arXiv subjects

Iain W. Stewart

Publications and source records attributed to Iain W. Stewart.

At least 37 records · Page 2Linked to original sources

arXiv2023

TMD Handbook

This handbook provides a comprehensive review of transverse-momentum-dependent parton distribution functions and fragmentation functions, commonly referred to as transverse momentum distributions (TMDs). TMDs describe the distribution of partons inside the proton and other hadrons with respect to both their longitudinal and transverse momenta. They provide unique insight into the internal momentum and spin structure of hadrons, and are a key ingredient in the description of many collider physics cross sections. Understanding TMDs requires a combination of theoretical techniques from quantum field theory, nonperturbative calculations using lattice QCD, and phenomenological analysis of experimental data. The handbook covers a wide range of topics, from theoretical foundations to experimental analyses, as well as recent developments and future directions. It is intended to provide an essential reference for researchers and graduate students interested in understanding the structure of hadrons and the dynamics of partons in high energy collisions.

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arXiv2022

50 Years of Quantum Chromodynamics

This paper presents a comprehensive review of both the theory and experimental successes of Quantum Chromodynamics, starting with its emergence as a well defined theory in 1972-73 and following developments and results up to the present day. Topics include a review of the earliest theoretical and experimental foundations; the fundamental constants of QCD; an introductory discussion of lattice QCD, the only known method for obtaining exact predictions from QCD; methods for approximating QCD, with special focus on effective field theories; QCD under extreme conditions; measurements and predictions of meson and baryon states; a special discussion of the structure of the nucleon; techniques for study of QCD at high energy, including treatment of jets and showers; measurements at colliders; weak decays and quark mixing; and a section on the future, which discusses new experimental facilities or upgrades currently funded. The paper is intended to provide a broad background for Ph.D. students and postdocs starting their career. Some contributions include personal accounts of how the ideas or experiments were developed.

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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.

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arXiv2022

Pure Quark and Gluon Observables in Collinear Drop

We construct a class of pure quark and gluon observables by using the collinear drop grooming technique. The construction is based on linear combinations of multiple cumulative distributions of the jet mass in collinear drop, whose specific weights are fully predicted perturbatively. This yields observables which obtain their values purely from quarks (or purely from gluons) in a wide region of phase space. We demonstrate this by showing that these observables are effective in two phase space regions, one dominated by perturbative resummation and one dominated by nonperturbative effects. The nonperturbative effects are included using shape functions which only appear as a common factor in the linear combinations constructed. We test this construction using a numerical analysis with next-to-leading logarithmic resummation and various shape function models, as well as analyzing these observables with Pythia and Vincia. Choices for the collinear drop parameters are optimized for experimental use.

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arXiv2022

One-loop matching for gluon lattice TMDs

Transverse-momentum-dependent parton distributions (TMDs) can be calculated from first principles by computing a related set of Euclidean lattice observables and connecting them via a factorization formula. This work focuses on the leading-power factorization formula connecting the lattice quasi-TMD and continuum Collins TMD for gluons. We calculate the one-loop gluon matching coefficient, which is known to be independent of spin and exhibits no mixing with quarks. We demonstrate that this coefficient satisfies Casimir scaling with respect to the quark matching coefficient at one-loop order. Our result facilitates reliable lattice QCD calculations of gluon TMDs.

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arXiv2022

Factorization connecting continuum and lattice TMDs

Transverse-momentum-dependent parton distribution functions (TMDs) can be studied from first principles by a perturbative matching onto lattice-calculable quantities: so-called lattice TMDs, which are a class of equal-time correlators that includes quasi-TMDs and TMDs in the Lorentz-invariant approach. We introduce a general correlator that includes as special cases these two Lattice TMDs and continuum TMDs, like the Collins scheme. Then, to facilitate the derivation of a factorization relation between lattice and continuum TMDs, we construct a new scheme, the Large Rapidity (LR) scheme, intermediate between the Collins and quasi-TMDs. The LR and Collins schemes differ only by an order of limits, and can be matched onto one another by a multiplicative kernel. We show that this same matching also holds between quasi and Collins TMDs, which enables us to prove a factorization relation between these quantities to all orders in $α_s$. Our results imply that there is no mixing between various quark flavors or gluons when matching Collins and quasi TMDs, making the lattice calculation of individual flavors and gluon TMDs easier than anticipated. We cross-check these results explicitly at one loop and discuss implications for other physical-to-lattice scheme factorizations.

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arXiv2021

An Effective Field Theory for Forward Scattering and Factorization Violation

Starting with QCD, we derive an effective field theory description for forward scattering and factorization violation as part of the soft-collinear effective field theory (SCET) for high energy scattering. These phenomena are mediated by long distance Glauber gluon exchanges, which are static in time, localized in the longitudinal distance, where $|t| \ll s$. In hard scattering, Glauber gluons can induce corrections which invalidate factorization. With SCET, Glauber exchange graphs can be calculated explicitly, and are distinct from graphs with soft, collinear, or ultrasoft gluons. We derive a complete basis of operators which describe the leading power effects of Glauber exchange. Key ingredients include regulating light-cone rapidity singularities and subtractions which prevent double counting. Our results include a novel all orders gauge invariant pure glue soft operator which appears between two collinear rapidity sectors. The 1-gluon Feynman rule for the soft operator coincides with the Lipatov vertex, but it also contributes to emissions with $\ge 2$ soft gluons. Our Glauber operator basis is derived using tree level and one-loop matching calculations from full QCD to SCET. The rapidity RGE yields gluon Reggeization at the amplitude level, and gives the BFKL equation for the soft and collinear functions in the forward scattering cross section. We derive an explicit rule for when eikonalization is valid, and provide a direct connection to the picture of multiple Wilson lines crossing a shockwave. In hard scattering operators Glauber subtractions for soft and collinear loop diagrams ensure that we are not sensitive to the directions for soft and collinear Wilson lines. Conversely, certain Glauber interactions can be absorbed into these soft and collinear Wilson lines by taking them to be in specific directions. We also discuss criteria for factorization violation.

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arXiv2021

Drell-Yan $q_T$ Resummation of Fiducial Power Corrections at N$^3$LL

We consider Drell-Yan production $pp\to V^* X \to L X$ at small $q_T \ll Q$. Experimental measurements require fiducial cuts on the leptonic state $L$, which introduce enhanced, linear power corrections in $q_T/Q$. We show that they can be unambiguously predicted from factorization, and resummed to the same order as the leading-power contribution. We thus obtain predictions for the fiducial $q_T$ spectrum to N3LL and next-to-leading-power in $q_T/Q$. Matching to full NNLO ($α_s^2$), we find that the linear power corrections are indeed the dominant ones, and the remaining fixed-order corrections become almost negligible below $q_T \lesssim 40$ GeV. We also discuss the implications for more complicated observables, and provide predictions for the fiducial $ϕ^*$ spectrum at N3LL+NNLO. We find excellent agreement with ATLAS and CMS measurements of $q_T$ and $ϕ^*$. We also consider the $p_T^\ell$ spectrum. We show that it develops leptonic power corrections in $q_T/(Q - 2p_T^\ell)$, which diverge near the Jacobian peak $p_T^\ell \sim Q/2$ and must be kept to all powers to obtain a meaningful result there. Doing so, we obtain for the first time an analytically resummed result for the $p_T^\ell$ spectrum around the Jacobian peak at N3LL+NNLO. Our method is based on performing a complete tensor decomposition for hadronic and leptonic tensors. In practice this is equivalent to often-used recoil prescriptions, for which our results now provide rigorous, formal justification. Our tensor decomposition yields nine Lorentz-scalar hadronic structure functions, which directly map onto the commonly used angular coefficients, but also holds for arbitrary leptonic final states. In particular, for suitably defined Born-projected leptons it still yields a LO-like angular decomposition even when including QED final-state radiation. We also discuss the application to $q_T$ subtractions.

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arXiv2021

Boosted Top Quarks in the Peak Region with N$^3$LL Resummation

We present results for the 2-jettiness differential distribution for boosted top quark pairs produced in $e^+e^-$ collisions in the peak region accounting for QCD large-logarithm resummation at next-to-next-to-next-to-leading logarithmic (N$^3$LL) order and fixed-order corrections to matrix elements at next-to-next-to-leading order (NNLO) calculated in the framework of soft-collinear effective theory and boosted heavy quark effective theory. Electroweak and finite-width effects are included at leading order. We study the perturbative convergence of the cross section in the pole and MSR mass schemes, with and without soft gap subtractions. We find that there is a partial cancellation between the pole mass and soft function renormalons. When renormalon subtractions concerning the top mass and the soft function are implemented, the perturbative uncertainties are, however, systematically smaller and an improvement in the stability of the peak position is observed. We find that the top MSR mass may be determined with perturbative uncertainties well below $100$\,MeV from the peak position of the 2-jettiness distribution. This result has important applications for Monte Carlo top quark mass calibrations.

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arXiv2021

EFT for Soft Drop Double Differential Cross Section

We develop a factorization framework to compute the double differential cross section in soft drop groomed jet mass and groomed jet radius. We describe the effective theories in the large, intermediate, and small groomed jet radius regions defined by the interplay of the jet mass and the groomed jet radius measurement. As an application we present the NLL$'$ results for the perturbative moments that are related to the coefficients $C_1$ and $C_2$ that specify the leading hadronization corrections up to three universal parameters. We compare our results with Monte Carlo simulations and a calculation using the coherent branching method.

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arXiv2020

Precision Global Determination of the $B\to X_sγ$ Decay Rate

We perform the first global fit to inclusive $B\to X_sγ$ measurements using a model-independent treatment of the nonperturbative $b$-quark distribution function, with next-to-next-to-leading logarithmic resummation and $\mathcal{O}(α_s^2)$ fixed-order contributions. The normalization of the $B\to X_sγ$ decay rate, given by $\lvert C_7^{\rm incl} V_{tb} V_{ts}^*\rvert^2$, is sensitive to physics beyond the Standard Model (SM). We determine $\lvert C_7^{\rm incl} V_{tb} V_{ts}^* \rvert = (14.77 \pm 0.51_{\rm fit} \pm 0.59_{\rm theory} \pm 0.08_{\rm param})\times 10^{-3}$, in good agreement with the SM prediction, and the $b$-quark mass $m_b^{1S} = (4.750 \pm 0.027_{\rm fit} \pm 0.033_{\rm theory} \pm 0.003_{\rm param})\,\mathrm{GeV}$. Our results suggest that the uncertainties in the extracted $B\to X_sγ$ rate have been underestimated by up to a factor of two, leaving more room for beyond-SM contributions.

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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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arXiv2020

One-loop Matching for Spin-Dependent Quasi-TMDs

Transverse momentum dependent parton distribution functions (TMDPDFs) provide a unique probe of the three-dimensional spin structure of hadrons. We construct spin-dependent quasi-TMDPDFs that are amenable to lattice QCD calculations and that can be used to determine spin-dependent TMDPDFs. We calculate the short-distance coefficients connecting spin-dependent TMDPDFs and quasi-TMDPDFs at one-loop order. We find that the helicity and transversity distributions have the same coefficient as the unpolarized TMDPDF. We also argue that the same is true for pretzelosity and that this spin universality of the matching will hold to all orders in $α_s$. Thus, it is possible to calculate ratios of these distributions as a function of longitudinal momentum and transverse position utilizing simpler Wilson line paths than have previously been considered.

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arXiv2020

Subleading Power Factorization with Radiative Functions

The study of amplitudes and cross sections in the soft and collinear limits allows for an understanding of their all orders behavior, and the identification of universal structures. At leading power soft emissions are eikonal, and described by Wilson lines. Beyond leading power the eikonal approximation breaks down, soft fermions must be added, and soft radiation resolves the nature of the energetic partons from which they were emitted. For both subleading power soft gluon and quark emissions, we use the soft collinear effective theory (SCET) to derive an all orders gauge invariant bare factorization, at both amplitude and cross section level. This yields universal multilocal matrix elements, which we refer to as radiative functions. These appear from subleading power Lagrangians inserted along the lightcone which dress the leading power Wilson lines. The use of SCET enables us to determine the complete set of radiative functions that appear to $\mathcal{O}(λ^2)$ in the power expansion, to all orders in $α_s$. For the particular case of event shape observables in $e^+e^-\to$ dijets we derive how the radiative functions contribute to the factorized cross section to $\mathcal{O}(λ^2)$.

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arXiv2020

Renormalization and Matching for the Collins-Soper Kernel from Lattice QCD

The Collins-Soper kernel, which governs the energy evolution of transverse-momentum dependent parton distribution functions (TMDPDFs), is required to accurately predict Drell-Yan like processes at small transverse momentum, and is a key ingredient for extracting TMDPDFs from experiment. Earlier we proposed a method to calculate this kernel from ratios of the so-called quasi-TMDPDFs determined with lattice QCD, which are defined as hadronic matrix elements of staple-shaped Euclidean Wilson line operators. Here we provide the one-loop renormalization of these operators in a regularization-independent momentum subtraction (RI$^\prime$/MOM) scheme, as well as the conversion factor from the RI$^\prime$/MOM-renormalized quasi-TMDPDF to the $\overline{\rm MS}$ scheme. We also propose a procedure for calculating the Collins-Soper kernel directly from position space correlators, which simplifies the lattice determination.

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arXiv2019

The One-Loop Correction to Heavy Dark Matter Annihilation

We calculate the one-loop corrections to TeV scale dark matter annihilation in a model where the dark matter is described by an SU(2)$_L$ triplet of Majorana fermions, such as the wino. We use this framework to determine the high and low-scale MS-bar matching coefficients at both the dark matter and weak boson mass scales at one loop. Part of this calculation has previously been performed in the literature numerically; we find our analytic result differs from the earlier work and discuss potential origins of this disagreement. Our result is used to extend the dark matter annihilation rate to NLL' (NLL+O($α_2$) corrections) which enables a precise determination of indirect detection signatures in present and upcoming experiments.

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arXiv2019

Towards Quasi-Transverse Momentum Dependent PDFs Computable on the Lattice

Transverse momentum dependent parton distributions (TMDPDFs) which appear in factorized cross sections involve infinite Wilson lines with edges on or close to the light-cone. Since these TMDPDFs are not directly calculable with a Euclidean path integral in lattice QCD, we study the construction of quasi-TMDPDFs with finite-length spacelike Wilson lines that are amenable to such calculations. We define an infrared consistency test to determine which quasi-TMDPDF definitions are related to the TMDPDF, by carrying out a one-loop study of infrared logarithms of transverse position $b_T\sim Λ_{\rm QCD}^{-1}$, which must agree between them. This agreement is a necessary condition for the two quantities to be related by perturbative matching. TMDPDFs necessarily involve combining a hadron matrix element, which nominally depends on a single light-cone direction, with soft matrix elements that necessarily depend on two light-cone directions. We show at one loop that the simplest definitions of the quasi hadron matrix element, the quasi soft matrix element, and the resulting quasi-TMDPDF all fail the infrared consistency test. Ratios of impact parameter quasi-TMDPDFs still provide nontrivial information about the TMDPDFs, and are more robust since the soft matrix elements cancel. We show at one loop that such quasi ratios can be matched to ratios of the corresponding TMDPDFs. We also introduce a modified "bent" quasi soft matrix element which yields a quasi-TMDPDF that passes the consistency test with the TMDPDF at one loop, and discuss potential issues at higher orders.

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arXiv2019

Collinear Drop

We introduce collinear drop jet substructure observables, which are unaffected by contributions from collinear radiation, and systematically probe soft radiation within jets. These observables can be designed to be either sensitive or insensitive to process-dependent soft radiation originating from outside the jet. Such collinear drop observables can be exploited as variables to distinguish quark, gluon, and color neutral initiated jets, for testing predictions for perturbative soft radiation in Monte Carlo simulations, for assessing models and universality for hadronization corrections, for examining the efficiency of pileup subtraction methods, and for any other application that leaves an imprint on soft radiation. We discuss examples of collinear drop observables that are based both on clustering and on jet shapes. Using the soft-collinear effective theory we derive factorization expressions for collinear drop observables from QCD jets, and carry out a resummation of logarithmically enhanced contributions at next-to-leading-logarithmic order. We also identify an infinite class of collinear drop observables for which the leading double logarithms are absent.

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