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We present a novel approach to compute generalized parton distributions within the lightfront wave function overlap framework. We show how to systematically extend generalized parton distributions computed within the DGLAP region to the ERBL one, fulfilling at the same time both the polynomiality and positivity conditions. We exemplify our method using pion lightfront wave functions inspired by recent results of non-perturbative continuum techniques and algebraic nucleon lightfront wave functions. We also test the robustness of our algorithm on reggeized phenomenological parameterizations. This approach paves the way to a better understanding of the nucleon structure from non-perturbative techniques and to a unification of generalized parton distributions and transverse momentum dependent parton distribution functions phenomenology through lightfront wave functions.

The unique experimental connection to the QCD energy–momentum tensor offered by generalised parton distributions has been strongly highlighted in the past few years with attempts to extract the pressure and shear forces distributions within the nucleon. If, in principle, this can be performed in a model independent way from experimental data, in practice, the current limited precision and kinematic coverage make such an extraction very challenging. Moreover, the limitation to a leading-order description in the strong coupling of the data has provided only an indirect and weakly sensitive access to gluon degrees of freedom, solely through their mixing to quarks via evolution. In this paper we address this issue by providing a next-to-leading order formalism allowing a reanalysis of global fits with genuine gluonic degrees of freedom. In addition, we provide an estimate of the reduction in uncertainty that could stem from the extended kinematic range relevant for the future Electron Ion Collider. Finally, we stress the connection between the analysis of the dispersion relation in terms of generalised parton distributions and the deconvolution problem.

We describe the architecture and functionalities of a C++ software framework, coined PARTONS, dedicated to the phenomenology of Generalized Parton Distributions. These distributions describe the three-dimensional structure of hadrons in terms of quarks and gluons, and can be accessed in deeply exclusive lepto- or photo-production of mesons or photons. PARTONS provides a necessary bridge between models of Generalized Parton Distributions and experimental data collected in various exclusive production channels. We outline the specification of the PARTONS framework in terms of practical needs, physical content and numerical capacity. This framework will be useful for physicists – theorists or experimentalists – not only to develop new models, but also to interpret existing measurements and even design new experiments.

This article summarizes the main ideas behind creating an open database proposed for use in the exploration of generalized parton distributions (GPDs). This lightweight database is well suited for GPD phenomenology and is designed to store both experimental and lattice-QCD data. It can also aid in benchmarking GPD-related developments, such as GPD models. The database utilizes a new data format based on the YAML serialization language, enabling the storage of essential information for modern analyses, such as replica values. It includes interfaces for both Python and C++, allowing straightforward integration with analysis codes.

We review recent works on the modelling of generalised parton distributions within the Dyson–Schwinger formalism. We highlight how covariant computations, using the impulse approximation, allows one to fulfil most of the theoretical constraints of the GPDs. Specific attention is brought to chiral properties and especially the so-called soft pion theorem, and its link with the Axial-Vector Ward–Takahashi identity. The limitation of the impulse approximation are also explained. Beyond impulse approximation computations are reviewed in the forward case. Finally, we stress the advantages of the overlap of lightcone wave functions, and possible ways to construct covariant GPD models within this framework, in a two-body approximation.

We analyze deeply virtual Compton scattering on pions projected for a future electron-ion collider and conveyed in the Sullivan process. The relevant amplitude is known to be parametrized by generalized parton distributions. Hence taking advantage of state-of-the-art models for them, supplemented with effective leading-order scale evolution, we evaluate the amplitude for the process to occur and examine the pion’s structure from the perspective of electron-ion colliders. We estimate the expected event-rates for the Sullivan process showing: first, that deeply virtual Compton scattering on pions may be measurable at forthcoming experimental facilities. Second, that gluons may be decisive in the description of pions, driving the behavior of the relevant amplitudes and modulating the expected event-rates.

The concept of Generalized Parton Distributions promises an understanding of the generation of the charge, spin, and energy-momentum structure of hadrons by quarks and gluons. Forthcoming measurements with unprecedented accuracy at Jefferson Lab and at CERN will challenge our quantitative description of the three-dimensional structure of hadrons. To fully exploit these future measurements, new tools and models are currently being developed. We explain the difficulties of Generalized Parton Distribution modeling, and present some recent progresses. In particular we describe the symmetry-preserving Dyson-Schwinger and Bethe-Salpeter framework. We also discuss various equivalent parameterizations and sketch how to combine them to obtain models satisfying a priori all required theoretical constraints. At last we explain why these developments naturally fit in a versatile software framework, named PARTONS, dedicated to the theory and phenomenology of GPDs.

We sketch here an approach to the computation of genaralised parton distributions (GPDs), based upon a rainbow-ladder (RL) truncation of QCD's Dyson-Schwinger equations and exemplified via the pion's valence dressed-quark GPD, Hvπ(x,ξ,t). Our analysis focuses on the case of zero skewness, ξ = 0, and underlines that the impulse-approximation used hitherto to define the pion's valence dressed-quark GPD is generally invalid owing to omission of contributions from the gluons which bind dressed-quarks into the pion. A simple correction enables us to identify a practicable improvement to the approximation for Hvπ(x,0,t), expressed as the Radon transform of a single amplitude. Therewith we obtain results for Hvπ(x,0,t) and the associated impact-parameter dependent distribution, , which provide a qualitatively sound picture of the pion's dressed-quark structure at an hadronic scale.

We compute the pion Generalized Parton Distribution (GPD) in a valence dressed quarks approach. We model the Mellin moments of the GPD using Ans\"atze for Green functions inspired by the numerical solutions of the Dyson-Schwinger Equations (DSE) and the Bethe-Salpeter Equation (BSE). Then, the GPD is reconstructed from its Mellin moment using the Double Distribution (DD) formalism. The agreement with available experimental data is very good.

Generalised parton distributions are instrumental to study both the three-dimensional structure and the energy-momentum tensor of the nucleon, and motivate numerous experimental programmes involving hard exclusive measurements. Based on a next-to-leading order analysis and a careful study of evolution effects, we exhibit non-trivial generalised parton distributions with arbitrarily small imprints on deeply virtual Compton scattering observables. This means that in practice the reconstruction of generalised parton distributions from measurements, known as the deconvolution problem, does not possess a unique solution for this channel. In this Letter we discuss the consequences on the extraction of generalised parton distributions from data and advocate for a multi-channel analysis.