Partonic quasidistributions in two-dimensional QCD

Jia, Yu; Liang, S.; Xiong, Xiaonu; Yu, Rui

doi:10.1103/physrevd.98.054011

Cited by 48 publications

(47 citation statements)

References 103 publications

(253 reference statements)

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“…[38,56,[61][62][63][64][65][66][67]. The new formulation and its successful implementation within lattice QCD has also led to a wider interest on phenomenological studies using models and toy theories of QCD [57,58,[68][69][70][71][72][73][74][75]. A detailed overview of the current status of lattice QCD calculation of PDFs and other partonic distributions can be found in the recent reviews of Refs.…”

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confidence: 99%

Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point

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We present a detailed study of the helicity-dependent and helicity-independent collinear parton distribution functions (PDFs) of the nucleon, using the quasi-PDF approach. The lattice QCD computation is performed employing twisted mass fermions with a physical value of the light quark mass. We give a systematic and in-depth account of the salient features entering in the evaluation of quasi-PDFs and their relation to the light-cone PDFs. In particular, we give details for the computation of the matrix elements, including the study of the various sources of systematic uncertainties, such as excited states contamination. In addition, we discuss the non-perturbative renormalization scheme used here and its systematics, effects of truncating the Fourier transform and different matching prescriptions. Finally, we show improved results for the PDFs and discuss future directions, challenges and prospects for evaluating precisely PDFs from lattice QCD with fully quantified uncertainties. arXiv:1902.00587v1 [hep-lat] 1 Feb 2019of the theoretical and numerical developments, see Ref.[33].On more general grounds, it is very important to realize that quasi-PDFs and light-cone PDFs have been shown to share the same infrared physics [34,35], which is the fundamental observation that allows one to relate both quantities using perturbation theory, provided that the hadron is moving with a large, although necessarily finite, momentum in a chosen spatial direction. It has also been proven that quasi-PDFs can be extracted from lattice QCD in Euclidean spacetime [35] and that they do not suffer from power-divergent mixings with lower-dimensional operators [36][37][38]. A factorization formula makes it possible to extract the PDFs from the quasi-PDFs, an operation called matching [19,20,29,31,34,[39][40][41][42][43]. In general, this procedure is based on a newly developed large-momentum effective theory (LaMET) [44], and it is renormalizable to all orders in perturbation theory [45][46][47][48]. Other approaches for a direct computation of the x-dependence of PDFs include the hadronic tensor [49][50][51], fictitious heavy quark [52], auxiliary light quark [53], good lattice cross sections [54,55] (closely related to the auxiliary light quark method), "OPE without OPE" [56] and pseudo-PDFs [57][58][59][60], where the latter can be seen as a generalization of PDFs off the light-cone. These alternative approaches have been explored in lattice QCD, and recent results can be found in Refs. [38,56,[61][62][63][64][65][66][67]. The new formulation and its successful implementation within lattice QCD has also led to a wider interest on phenomenological studies using models and toy theories of QCD [57,58,[68][69][70][71][72][73][74][75]. A detailed overview of the current status of lattice QCD calculation of PDFs and other partonic distributions can be found in the recent reviews of Refs. [33,76].The remainder of the paper is organized as follows: In Sec. II, we provide the general theoretical aspects, lattice QCD action and parameters. We di...

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Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point

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“…Following the NRQCD investigation, Y. Jia and X. Xiong continued their work related to model quasidistributions of mesons. In 2018, together with S. Liang and R. Yu [130], they presented results on meson quasi-PDFs and quasi-DAs in two-dimensional QCD in its large-N c limit, often referred to as the 't Hooft model [131]. The Authors used the Hamiltonian operator approach and Bars-Green equations in equal-time quantization [132], instead of the more standard diagrammatic approach in light-cone quantization.…”

Section: Quasi-distributions For Mesons In Nrqcd and Two-dimensionmentioning

confidence: 99%

A Guide to Light-Cone PDFs from Lattice QCD: An Overview of Approaches, Techniques, and Results

Cichy

Constantinou

2019

Advances in High Energy Physics

220

168

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Within the theory of Quantum Chromodynamics (QCD), the rich structure of hadrons can be quantitatively characterized, among others, using a basis of universal non-perturbative functions: parton distribution functions (PDFs), generalized parton distributions (GPDs), transversemomentum dependent parton distributions (TMDs) and distribution amplitudes (DAs). For more than half a century, there has been a joint experimental and theoretical effort to obtain these partonic functions. However, the complexity of the strong interactions has placed severe limitations, and first-principle information on these distributions was extracted mostly from their moments computed in Lattice QCD. Recently, breakthrough ideas changed the landscape and several approaches were proposed to access the distributions themselves on the lattice.In this paper, we review in considerable detail approaches directly related to partonic distributions. We highlight a recent idea proposed by X. Ji on extracting quasi-distributions that spawned renewed interest in the whole field and sparked the largest amount of numerical studies within Lattice QCD. We discuss theoretical and practical developments, including challenges that had to be overcome, with some yet to be handled. We also review numerical results, including a discussion based on evolving understanding of the underlying concepts and the theoretical and practical progress. Particular attention is given to important aspects that validated the quasi-distribution approach, such as renormalization, matching to light-cone distributions and lattice techniques.In addition to a thorough discussion of quasi-distributions, we consider other approaches: hadronic tensor, auxiliary quark methods, pseudo-distributions, OPE without OPE and good lattice cross sections. In the last part of the paper, we provide a summary and prospects of the field, with emphasis on the necessary conditions to obtain results with controlled uncertainties.

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“…(9) has been numerically solved for stationary [7] and moving [8] mesons, for a variety of quark mass. To simultaneously handel both stationary and moving mesons, we deliberately choose the orthogonality condition of wave functions that differs from [8,9] by a factor of |P|:…”

Section: Bound-state Solutions In Qcdmentioning

confidence: 99%

“…To compute hadronic matrix elements involving these operators, rather than utilize the diagrammatic Bethe-Salpeter approach [5], it turns much more transparent to invoke the operator method, that is, the bosonization technique equipped with Bogoliubov transformation [6]. In fact, these techniques have recently been applied to systematically investigate the partonic quasi distributions in 't Hooft model [9]. Following the steps expounded in [6,9], and going through some tedious but straightforward algebras, we end up with the following expectation values when sandwiched between the n-th mesonic state:…”

Section: Energy Decomposition Of a Moving Mesonmentioning

confidence: 99%

“…In fact, these techniques have recently been applied to systematically investigate the partonic quasi distributions in 't Hooft model [9]. Following the steps expounded in [6,9], and going through some tedious but straightforward algebras, we end up with the following expectation values when sandwiched between the n-th mesonic state:…”

Section: Energy Decomposition Of a Moving Mesonmentioning

confidence: 99%

See 1 more Smart Citation

Gauge-invariant decomposition of meson energy in two-dimensional QCD

Jia¹,

Yu²,

Xiong³

2018

Phys. Rev. D

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This work is driven by our curiosity towards some basic questions in QCD: how is the energy of a moving hadron partitioned among different gauge-invariant sectors in QCD Hamiltonian? How is the energy of an massless pion separated between quark and gluon sectors, particularly in the soft pion limit? Is it possible to decompose the celebrated Gell-Mann-Oakes-Renner (GOR) relation? To what extent can we justify the quark potential model from the field-theoretical mass decomposition for heavy quarkonium? Due to limitation of contemporary nonperturbative tools, we do not yet know answers to these questions in realistic QCD. In this work, we take the 't Hooft model (two-dimensional QCD in large-N limit) as a prototype model that mimics some essential aspects of the true QCD. We investigate the gauge-invariant energy decomposition of a flavorneutral meson that can carry an arbitrary momentum (including stationary case), with meson species ranging from massless pion to bottomonium. All the aforementioned questions can be addressed satisfactorily within this model, in particular some unexpected patterns related to pion are discovered for the first time in two-dimensional QCD. We hope that our study can offer some useful clues and stimulation for future investigations on hadron energy decomposition in realistic QCD.

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Partonic quasidistributions in two-dimensional QCD

Cited by 48 publications

References 103 publications

Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point

Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point

A Guide to Light-Cone PDFs from Lattice QCD: An Overview of Approaches, Techniques, and Results

Gauge-invariant decomposition of meson energy in two-dimensional QCD

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