arXiv subjects

Matthew D. Schwartz

Publications and source records attributed to Matthew D. Schwartz.

At least 37 records · Page 2Linked to original sources

arXiv2023

Implications of the Landau Equations for Iterated Integrals

We introduce a method for deriving constraints on the symbol of Feynman integrals from the form of their asymptotic expansions in the neighborhood of Landau loci. In particular, we show that the behavior of these integrals near singular points is directly related to the position in the symbol where one of the letters vanishes or becomes infinite. We illustrate this method on integrals with generic masses, and as a corollary prove the conjectured bound of $\lfloor \frac {D \ell} 2\rfloor$ on the transcendental weight of polylogarithmic $\ell$-loop integrals of this type in integer numbers of dimensions $D$. We also derive new constraints on the kinematic dependence of certain products of symbol letters that remain finite near singular points.

hep-th↗

arXiv2022

Constraints on Sequential Discontinuities from the Geometry of On-shell Spaces

We present several classes of constraints on the discontinuities of Feynman integrals that go beyond the Steinmann relations. These constraints follow from a geometric formulation of the Landau equations that was advocated by Pham, in which the singularities of Feynman integrals correspond to critical points of maps between on-shell spaces. To establish our results, we review elements of Picard-Lefschetz theory, which connect the homotopy properties of the space of complexified external momenta to the homology of the combined space of on-shell internal and external momenta. An important concept that emerges from this analysis is the question of whether or not a pair of Landau singularities is compatible-namely, whether or not the Landau equations for the two singularities can be satisfied simultaneously. Under conditions we describe, sequential discontinuities with respect to non-compatible Landau singularities must vanish. Although we only rigorously prove results for Feynman integrals with generic masses in this paper, we expect the geometric and algebraic insights that we gain will also assist in the analysis of more general Feynman integrals.

hep-th↗

arXiv2022

Sudakov Shoulder Resummation for Thrust and Heavy Jet Mass

When the allowed range of an observable grows order-by-order in perturbation theory, its perturbative expansion can have discontinuities (as in the $C$ parameter) or discontinuities in its derivatives (as in thrust or heavy jet mass) called Sudakov shoulders. We explore the origin of these logarithms using both perturbation theory and effective field theory. We show that for thrust and heavy jet mass, the logarithms arise from kinematic configurations with narrow jets and deduce the next-to-leading logarithmic series. The left-shoulder logarithms in heavy jet mass ($ρ$) of the form $r\ α_s^n \ln^{2n}r $ with $r=\frac{1}{3}-ρ$ are particularly dangerous, because they invalidate fixed order perturbation theory in regions traditionally used to extract $α_s$. Although the factorization formula shows there are no non-global logarithms, we find Landau-pole like singularities in the resummed distribution associated with the cusp anomalous dimension, and that power corrections are exceptionally important.

hep-ph↗

arXiv2022

Prospects for strong coupling measurement at hadron colliders using soft-drop jet mass

We compute the soft-drop jet-mass distribution from $pp$ collisions to NNLL accuracy while including nonperturbative corrections through a field-theory based formalism. Using these calculations, we assess the theoretical uncertainties on an $α_s$ precision measurement due to higher order perturbative effects, nonperturbative corrections, and PDF uncertainty. We identify which soft-drop parameters are well-suited for measuring $α_s$, and find that higher-logarithmic resummation has a qualitatively important effect on the shape of the jet-mass distribution. We find that quark jets and gluon jets have similar sensitivity to $α_s$, and emphasize that experimentally distinguishing quark and gluon jets is not required for an $α_s$ measurement. We conclude that measuring $α_s$ to the 10% level is feasible now, and with improvements in theory a 5% level measurement is possible. Getting down to the 1% level to be competitive with other state-of-the-art measurements will be challenging.

hep-ph↗

arXiv2022

Simplifying Polylogarithms with Machine Learning

Polylogrithmic functions, such as the logarithm or dilogarithm, satisfy a number of algebraic identities. For the logarithm, all the identities follow from the product rule. For the dilogarithm and higher-weight classical polylogarithms, the identities can involve five functions or more. In many calculations relevant to particle physics, complicated combinations of polylogarithms often arise from Feynman integrals. Although the initial expressions resulting from the integration usually simplify, it is often difficult to know which identities to apply and in what order. To address this bottleneck, we explore to what extent machine learning methods can help. We consider both a reinforcement learning approach, where the identities are analogous to moves in a game, and a transformer network approach, where the problem is viewed analogously to a language-translation task. While both methods are effective, the transformer network appears more powerful and holds promise for practical use in symbolic manipulation tasks in mathematical physics.

cs.LG↗

arXiv2021

Challenges for Unsupervised Anomaly Detection in Particle Physics

Anomaly detection relies on designing a score to determine whether a particular event is uncharacteristic of a given background distribution. One way to define a score is to use autoencoders, which rely on the ability to reconstruct certain types of data (background) but not others (signals). In this paper, we study some challenges associated with variational autoencoders, such as the dependence on hyperparameters and the metric used, in the context of anomalous signal (top and $W$) jets in a QCD background. We find that the hyperparameter choices strongly affect the network performance and that the optimal parameters for one signal are non-optimal for another. In exploring the networks, we uncover a connection between the latent space of a variational autoencoder trained using mean-squared-error and the optimal transport distances within the dataset. We then show that optimal transport distances to representative events in the background dataset can be used directly for anomaly detection, with performance comparable to the autoencoders. Whether using autoencoders or optimal transport distances for anomaly detection, we find that the choices that best represent the background are not necessarily best for signal identification. These challenges with unsupervised anomaly detection bolster the case for additional exploration of semi-supervised or alternative approaches.

hep-ph↗

arXiv2021

Parameter Inference from Event Ensembles and the Top-Quark Mass

One of the key tasks of any particle collider is measurement. In practice, this is often done by fitting data to a simulation, which depends on many parameters. Sometimes, when the effects of varying different parameters are highly correlated, a large ensemble of data may be needed to resolve parameter-space degeneracies. An important example is measuring the top-quark mass, where other physical and unphysical parameters in the simulation must be marginalized over when fitting the top-quark mass parameter. We compare three different methodologies for top-quark mass measurement: a classical histogram fitting procedure, similar to one commonly used in experiment optionally augmented with soft-drop jet grooming; a machine-learning method called DCTR; and a linear regression approach, either using a least-squares fit or with a dense linearly-activated neural network. Despite the fact that individual events are totally uncorrelated, we find that the linear regression methods work most effectively when we input an ensemble of events sorted by mass, rather than training them on individual events. Although all methods provide robust extraction of the top-quark mass parameter, the linear network does marginally best and is remarkably simple. For the top study, we conclude that the Monte-Carlo-based uncertainty on current extractions of the top-quark mass from LHC data can be reduced significantly (by perhaps a factor of 2) using networks trained on sorted event ensembles. More generally, machine learning from ensembles for parameter estimation has broad potential for collider physics measurements.

hep-ph↗

arXiv2021

Quark-Gluon Backscattering in the Regge Limit at One-Loop

At small momentum transfer, the quark-gluon scattering cross section dσ/dt has a power-law divergence in the backward scattering region where the outgoing quark is nearly collinear to the incoming gluon. In this Regge limit |t|<< s, the leading behavior of the 2 2 amplitude can be described by the exchange of Glauber quarks. In Soft-Collinear Effective Theory (SCET) at leading power, Glauber quark exchange is given by five non-local Glauber quark operators, of which only one is generated at tree-level. We show that at leading power the QCD amplitude for quark-gluon backscattering at one-loop can be exactly reproduced by SCET using the tree-level Glauber operator. The agreement between QCD and SCET of the ultraviolet, infrared, and rapidity divergences as well as all logarithms, Glauber phases and finite parts for all polarizations of the external gluons is a strong check on the effective theory. We find that the entire one-loop matching vanishes -- there is no correction to the operator generated at tree-level, and the coefficients of the other four operators remain zero at one-loop. This suggests that SCET with Glauber operators may be useful for uncovering new aspects of Regge physics in a systematically improveable way.

hep-ph↗

arXiv2021

The Compton Scattering Total Cross Section at Next-to-Leading Order

An analytic formula is given for the total scattering cross section of an electron and a photon at order $α^3$. This includes both the double-Compton scattering real-emission contribution as well as the virtual Compton scattering part. When combined with the recent analytic result for the pair-production cross section, the complete $α^3$ cross section is now known. Both the next-to-leading order calculation as well as the pair-production cross section are computed using modern multiloop calculation techniques, where cut diagrams are decomposed into a set of master integrals that are then computed using differential equations.

hep-ph↗

arXiv2021

Modern Machine Learning and Particle Physics

Over the past five years, modern machine learning has been quietly revolutionizing particle physics. Old methodology is being outdated and entirely new ways of thinking about data are becoming commonplace. This article will review some aspects of the natural synergy between modern machine learning and particle physics, focusing on applications at the Large Hadron Collider. A sampling of examples is given, from signal/background discrimination tasks using supervised learning to direct data-driven approaches. Some comments on persistent challenges and possible future directions for the field are included at the end.

hep-ph↗

arXiv2020

A Finite $S$-Matrix

When massless particles are involved, the traditional scattering matrix ($S$-matrix) does not exist: it has no rigorous non-perturbative definition and has infrared divergences in its perturbative expansion. The problem can be traced to the impossibility of isolating single-particle states at asymptotic times. On the other hand, the troublesome non-separable interactions are often universal: in gauge theories they factorize so that the asymptotic evolution is independent of the hard scattering. Exploiting this factorization property, we show how a finite "hard" $S$-matrix, $S_H$, can be defined by replacing the free Hamiltonian with a soft-collinear asymptotic Hamiltonian. The elements of $S_H$ are gauge invariant and infrared finite, and exist even in conformal field theories. One can interpret elements of $S_H$ alternatively 1) as elements of the traditional $S$-matrix between dressed states, 2) as Wilson coefficients, or 3) as remainder functions. These multiple interpretations provide different insights into the rich structure of $S_H$.

hep-th↗

arXiv2020

An $S$-Matrix for Massless Particles

The traditional $S$-matrix does not exist for theories with massless particles, such as quantum electrodynamics. The difficulty in isolating asymptotic states manifests itself as infrared divergences at each order in perturbation theory. Building on insights from the literature on coherent states and factorization, we construct an $S$-matrix that is free of singularities order-by-order in perturbation theory. Factorization guarantees that the asymptotic evolution in gauge theories is universal, i.e. independent of the hard process. Although the hard $S$-matrix element is computed between well-defined few particle Fock states, dressed/coherent states can be seen to form as intermediate states in the calculation of hard $S$-matrix elements. We present a framework for the perturbative calculation of hard $S$-matrix elements combining Lorentz-covariant Feynman rules for the dressed-state scattering with time-ordered perturbation theory for the asymptotic evolution. With hard cutoffs on the asymptotic Hamiltonian, the cancellation of divergences can be seen explicitly. In dimensional regularization, where the hard cutoffs are replaced by a renormalization scale, the contribution from the asymptotic evolution produces scaleless integrals that vanish. A number of illustrative examples are given in QED, QCD, and $\mathcal{N}=4$ super Yang-Mills theory.

hep-th↗

arXiv2020

ABCDisCo: Automating the ABCD Method with Machine Learning

The ABCD method is one of the most widely used data-driven background estimation techniques in high energy physics. Cuts on two statistically-independent classifiers separate signal and background into four regions, so that background in the signal region can be estimated simply using the other three control regions. Typically, the independent classifiers are chosen "by hand" to be intuitive and physically motivated variables. Here, we explore the possibility of automating the design of one or both of these classifiers using machine learning. We show how to use state-of-the-art decorrelation methods to construct powerful yet independent discriminators. Along the way, we uncover a previously unappreciated aspect of the ABCD method: its accuracy hinges on having low signal contamination in control regions not just overall, but relative to the signal fraction in the signal region. We demonstrate the method with three examples: a simple model consisting of three-dimensional Gaussians; boosted hadronic top jet tagging; and a recasted search for paired dijet resonances. In all cases, automating the ABCD method with machine learning significantly improves performance in terms of ABCD closure, background rejection and signal contamination.

hep-ph↗

arXiv2020

Sequential Discontinuities of Feynman Integrals and the Monodromy Group

We generalize the relation between discontinuities of scattering amplitudes and cut diagrams to cover sequential discontinuities (discontinuities of discontinuities) in arbitrary momentum channels. The new relations are derived using time-ordered perturbation theory, and hold at phase-space points where all cut momentum channels are simultaneously accessible. As part of this analysis, we explain how to compute sequential discontinuities as monodromies and explore the use of the monodromy group in characterizing the analytic properties of Feynman integrals. We carry out a number of cross-checks of our new formulas in polylogarithmic examples, in some cases to all loop orders.

hep-th↗

arXiv2019

Binary JUNIPR: an interpretable probabilistic model for discrimination

JUNIPR is an approach to unsupervised learning in particle physics that scaffolds a probabilistic model for jets around their representation as binary trees. Separate JUNIPR models can be learned for different event or jet types, then compared and explored for physical insight. The relative probabilities can also be used for discrimination. In this paper, we show how the training of the separate models can be refined in the context of classification to optimize discrimination power. We refer to this refined approach as Binary JUNIPR. Binary JUNIPR achieves state-of-the-art performance for quark/gluon discrimination and top-tagging. The trained models can then be analyzed to provide physical insight into how the classification is achieved. As examples, we explore differences between quark and gluon jets and between gluon jets generated with two different simulations.

hep-ph↗

arXiv2018

Infrared Finiteness and Forward Scattering

Infrared divergences have long been heralded to cancel in sufficiently inclusive cross-sections, according to the famous Kinoshita-Lee-Nauenberg theorem which mandates an initial and final state sum. While well-motivated, this theorem is much weaker than necessary: for finiteness, one need only sum over initial $\textit{or}$ final states. Moreover, the cancellation generically requires the inclusion of the forward scattering process. We provide a number of examples showing the importance of this revised understanding: in $e^+e^- \to Z$ at next-to-leading order, one can sum over certain initial and final states with an arbitrary number of extra photons, or only over final states with a finite number of photons, if forward scattering is included. For Compton scattering, infrared finiteness requires the indistinguishability of hard forward-scattered electrons and photons. This implies that in addition to experimental limits on the energy and angular resolution, there must also be an experimental limit on the momentum at which electric charge can be observed. Similar considerations are required to explain why the rate for $γγ$ to scatter into photons alone is infrared divergent but the rate for $γγ$ to scatter into photons or charged particles is finite. This new understanding sheds light on the importance of including degenerate initial states in physical predictions, the relevance of disconnected Feynman diagrams, the importance of dressing initial or final-state charged particles, and the quest to properly define the $S$ matrix.

hep-ph↗

arXiv2018

Jet Charge and Machine Learning

Modern machine learning techniques, such as convolutional, recurrent and recursive neural networks, have shown promise for jet substructure at the Large Hadron Collider. For example, they have demonstrated effectiveness at boosted top or W boson identification or for quark/gluon discrimination. We explore these methods for the purpose of classifying jets according to their electric charge. We find that both neural networks that incorporate distance within the jet as an input and boosted decision trees including radial distance information can provide significant improvement in jet charge extraction over current methods. Specifically, convolutional, recurrent, and recursive networks can provide the largest improvement over traditional methods, in part by effectively utilizing distance within the jet or clustering history. The advantages of using a fixed-size input representation (as with the CNN) or a small input representation (as with the RNN) suggest that both convolutional and recurrent networks will be essential to the future of modern machine learning at colliders.

hep-ph↗

arXiv2018

Deep learning in color: towards automated quark/gluon jet discrimination

Artificial intelligence offers the potential to automate challenging data-processing tasks in collider physics. To establish its prospects, we explore to what extent deep learning with convolutional neural networks can discriminate quark and gluon jets better than observables designed by physicists. Our approach builds upon the paradigm that a jet can be treated as an image, with intensity given by the local calorimeter deposits. We supplement this construction by adding color to the images, with red, green and blue intensities given by the transverse momentum in charged particles, transverse momentum in neutral particles, and pixel-level charged particle counts. Overall, the deep networks match or outperform traditional jet variables. We also find that, while various simulations produce different quark and gluon jets, the neural networks are surprisingly insensitive to these differences, similar to traditional observables. This suggests that the networks can extract robust physical information from imperfect simulations.

hep-ph↗