School at the University of Pittsburgh and the 2018 CTEQ Summer School at the University of Puerto Rico, Mayaguez. The title is a reference to hep-th/0309149 and introduces perturbative QCD and its application to jet substructure from a bottom-up perspective based on the approximation of QCD as a weakly-coupled, conformal field theory. Using this approach, a simple derivation of the Sudakov form factor with soft gluon emission modeled as a Poisson process is presented. Topics of the identification and discrimination of quark- versus gluon-initiated jets and jet grooming are also discussed.

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arXiv2018

Novel Jet Observables from Machine Learning

Previous studies have demonstrated the utility and applicability of machine learning techniques to jet physics. In this paper, we construct new observables for the discrimination of jets from different originating particles exclusively from information identified by the machine. The approach we propose is to first organize information in the jet by resolved phase space and determine the effective $N$-body phase space at which discrimination power saturates. This then allows for the construction of a discrimination observable from the $N$-body phase space coordinates. A general form of this observable can be expressed with numerous parameters that are chosen so that the observable maximizes the signal vs.~background likelihood. Here, we illustrate this technique applied to discrimination of $H\to b\bar b$ decays from massive $g\to b\bar b$ splittings. We show that for a simple parametrization, we can construct an observable that has discrimination power comparable to, or better than, widely-used observables motivated from theory considerations. For the case of jets on which modified mass-drop tagger grooming is applied, the observable that the machine learns is essentially the angle of the dominant gluon emission off of the $b\bar b$ pair.

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arXiv2017

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. 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.

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arXiv2017

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.

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arXiv2017

Analytic Boosted Boson Discrimination at the Large Hadron Collider

Jet substructure is playing a central role at the Large Hadron Collider (LHC) probing the Standard Model in extreme regions of phase space and providing innovative ways to search for new physics. Analytic calculations of experimentally successful observables are a primary catalyst driving developments in jet substructure, allowing for a deeper understanding of observables and for the exploitation of increasingly subtle features of jets. In this paper we present a field theoretic framework enabling systematically improvable calculations of groomed multi-prong substructure observables, which builds on recent developments in multi-scale effective theories. We use this framework to compute for the first time the full spectrum for groomed tagging observables at the LHC, carefully treating both perturbative and non-perturbative contributions in all regions. Our analysis enables a precision understanding which we hope will improve the reach and sophistication of jet substructure techniques at the LHC.

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arXiv2017

Soft-Collinear Supersymmetry

Soft-Collinear Effective 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 effective Lagrangian for $\mathcal{N} = 1$ SUSY Yang-Mills is constructed and shown to be a complete description for the infrared of this model. For contrast, we also construct the effective Lagrangian for chiral SUSY theories with Yukawa couplings, specifically the single flavor 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 fields along a light-like direction and then subsequently integrating out degrees-of-freedom that are away from the light-cone. Defining the theory with respect to a specific 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 superfields. As a byproduct, bootstrapping up to the full theory yields the first algorithmic approach for determining the SUSY Yang-Mills on-shell superspace action. This work paves the way toward discovering the effective theory for the collinear limit of $\mathcal{N} = 4$ SUSY Yang-Mills.

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arXiv2016

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 expansion 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. This allows us to calculate the NGL distribution for all values of $α_s$log from the coefficients of the fixed order expansion.

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arXiv2016

Factorization for groomed jet substructure beyond the next-to-leading logarithm

Jet grooming algorithms are widely used in experimental analyses at hadron colliders to remove contaminating radiation from within jets. While the algorithms perform a great service to the experiments, their intricate algorithmic structure and multiple parameters has frustrated precision theoretic understanding. In this paper, we demonstrate that one particular groomer called soft drop actually makes precision jet substructure easier. In particular, we derive a factorization formula for a large class of soft drop jet substructure observables, including jet mass. The essential observation that allows for this factorization is that, without the soft wide-angle radiation groomed by soft drop, all singular contributions are collinear. The simplicity and universality of the collinear limit in QCD allows us to show that to all orders, the normalized differential cross section has no contributions from non-global logarithms. It is also independent of process, up to the relative fraction of quark and gluon jets. In fact, soft drop allows us to define this fraction precisely. The factorization theorem also explains why soft drop observables are less sensitive to hadronization than their ungroomed counterparts. Using the factorization theorem, we resum the soft drop jet mass to next-to-next-to-leading logarithmic accuracy. This requires calculating some clustering effects that are closely related to corresponding effects found in jet veto calculations. We match our resummed calculation to fixed order results for both $e^+e^-\to$ dijets and $pp\to Z+j$ events, producing the first jet substructure predictions (groomed or ungroomed) to this accuracy for the LHC.

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arXiv2016

Building a Better Boosted Top Tagger

Distinguishing hadronically decaying boosted top quarks from massive QCD jets is an important challenge at the Large Hadron Collider. In this paper we use the power counting method to study jet substructure observables designed for top tagging, and gain insight into their performance. We introduce a powerful new family of discriminants formed from the energy correlation functions which outperform the widely used N-subjettiness. These observables take a highly non-trivial form, demonstrating the importance of a systematic approach to their construction.

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arXiv2016

Analytic Boosted Boson Discrimination

Observables which discriminate boosted topologies from massive QCD jets are of great importance for the success of the jet substructure program at the Large Hadron Collider. Such observables, while both widely and successfully used, have been studied almost exclusively with Monte Carlo simulations. In this paper we present the first all-orders factorization theorem for a two-prong discriminant based on a jet shape variable, $D_2$, valid for both signal and background jets. Our factorization theorem simultaneously describes the production of both collinear and soft subjets, and we introduce a novel zero-bin procedure to correctly describe the transition region between these limits. By proving an all orders factorization theorem, we enable a systematically improvable description, and allow for precision comparisons between data, Monte Carlo, and first principles QCD calculations for jet substructure observables. Using our factorization theorem, we present numerical results for the discrimination of a boosted $Z$ boson from massive QCD background jets. We compare our results with Monte Carlo predictions which allows for a detailed understanding of the extent to which these generators accurately describe the formation of two-prong QCD jets, and informs their usage in substructure analyses. Our calculation also provides considerable insight into the discrimination power and calculability of jet substructure observables in general.

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arXiv2016

Collinear Superspace

This letter provides a superfield based approach to constructing a collinear slice of $\mathcal{N}$ = 1 superspace. The strategy is analogous to integrating out anti-collinear fermionic degrees-of-freedom as was developed in the context of soft-collinear effective theory. The resulting Lagrangian can be understood as an integral over collinear superspace, where half the supercoordinates have been integrated out. The application to $\mathcal{N}$ = 1 super Yang-Mills is presented. Collinear superspace provides the foundation for future explorations of supersymmetric soft-collinear effective theory.

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arXiv2016

Precision physics with pile-up insensitive observables

To deepen the search for beyond the Standard Model physics, the Large Hadron Collider is pushing to higher and higher luminosity. At high luminosity, precision physics becomes increasingly difficult due to contamination from additional proton collisions per bunch crossing called pile-up. In recent years, many methods have been developed to cull this excess mostly low-energy radiation away from important signal regions, but it has been unclear if these methods were amenable to systematically-improvable theoretical understanding. In this paper, it is shown that one such method, soft drop jet grooming, has excellent theoretical properties: it is ultra-local, depending on only radiation within a jet, and it is free of non-global logarithms. Calculations of the soft drop jet mass and related observables are presented at next-to-next-to-leading logarithmic accuracy matched to next-to-next-to-leading fixed-order in perturbative Quantum Chromodynamics. Once measured at the Large Hadron Collider, precision comparisons between theory and data can be made, essentially independent of the amount of pile-up contamination.

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