Recent progress in hadron structure from Lattice QCD

Constantinou, Martha

doi:10.22323/1.253.0009

Cited by 18 publications

(24 citation statements)

References 105 publications

(186 reference statements)

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“…It is important to emphasize that while the impact of some systematics is already known to a reasonable degree, reliable estimates of certain types of effects are still largely unknown. Nevertheless, rough assessments can be made even in the case of missing lattice data, by looking at the behaviour of related observables such as the average quark momentum fraction or nucleon charges that have a long history of evaluations on the lattice [66][67][68][69][70]. This allows us to build scenarios describing the potential impact of the systematics on the matrix elements of quasi-PDFs.…”

Section: Systematics In Matrix Elements Of Quasi-pdfsmentioning

confidence: 99%

Parton distributions from lattice data: the nonsinglet case

Cichy

Debbio

Giani

2019

J. High Energ. Phys.

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We revise the relation between Parton Distribution Functions (PDFs) and matrix elements computable from lattice QCD, focusing on the quasi-Parton Distribution Functions (qPDFs) approach. We exploit the relation between PDFs and qPDFs in the case of the unpolarized isovector parton distribution to obtain a factorization formula relating the real and imaginary part of qPDFs matrix elements to specific nonsinglet distributions, and we propose a general framework to extract PDFs from the available lattice data, treating them on the same footing as experimental data. We implement the proposed approach within the NNPDF framework, and we study the potentiality of such lattice data in constraining PDFs, assuming some plausible scenarios to assess the unknown systematic uncertainties. We finally extract the two nonsinglet distributions involved in our analysis from a selection of the available lattice data.

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Section: Systematics In Matrix Elements Of Quasi-pdfsmentioning

confidence: 99%

Parton distributions from lattice data: the nonsinglet case

Cichy

Debbio

Giani

2019

J. High Energ. Phys.

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“…As a test of differentiability, the Jensen-Shannon divergences were calculated between all pairs of three-dimensional probability distributions defined by the three dominant eigenvectors of the loop correlation matrix for each ensemble in Grid A. 5 To do this, each distribution was first interpolated over the samples from the given ensemble using smooth kernel distributions. The resulting values of D JS are shown pictorially in Fig.…”

Section: B Ensemble Discrimination Using Principle Component Analysismentioning

confidence: 99%

“…Figure 8 shows histograms of the combinations of Wilson loops corresponding to the dominant eigenvectors of the loop correlation matrix for ensemble Sets D and E, while 5 On a given ensemble e, this three-dimensional probability distribution is given by P e ðs i ; s 2 ; s 3 Þ where and where v i is the ith eigenvector of the PCA. Additional tests with the largest two or four eigenvectors gave qualitatively similar results.…”

Section: B Ensemble Discrimination Using Principle Component Analysismentioning

confidence: 99%

“…High-precision LQCD calculations are important in determining the parameters of the SM and guide searches for evidence of new physics beyond it [4]. Recent LQCD calculations also provide new insights into the quark and gluon structure of protons [5] and the structure and interactions of light nuclei [6,7]. Similarly, LQCD calculations have enabled investigations of QCD matter at extreme temperatures, and efforts to understand QCD matter at high density are underway [8].…”

Section: Introductionmentioning

confidence: 99%

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Machine learning action parameters in lattice quantum chromodynamics

2018

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Numerical lattice quantum chromodynamics studies of the strong interaction are important in many aspects of particle and nuclear physics. Such studies require significant computing resources to undertake. A number of proposed methods promise improved efficiency of lattice calculations, and access to regions of parameter space that are currently computationally intractable, via multi-scale action-matching approaches that necessitate parametric regression of generated lattice datasets. The applicability of machine learning to this regression task is investigated, with deep neural networks found to provide an efficient solution even in cases where approaches such as principal component analysis fail. The high information content and complex symmetries inherent in lattice QCD datasets require custom neural network layers to be introduced and present opportunities for further development.

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“…Realistically, only the lowest moments of PDFs and GPDs can be computed (see e.g. [39][40][41][42][43][44]) due to large gauge noise in high moments, and also unavoidable power-divergent mixing with lower-dimensional operators. Combination of the two prevents a reliable and accurate calculation of moments beyond the second or third, and the reconstruction of the PDFs becomes unrealistic.…”

Section: Introductionmentioning

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

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208

167

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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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Recent progress in hadron structure from Lattice QCD

Cited by 18 publications

References 105 publications

Parton distributions from lattice data: the nonsinglet case

Parton distributions from lattice data: the nonsinglet case

Machine learning action parameters in lattice quantum chromodynamics

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

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