arXiv subjects

Ian Moult

Publications and source records attributed to Ian Moult.

At least 73 records · Page 4Linked to original sources

arXiv2023

Analyzing N-point Energy Correlators Inside Jets with CMS Open Data

Jets of hadrons produced at high-energy colliders provide experimental access to the dynamics of asymptotically free quarks and gluons and their confinement into hadrons. In this paper, we show that the high energies of the Large Hadron Collider (LHC), together with the exceptional resolution of its detectors, allow multipoint correlation functions of energy flow operators to be directly measured within jets for the first time. Using Open Data from the CMS experiment, we show that reformulating jet substructure in terms of these correlators provides new ways of probing the dynamics of QCD jets, which enables direct imaging of the confining transition to free hadrons as well as precision measurements of the scaling properties and interactions of quarks and gluons. This opens a new era in our understanding of jet substructure and illustrates the immense unexploited potential of high-quality LHC data sets for elucidating the dynamics of QCD.

hep-ph↗

arXiv2023

Anomalous Dimensions from Soft Regge Constants

Using an effective field theory (EFT) formalism for forward scattering, we reconsider the factorization of $2\to 2$ scattering amplitudes in the Regge limit. Expanding the amplitude in gauge invariant operators labelled by the number of Glauber exchanges, allows us to further factorize the standard impact factors into separate collinear and soft functions. The soft functions are universal, and describe radiative corrections to the Reggeized gluon states exchanged by the collinear projectiles. Remarkably, we find that the one-loop soft function for the single Reggeized gluon state is given to $\mathcal{O}(ε)$ in terms of the two-loop cusp and two-loop rapidity anomalous dimensions. We argue that this iterative structure follows from the simple action of crossing symmetry in the forward scattering limit, which in the EFT allows us to replace the divergent part of a soft loop by a much simpler Glauber loop. We use this correspondence to provide a simple calculation of the two-loop Regge trajectory using the EFT. We then explore its implications at higher perturbative orders, and derive the maximally matter dependent contributions to the Regge trajectory to all loop orders, i.e.~the terms $\sim α_s^{k+1}n_f^k$ for any $k$, where $n_f$ is the number of massless flavors. These simplifications suggests that the EFT approach to the Regge limit will be helpful to explore and further understand the structure of the Regge limit.

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arXiv2023

Resolving the Scales of the Quark-Gluon Plasma with Energy Correlators

Jets provide us with ideal probes of the quark-gluon plasma (QGP) produced in heavy-ion collisions, since its dynamics at its different scales is imprinted into the multi-scale substructure of the final state jets. We present a new approach to jet substructure in heavy-ion collisions based on the study of correlation functions of energy flow operators. By analysing the two-point correlator of an in-medium quark jet, we demonstrate that the spectra of correlation functions robustly identify the scales defined by the properties of the QGP, particularly those associated with the onset of colour coherence.

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arXiv2023

The International Linear Collider: Report to Snowmass 2021

The International Linear Collider (ILC) is on the table now as a new global energy-frontier accelerator laboratory taking data in the 2030s. The ILC addresses key questions for our current understanding of particle physics. It is based on a proven accelerator technology. Its experiments will challenge the Standard Model of particle physics and will provide a new window to look beyond it. This document brings the story of the ILC up to date, emphasizing its strong physics motivation, its readiness for construction, and the opportunity it presents to the US and the global particle physics community.

physics.acc-ph↗

arXiv2022

Systematic Quark/Gluon Identification with Ratios of Likelihoods

Discriminating between quark- and gluon-initiated jets has long been a central focus of jet substructure, leading to the introduction of numerous observables and calculations to high perturbative accuracy. At the same time, there have been many attempts to fully exploit the jet radiation pattern using tools from statistics and machine learning. We propose a new approach that combines a deep analytic understanding of jet substructure with the optimality promised by machine learning and statistics. After specifying an approximation to the full emission phase space, we show how to construct the optimal observable for a given classification task. This procedure is demonstrated for the case of quark and gluons jets, where we show how to systematically capture sub-eikonal corrections in the splitting functions, and prove that linear combinations of weighted multiplicity is the optimal observable. In addition to providing a new and powerful framework for systematically improving jet substructure observables, we demonstrate the performance of several quark versus gluon jet tagging observables in parton-level Monte Carlo simulations, and find that they perform at or near the level of a deep neural network classifier. Combined with the rapid recent progress in the development of higher order parton showers, we believe that our approach provides a basis for systematically exploiting subleading effects in jet substructure analyses at the Large Hadron Collider (LHC) and beyond.

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arXiv2022

Collinear Parton Dynamics Beyond DGLAP

Renormalization group evolution equations describing the scale dependence of quantities in quantum chromodynamics (QCD) play a central role in the interpretation of experimental data. Arguably the most important evolution equations for collider physics applications are the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations, which describe the evolution of a quark or gluon fragmenting into hadrons, with only a single hadron identified at a time. In recent years, the study of the correlations of energy flow within jets has come to play a central role at collider experiments, necessitating an understanding of correlations, going beyond the standard DGLAP paradigm. In this Letter we derive a general renormalization group equation describing the collinear dynamics that account for correlations in the fragmentation. We compute the kernel of this evolution equation at next-to-leading order (NLO), where it involves the $1\to 3$ splitting functions, and develop techniques to solve it numerically. We show that our equation encompasses all previously-known collinear evolution equations, namely DGLAP and the evolution of multi-hadron fragmentation functions. As an application of our results, we consider the phenomenologically-relevant example of energy flow on charged particles, computing the energy fraction in charged particles in $e^+e^- \to$ hadrons at NNLO. Our results are an important step towards improving the understanding of the collinear dynamics of jets, with broad applications in jet substructure, ranging from the study of multi-hadron correlations, to the description of inclusive (sub)jet production, and the advancement of modern parton showers.

hep-ph↗

arXiv2022

Beautiful and Charming Energy Correlators

Understanding the detailed structure of energy flow within jets, a field known as jet substructure, plays a central role in searches for new physics, and precision studies of QCD. Many applications of jet substructure require an understanding of jets initiated by heavy quarks, whose description has lagged behind remarkable recent progress for massless jets. In this Letter, we initiate a study of correlation functions of energy flow operators on beauty and charm jets to illuminate the effects of the intrinsic mass of the elementary particles of QCD. We present a factorization theorem incorporating the mass of heavy quarks, and show that the heavy quark jet functions for energy correlators have a simple structure in perturbation theory. Our results achieve the very first full next-to-leading-logarithmic calculation of the heavy quark jet substructure observable at the LHC. Using this framework, we study the behavior of the correlators, and show that they exhibit a clear transition from a massless scaling regime, at precisely the scale of the heavy quark mass. This manifests the long-sought-after dead-cone effect and illustrates fundamental effects from the intrinsic mass of beauty and charm quarks in a perturbative regime, before they are confined inside hadrons. Our theoretical framework for studying energy correlators using heavy jets has many exciting applications for improving the description of mass effects in next generation parton shower event generators, probing the QGP, and studying heavy flavor fragmentation functions.

hep-ph↗

arXiv2022

The Four Loop QCD Rapidity Anomalous Dimension

The rapidity anomalous dimension controls the scaling of transverse momentum dependent observables in the Sudakov region. In a conformal theory it is equivalent to the soft anomalous dimension, but in QCD this relation is broken by anomalous terms proportional to the $β$-function. In this paper we first give a simple proof of this relation using two different representations of the energy-energy correlator observable. We then calculate the anomalous terms to three loops by computing the three-loop fully differential soft function to $\mathcal{O}(ε)$. Combined with recent perturbative data from the study of on-shell form factors and splitting functions, this allows us to derive the four loop rapidity anomalous dimension in QCD.

hep-ph↗

arXiv2022

Non-Gaussianities in Collider Energy Flux

The microscopic dynamics of particle collisions is imprinted into the statistical properties of asymptotic energy flux, much like the dynamics of inflation is imprinted into the cosmic microwave background. This energy flux is characterized by correlation functions $\langle \mathcal{E}(\vec n_1)\cdots \mathcal{E}(\vec n_k) \rangle$ of energy flow operators $ \mathcal{E}(\vec n)$. There has been significant recent progress in studying energy flux, including the calculation of multi-point correlation functions and their direct measurement inside high-energy jets at the Large Hadron Collider (LHC). In this paper, we build on these advances by defining a notion of "celestial non-gaussianity" as a ratio of the three-point function to a product of two-point functions. We show that this celestial non-gaussianity is under perturbative control within jets at the LHC, allowing us to cleanly access the non-gaussian interactions of quarks and gluons. We find good agreement between perturbative calculations of the non-gaussianity and a charged-particle-based analysis using CMS Open Data, and we observe a strong non-gaussianity peaked in the "flattened triangle" regime. The ability to robustly study three-point correlations is a significant step in advancing our understanding of jet substructure at the LHC. We anticipate that the celestial non-gaussianity, and its generalizations, will play an important role in the development of higher-order parton showers simulations and in the hunt for ever more subtle signals of potential new physics within jets.

hep-ph↗

arXiv2022

Conformal Colliders Meet the LHC

The remarkably high energies of the Large Hadron Collider (LHC) have allowed for the first measurements of the shapes and scalings of multi-point correlators of energy flow operators, $\langle Ψ| \mathcal{E}(\vec n_1) \mathcal{E}(\vec n_2) \cdots \mathcal{E}(\vec n_k) |Ψ\rangle$, providing new insights into the Lorentzian dynamics of quantum chromodynamics (QCD). In this Letter, we use recent advances in effective field theory to derive a rigorous factorization theorem for the light-ray density matrix, $ρ= |Ψ\rangle \langle Ψ|$, inside high transverse momentum jets at the LHC. Using the light-ray operator product expansion, the scaling behavior of multi-point correlators can be computed from the expectation value of the twist-2 spin-$J$ light-ray operators, $\mathbb{O}^{[J]}$, in this state, $\text{Tr}[ ρ~\mathbb{O}^{[J]} ]$. We compute the light-ray density matrix at next-to-leading order, and combine this with results for the next-to-leading logarithmic scaling behavior of the correlators up to six-points, comparing with CMS Open Data. This theoretical accuracy allows us to resolve the quantum scaling dimensions of QCD light-ray operators inside jets at the LHC. Our factorization theorem for the light-ray density matrix at the LHC completes the link between recent developments in the study of energy correlators and LHC phenomenology, opening the door to a wide variety of precision jet substructure studies.

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arXiv2022

Extending Precision Perturbative QCD with Track Functions

Collider experiments often exploit information about the quantum numbers of final state hadrons to maximize their sensitivity, with applications ranging from the use of tracking information (electric charge) for precision jet substructure measurements, to flavor tagging for nucleon structure studies. For such measurements, perturbative calculations in terms of quarks and gluons are insufficient, and non-perturbative track functions describing the energy fraction of a quark or gluon converted into a subset of hadrons (e.g., charged hadrons) must be incorporated. Unlike fragmentation functions, track functions describe correlations between hadrons and therefore satisfy complicated non-linear evolution equations whose structure has so far eluded calculation beyond the leading order. In this Letter, we develop an understanding of track functions and their interplay with energy flow observables beyond the leading order, allowing them to be used in state-of-the-art perturbative calculations for the first time. We identify a shift symmetry in the evolution of their moments that fixes their structure, and we explicitly compute the evolution of the first three moments at next-to-leading order, allowing for the description of up to three-point energy correlations. We then calculate the two-point energy correlator on charged particles at $O(α_s^2)$, illustrating explicitly that infrared singularities in perturbation theory are absorbed by moments of the track functions and also highlighting how these moments seamlessly interplay with modern techniques for perturbative calculations. Our results extend the boundaries of traditional perturbative QCD, enabling precision perturbative predictions for energy flow observables sensitive to the quantum numbers of hadronic states.

hep-ph↗

arXiv2022

Celestial Blocks and Transverse Spin in the Three-Point Energy Correlator

Quantitative theoretical techniques for understanding the substructure of jets at the LHC enable new insights into the dynamics of QCD, and novel approaches to search for new physics. Recently, there has been a program to reformulate jet substructure in terms of correlation functions, $\langle \mathcal{E}(\vec n_1) \mathcal{E}(\vec n_2) \cdots \mathcal{E}(\vec n_k) \rangle$, of light-ray operators, $\mathcal{E}(\vec n)$, allowing the application of techniques developed in the study of Conformal Field Theories (CFTs). In this paper we further develop these techniques in the particular context of the three-point correlator $\langle \mathcal{E}(\vec n_1) \mathcal{E}(\vec n_2) \mathcal{E}(\vec n_3) \rangle$, using recently computed perturbative data in both QCD and $\mathcal{N}=4$ sYM. We derive the celestial blocks appearing in the light-ray operator product expansion (OPE) of the three-point correlator, and use the Lorentzian inversion formula to extract the spectrum of light-ray operators appearing in the expansion, showing, in particular, that the OPE data is analytic in transverse spin. Throughout our presentation, we highlight the relation between the OPE approach, and more standard splitting function based approaches of perturbative QCD, emphasizing the utility of the OPE approach for incorporating symmetries in jet substructure calculations. We hope that our presentation introduces a number of new techniques to the jet substructure community, and also illustrates the phenomenological relevance of the study of light-ray operators in the OPE limit to the CFT community.

hep-ph↗

arXiv2021

Spinning Gluons from the QCD Light-Ray OPE

We study the transverse spin structure of the squeezed limit of the three-point energy correlator, $\langle \mathcal{E}(\vec n_1) \mathcal{E}(\vec n_2) \mathcal{E}(\vec n_3) \rangle$. To describe its all orders perturbative behavior, we develop the light-ray operator product expansion (OPE) in QCD. At leading twist the iterated OPE of $\mathcal{E}(\vec n_i)$ operators closes onto light-ray operators $\mathbb{O}^{[J]}(\vec n)$ with spin $J$, and transverse spin $j=0,2$. We compute the $\mathcal{E}(\vec n_1) \mathcal{E}(\vec n_2)$, $\mathcal{E}(\vec n_1) \mathbb{O}^{[J]}(\vec n_2) $ and $\mathbb{O}^{[J_1]}(\vec n_1) \mathbb{O}^{[J_2]}(\vec n_2) $ OPEs as analytic functions of $J$, which allows for the description of arbitrary squeezed limits of $N$-point correlators in QCD. We use these results with $J=3$ to reproduce the perturbative expansion in the squeezed limit of the three-point correlator, as well as to resum the leading twist singular structure for both quark and gluon jets, including transverse spin contributions, as required for phenomenological applications. Finally, we briefly comment on the transverse spin structure at higher twists, and show that to all orders in the twist expansion the highest transverse spin contributions are universal between quark and gluon jets, and are descendants of the leading twist transverse spin-2 operator, allowing their resummation into a simple two-dimensional Euclidean conformal block. Due to the general applicability of our results to arbitrary correlation functions of energy flow operators, we anticipate that they can be widely applied to improving our understanding of jet substructure at the LHC.

hep-ph↗

arXiv2021

Quantum Interference in Jet Substructure from Spinning Gluons

Collimated sprays of hadrons, called jets, are an emergent phenomenon of Quantum Chromodynamics (QCD) at collider experiments, whose detailed internal structure encodes valuable information about the interactions of high energy quarks and gluons, and their confinement into color-neutral hadrons. The flow of energy within jets is characterized by correlation functions of energy flow operators, with the three-point correlator, being the first correlator with non-trivial shape dependence, playing a special role in unravelling the dynamics of QCD. In this Letter we initiate a study of the three-point energy correlator to all orders in the strong coupling constant, in the limit where two of the detectors are squeezed together. We show that by rotating the two squeezed detectors with respect to the third by an angle $ϕ$, a $\cos (2ϕ)$ dependence arising from the quantum interference between intermediate virtual gluons with $+/-$ helicity is imprinted on the detector. This can be regarded as a double slit experiment performed with jet substructure, and it provides a direct probe of the ultimately quantum nature of the substructure of jets, and of transverse spin physics in QCD. To facilitate our all-orders analysis, we adopt the Operator Product Expansion (OPE) for light-ray operators in conformal field theory and develop it in QCD. Our application of the light-ray OPE in real world QCD establishes it as a powerful theoretical tool with broad applications for the study of jet substructure.

hep-ph↗

arXiv2020

Three Point Energy Correlators in the Collinear Limit: Symmetries, Dualities and Analytic Results

Energy Correlators measure the energy deposited in multiple detectors as a function of the angles between the detectors. In this paper, we analytically compute the three particle correlator in the collinear limit in QCD for quark and gluon jets, and also in $\mathcal{N}=4$ super Yang-Mills theory. We find an intriguing duality between the integrals for the energy correlators and infrared finite Feynman parameter integrals, which maps the angles of the correlators to dual momentum variables. In $\mathcal{N}=4$, we use this duality to express our result as a rational sum of simple Feynman integrals (triangles and boxes). In QCD our result is expressed as a sum of the same transcendental functions, but with more complicated rational functions of cross ratio variables as coefficients. Our results represent the first analytic calculation of a three-prong jet substructure observable of phenomenological relevance for the LHC, revealing unexplored simplicity in the energy flow of QCD jets. They also provide valuable data for improving the understanding of the light-ray operator product expansion.

hep-ph↗

arXiv2020

Rethinking Jets with Energy Correlators: Tracks, Resummation and Analytic Continuation

We introduce an infinite set of jet substructure observables, derived as projections of $N$-point energy correlators, that are both convenient for experimental studies and maintain remarkable analytic properties derived from their representations in terms of a finite number of light ray operators. We show that these observables can be computed using tracking or charge information with a simple reweighting by integer moments of non-perturbative track or fragmentation functions. Our results for the projected $N$-point correlators are analytic functions of $N$, allowing us to derive resummed results to next-to-leading logarithmic accuracy for all $N$. We analytically continue our results to non-integer values of $N$ and define a corresponding analytic continuation of the observable, which we term a $ν$-correlator, that can be measured on jets of hadrons at the LHC. This enables observables that probe the leading twist collinear dynamics of jets to be placed into a single analytic family, which we hope will lead to new insights into jet substructure.

hep-ph↗

arXiv2020

Subleading Power Resummation of Rapidity Logarithms: The Energy-Energy Correlator in $\mathcal{N}=4$ SYM

We derive and solve renormalization group equations that allow for the resummation of subleading power rapidity logarithms. Our equations involve operator mixing into a new class of operators, which we term the "rapidity identity operators", that will generically appear at subleading power in problems involving both rapidity and virtuality scales. To illustrate our formalism, we analytically solve these equations to resum the power suppressed logarithms appearing in the back-to-back (double light cone) limit of the Energy-Energy Correlator (EEC) in $\mathcal{N}$=4 super-Yang-Mills. These logarithms can also be extracted to $\mathcal{O}(α_s^3)$ from a recent perturbative calculation, and we find perfect agreement to this order. Instead of the standard Sudakov exponential, our resummed result for the subleading power logarithms is expressed in terms of Dawson's integral, with an argument related to the cusp anomalous dimension. We call this functional form "Dawson's Sudakov". Our formalism is widely applicable for the resummation of subleading power rapidity logarithms in other more phenomenologically relevant observables, such as the EEC in QCD, the $p_T$ spectrum for color singlet boson production at hadron colliders, and the resummation of power suppressed logarithms in the Regge limit.

hep-ph↗

arXiv2020

The Soft Quark Sudakov

There has been recent interest in understanding the all loop structure of the subleading power soft and collinear limits, with the goal of achieving a systematic resummation of subleading power infrared logarithms. Most of this work has focused on subleading power corrections to soft gluon emission, whose form is strongly constrained by symmetries. In this paper we initiate a study of the all loop structure of soft fermion emission. In $\mathcal{N}=1$ QCD we perform an operator based factorization and resummation of the associated infrared logarithms, and prove that they exponentiate into a Sudakov due to their relation to soft gluon emission. We verify this result through explicit calculation to $\mathcal{O}(α_s^3)$. We show that in QCD, this simple Sudakov exponentiation is violated by endpoint contributions proportional to $(C_A-C_F)^n$ which contribute at leading logarithmic order. Combining our $\mathcal{N}=1$ result and our calculation of the endpoint contributions to $\mathcal{O}(α_s^3)$, we conjecture a result for the soft quark Sudakov in QCD, a new all orders function first appearing at subleading power, and give evidence for its universality. Our result, which is expressed in terms of combinations of cusp anomalous dimensions in different color representations, takes an intriguingly simple form and also exhibits interesting similarities to results for large-x logarithms in the off diagonal splitting functions.

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