An Introductory Lecture on Generalised Parton Distributions

Mezrag, Cédric

doi:10.1007/s00601-022-01765-x

Cited by 16 publications

(6 citation statements)

References 165 publications

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“…Through straightforward computations (see, e.g., [41]), one can connect these Mellin moments to local twist-two operators (we remain with the lightcone gauge and the pion case here):…”

Section: Local Operators Analysismentioning

confidence: 99%

“…Finally, let us mention that the way to decompose the GPD between a Double Distribution and a D-term is not unique. This is a technical point and it has been discussed in the literature in detail (see [39,41,82,83]).…”

Section: The Radon Transform and The Specific Role Of The D-termmentioning

confidence: 99%

“…In this review article, we will focus on GPDs. The latter have already been the main topic of several theoretically oriented [38,39] and phenomenologically oriented [40] review papers and lectures (see, for instance, [41]). Here, we will highlight the efforts in the last decade regarding their computations using continuum formalisms, and thus partly updating them [42].…”

Section: Introductionmentioning

confidence: 99%

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Generalised Parton Distributions in Continuum Schwinger Methods: Progresses, Opportunities and Challenges

Mezrag

2023

Particles

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This paper review the modelling efforts regarding Generalised Parton Distributions (GPDs) using continuum techniques relying on Dyson–Schwinger and Bethe–Salpeter equations. The definition and main properties of the GPDs are first recalled. Then, we detail the strategies developed in the last decade in the meson sector, highlighting that observables connected to the pion GPDs may be measured at future colliders. We also highlight the challenges one will face when targeting baryons in the future.

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“…Through straightforward computations (see, e.g., [41]), one can connect these Mellin moments to local twist-two operators (we remain with the lightcone gauge and the pion case here):…”

Section: Local Operators Analysismentioning

confidence: 99%

Section: The Radon Transform and The Specific Role Of The D-termmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Generalised Parton Distributions in Continuum Schwinger Methods: Progresses, Opportunities and Challenges

Mezrag

2023

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“…GPDs are formally defined by bilocal light cone correlators of quark and gluon fields [7][8][9][10][11][12] and contain a wealth of information on the momentum and spin distributions of the partons (for some comprehensive reviews see Refs. [13][14][15][16][17]). For example, the first and second Mellin moments of the leading twist spin-independent GPDs give the electromagnetic and energy-momentum tensor (or gravitational) form factors, respectively, and in the forward limit a subset of the GPDs reduce to the familiar one-dimensional collinear parton distribution functions (PDFs).…”

Section: Introductionmentioning

confidence: 99%

Shedding light on shadow generalized parton distributions

Moffat¹,

Freese²,

Cloët³

et al. 2023

Preprint

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The feasibility of extracting generalized parton distributions (GPDs) from deeply-virtual Compton scattering (DVCS) data has recently been questioned because of the existence of an infinite set of so-called "shadow GPDs" (SGPDs). These SGPDs depend on the process and manifest as multiple solutions (at a fixed scale 𝑄 2 ) to the inverse problem that needs to be solved to infer GPDs from DVCS data. SGPDs therefore pose a significant challenge for extracting GPDs from DVCS data. With this motivation we study the extent to which QCD evolution can provide constraints on SGPDs. This is possible because the known classes of SGPDs begin to contribute to observables after evolution, and can then be constrained (at the input scale 𝑄 2 0 ) by data that has a finite 𝑄 2 range. The impact that SGPDs could have on determining the total angular momentum, pressure and sheer force distributions, and tomography is also discussed. Our key finding is that scale evolution, coupled with data over a wide range of skewness 𝜉 and 𝑄 2 , can constrain the class of SGPDs that we studied and potentially make possible the extraction of GPDs from DVCS data over a limited range in the GPD variables.

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“…A quantity that encodes answers to this fundamental question is the generalized parton distribution (GPD) [4][5][6][7][8][9], which is non-perturbative and contains information on both the longitudinal-momentum and the transverse spatial distributions. In addition, the GPD is deeply connected to hadron properties [10], for example, lower order moments of the GPD can be linked to hadron form factors and the energy-momentum tensor [4], and so charge and mass distributions, as well as pressure and shear forces inside hadrons [11].…”

mentioning

confidence: 99%

A fresh look at the generalized parton distributions of light pseudoscalar mesons

Xing¹,

Ding²,

Raya³

et al. 2023

Preprint

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We present a symmetry-preserving scheme to derive the pion and kaon generalized parton distributions (GPDs) in Euclidean space. The key to maintaining crucial symmetries under this approach is the treatment of the scattering amplitude, such that it contains both the traditional leading-order contributions and the scalar/vector pole contribution automatically, the latter being necessary to ensure the soft-pion theorem. The GPD is extracted analytically via the uniqueness and definition of the Mellin moments and we find that it naturally matches the double distribution; consequently, the polynomiality condition and sum rules are satisfied. The present scheme thus paves the way for the extraction of the GPD in Euclidean space using the Dyson-Schwinger equation framework or similar continuum approaches.

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An Introductory Lecture on Generalised Parton Distributions

Abstract: These lecture notes on Generalised Parton Distributions aim at providing a general picture of the field on the theoretical and phenomenological sides to master and Ph.D. students. They go along with the lecture given at the Baryon International School of Physics in 2021.

Cited by 16 publications

References 165 publications

Generalised Parton Distributions in Continuum Schwinger Methods: Progresses, Opportunities and Challenges

Generalised Parton Distributions in Continuum Schwinger Methods: Progresses, Opportunities and Challenges

Shedding light on shadow generalized parton distributions

A fresh look at the generalized parton distributions of light pseudoscalar mesons

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