Generalized Parton Distributions Research Articles

Unraveling generalized parton distributions through Lorentz symmetry and partial DGLAP knowledge

Relying on the polynomiality property of generalized parton distributions, which roots on Lorentz covariance, we prove that it is enough to know them at vanishing and low skewness within the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi region to obtain a unique extension to their entire support up to a D term. We put this idea in practice using two methods: reconstruction using artificial neural networks and finite-elements methods. We benchmark our results against standard models for generalized parton distributions. In agreement with the formal expectation, we obtain very a accurate reconstruction for a maximal value of the skewness as low as 20% of the longitudinal momentum fraction. This result might be relevant for reconstruction of generalized parton distribution from experimental and lattice QCD data, where computations are, for now, restricted in skewness. Published by the American Physical Society 2024

Transversity generalized parton distributions in spin- 3/2 particles

The definitions of the quark and gluon transversity generalized parton distributions (GPDs) in spin-3/2 particles are obtained in the light-cone gauge. It is found that they contain 16 independent components for each parton. Their even or odd property is found in terms of a skewness variable, and the odd transversity GPDs vanish in the forward limit. There are 16 amplitudes with helicity flip of quark or gluon. We conclude that all the amplitudes, unpolarized, polarized, and transversity amplitudes, have a common factor F(ζ) carrying all the complex parts. Here, the variable ζ is the helicity difference ζ=(λ′−λ)−(μ′−μ) for the amplitude Aλ′μ′,λμ. This kinematical factor is associated with the transfer of the orbital angular momentum in the quark- and gluon-spin-3/2 particle scattering amplitudes. We also derive another main physical quantity, transversity distribution, from the transversity GPDs in the forward limit for the spin-3/2 particles. Published by the American Physical Society 2024

Impact of JLab data on the determination of GPDs at zero skewness and new insights from transition form factors N→Δ

It is well-established now that the generalized parton distributions (GPDs) at zero skewness are playing important roles in some physical process such as elastic electron-nucleon scattering, elastic (anti)neutrino-nucleon scattering, and wide-angle Compton scattering (WACS) via various types of form factors (FFs). In this study, we are going to utilize the recent JLab measurements of the elastic electron-nucleon scattering reduced cross section, namely GMp12, as a touchstone to unravel the tension observed between the measurements of the WACS cross section and the data of the proton magnetic FF GMp. We also investigate the impact of GMp12 data on valence unpolarized GPDs Hvq and Evq at zero skewness by performing some χ2 analyses of the related experimental data. By calculating the electric and scalar quadrupole ratios, REM and RSM, and magnetic transition FF GM*/3GD related to the nucleon-to-delta (N→Δ) transition using the extracted GPDs and comparing the results with corresponding experimental measurements, we show that our results are in an excellent consistency with experiments, indicating the universality property of GPDs. We emphasize that the inclusion of these data in the future analysis of GPDs can significantly affect the extracted GPDs especially their uncertainties at smaller values of Q2. Published by the American Physical Society 2024

Extracting transition generalized parton distributions from hard exclusive pion-nucleon scattering

Extracting transition generalized parton distributions from hard exclusive pion-nucleon scattering

Exploring twist-4 chiral-even GPDs in the light-front quark-diquark model

In this work, we delve into the realm of quantum chromodynamics (QCD) by calculating twist-4 chiral-even generalized parton distributions (GPDs), within the context of the light-front quark-diquark model (LFQDM), focusing specifically on the intriguing case of zero skewness. To shed light on the behavior of twist-4 chiral-even GPDs, we present comprehensive two-dimensional (2-D) and 3-dimensional (3-D) plots, mapping their dependence on the longitudinal momentum fraction (x) and the momentum transfer (t). Furthermore, our research looks into the profound connection between twist-4 chiral-even GPDs and other distribution functions (DFs), including parton distribution functions (PDFs), transverse momentum-dependent parton distributions (TMDs) and generalized transverse-momentum dependent parton distributions (GTMDs). Additionally, our investigation extends to the exploration of related higher twist form factors (FFs), which play a pivotal role in elucidating the internal structure of hadrons. To provide significant insights into the partons spatial distribution, we have also yielded impact parameter GPD plots.

Twist-3 generalized parton distribution for the proton from basis light-front quantization

Twist-3 generalized parton distribution for the proton from basis light-front quantization

Combining lattice QCD and phenomenological inputs on generalised parton distributions at moderate skewness

We present a systematic study demonstrating the impact of lattice QCD data on the extraction of generalised parton distributions (GPDs). For this purpose, we use a previously developed modelling of GPDs based on machine learning techniques fulfilling the theoretical requirements of polynomiality, a form of positivity constraint and known reduction limits. A special care is given to estimate the uncertainty stemming from the ill-posed character of the connection between GPDs and the experimental processes usually considered to constrain them, like deeply virtual Compton scattering (DVCS). Moke lattice QCD data inputs are included in a Bayesian framework to a prior model based on an Artificial Neural Network. This prior model is fitted to reproduce the most experimentally accessible information of a phenomenological extraction by Goloskokov and Kroll. We highlight the impact of the precision, correlation and kinematic coverage of lattice data on GPD extraction at moderate ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document} which has only been brushed in the literature so far, paving the way for a joint extraction of GPDs.

Generalized parton distributions from lattice QCD with asymmetric momentum transfer: Axial-vector case

Generalized parton distributions from lattice QCD with asymmetric momentum transfer: Axial-vector case

Fresh look at the generalized parton distributions of light pseudoscalar mesons

Fresh look at the generalized parton distributions of light pseudoscalar mesons

Beam spin asymmetry measurements of deeply virtual π0 production with CLAS12

The new experimental measurements of beam spin asymmetry were performed for the deeply virtual exclusive π0 production in a wide kinematic region with the photon virtualities Q2 up to 6.6 GeV2 and the Bjorken scaling variable xB in the valence regime. The data were collected by the CEBAF Large Acceptance Spectrometer (CLAS12) at Jefferson Lab with longitudinally polarized 10.6 GeV electrons scattered on an unpolarized liquid-hydrogen target. Sizable asymmetry values indicate a substantial contribution from transverse virtual photon amplitudes to the polarized structure functions. The interpretation of these measurements in terms of the Generalized Parton Distributions (GPDs) demonstrates their sensitivity to the chiral-odd GPD E¯T, which contains information on quark transverse spin densities in unpolarized and polarized nucleons and provides access to the nucleon's transverse anomalous magnetic moment. Additionally, the data were compared to a theoretical model based on a Regge formalism that was extended to the high photon virtualities.

Inside the Nucleon: Tomographic Interpretations and Universality of GPDs with DDVCS

The goal of Double Deeply Virtual Compton Scattering (DDVCS) experiments is to better understand the internal structure of the nucleon. Previous attempts to resolve the internal structure of nucleons have resulted in electromagnetic form factors and parton distribution functions for elastic scattering and deep inelastic scattering processes, respectively. Generalized Parton Distributions (GPDs) are the latest attempt to unify these models of nucleon structure. The GPDs of DDVCS give us ability to investigate off of the diagonal where x ̸= ±ξ. The main goal of our analysis is to determine the best experimental setup in order to deduce the kinematic variables on which GPDs depend from the lab observables. The effectiveness of our data collection in the laboratory is by determined the physical kinematics, Q2, Q′2,t, xi,ϕLM, ϕCMV , and θCMV . We can then run DDVCS experiments and collect data on observables to improve upon the current models for GPDs of the nucleon.

NLO corrections to the deeply virtual meson production revisited: impact on the extraction of generalized parton distributions

We revisit the next-to-leading order (NLO) perturbative QCD corrections for the deeply virtual meson production (DVMP) process, exploring its phenomenology both in isolation and in a multichannel fit combined with deeply virtual Compton scattering (DVCS). Our approach involves the conformal partial wave (CPaW) formalism, which allows for the straightforward inclusion of higher-order contributions and evolutionary effects. Our findings indicate that a description of the longitudinal component of the vector meson DVMP cross-section at high energies is achievable only at NLO within the standard collinear approach. Furthermore, we demonstrate a simultaneous description of DIS, DVCS, and DVMP processes, providing insights into the proton structure described at NLO by unique universal generalized parton distribution (GPD) functions.

Instanton effects in twist-3 generalized parton distributions

The instanton vacuum picture is used to study hadronic matrix elements of the twist-3 (dimension-4, spin-1) QCD operators measuring the quark spin density and spin-orbit correlations. The QCD operators are converted to effective operators in the low-energy effective theory emerging after chiral symmetry breaking, in a systematic approach based on the diluteness of the instanton medium and the 1/Nc expansion. The instanton fields induce spin-flavor-dependent “potential” terms in the effective operators, complementing the “kinetic” terms from the quark field momenta. As a result, the effective operators obey the same equation-of-motion relations as the original QCD operators. The spin-orbit correlations are qualitatively different from naive quark model expectations.

Generalized parton distributions of gluon in proton: A light-front quantization approach

We solve for the gluon generalized parton distributions (GPDs) inside the proton at zero skewness, focusing specifically on leading twist chiral-even GPDs. We obtain and employ the light-front wavefunctions (LFWFs) of the proton from a light-front quantized Hamiltonian with Quantum Chromodynamics input using basis light-front quantization (BLFQ). Our investigation incorporates the valence Fock sector with three constituent quarks and an additional Fock sector, encompassing three quarks and a dynamical gluon. We examine the GPDs within impact parameter space and evaluate the x-dependence of the transverse square radius. We find that the transverse size of the gluon at lower-x is larger than that of the quark, while it exhibits opposite behavior at large-x. Using the proton spin sum rule, we also determine the relative contributions of quarks and the gluon to the total angular momentum of the proton.

Kinematic twist-three contributions to pseudo- and quasi-GPDs and translation invariance

We present explicit expressions for the tree-level “kinematic” twist-three contributions to the nucleon matrix elements of gauge-invariant nonlocal quark-antiquark operators which can be used in lattice calculations of generalized parton distributions (GPDs). These contributions in particular restore the translation invariance of the results up to higher twist four. The calculated twist-three corrections are logarithmically enhanced as compared to the leading twist, and are discontinuous at the kinematic points x = ±ξ.

Extraction of the Parton Momentum-Fraction Dependence of Generalized Parton Distributions from Exclusive Photoproduction.

The x dependence of hadrons' generalized parton distributions (GPDs) F(x,ξ,t) is the most difficult to extract from the existing known processes, while the ξ and t dependence are uniquely determined by the kinematics of the scattered hadron. We study the single diffractive hard exclusive processes for extracting GPDs in the photoproduction. We demonstrate quantitatively the enhanced sensitivity on extracting the x dependence of various GPDs from the photoproduction cross sections, as well as the asymmetries constructed from photon polarization and hadron spin that could be measured at JLab Hall D by GlueX Collaboration and future facilities.

Spin density matrix elements in exclusive ρ0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho ^0$$\\end{document} meson muoproduction

We report on a measurement of Spin Density Matrix Elements (SDMEs) in hard exclusive ρ0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho ^0$$\\end{document} meson muoproduction at COMPASS using 160 GeV/c polarised μ+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mu ^{+}$$\\end{document} and μ-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mu ^{-}$$\\end{document} beams impinging on a liquid hydrogen target. The measurement covers the kinematic range 5.0 GeV/c2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c^2$$\\end{document}<W<\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$< W<$$\\end{document} 17.0 GeV/c2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c^2$$\\end{document}, 1.0 (GeV/c)2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^2$$\\end{document}<Q2<\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$< Q^2<$$\\end{document} 10.0 (GeV/c)2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^2$$\\end{document} and 0.01 (GeV/c)2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^2$$\\end{document}<pT2<\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$< p_{\ extrm{T}}^2<$$\\end{document} 0.5 (GeV/c)2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^2$$\\end{document}. Here, W denotes the mass of the final hadronic system, Q2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q^2$$\\end{document} the virtuality of the exchanged photon, and pT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_{\ extrm{T}}$$\\end{document} the transverse momentum of the ρ0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho ^0$$\\end{document} meson with respect to the virtual-photon direction. The measured non-zero SDMEs for the transitions of transversely polarised virtual photons to longitudinally polarised vector mesons (γT∗→VL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma ^*_T \\rightarrow V^{ }_L$$\\end{document}) indicate a violation of s-channel helicity conservation. Additionally, we observe a dominant contribution of natural-parity-exchange transitions and a very small contribution of unnatural-parity-exchange transitions, which is compatible with zero within experimental uncertainties. The results provide important input for modelling Generalised Parton Distributions (GPDs). In particular, they may allow one to evaluate in a model-dependent way the role of parton helicity-flip GPDs in exclusive ρ0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho ^0$$\\end{document} production.

Deeply virtual compton scattering at future electron-ion colliders

The study of hadronic structure has been carried out for many years. Generalized parton distribution functions (GPDs) provide broad information on the internal structure of hadrons. Combining GPDs and high-energy scattering experiments, we expect yielding three-dimensional physical quantities from experiments. The Deeply Virtual Compton Scattering (DVCS) process is a powerful tool for studying GPDs. It is one of the important experiments of Electron Ion Collider (EIC) and Electron ion collider at China (EicC) in the future. In the initial stage, the proposed EicC will have polarized electrons with energies of 3∼5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3 \\sim 5$$\\end{document} GeV colliding with polarized protons with energies of 12∼25\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$12 \\sim 25$$\\end{document} GeV, with luminosity up to 1∼2×1033\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1 \\sim 2 \ imes 10^{33}$$\\end{document} cm-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-2}$$\\end{document} s-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-1}$$\\end{document}. EIC, which will be constructed in the coming years, will cover center-of-mass energies ranging from 30 to 50 GeV, with a luminosity of about 1033∼1034\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{33} \\sim 10^{34}$$\\end{document} cm-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-2}$$\\end{document} s-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-1}$$\\end{document}. In this work, we present a detailed simulation of DVCS to study the feasibility of experiments at EicC and EIC. Referring the method used by HERMES Collaboration, and comparing the model calculations with pseudo data of asymmetries attributed to the DVCS, we obtained a model-dependent constraint on the total angular momentum of up and down quarks in the proton.

Gluon generalized parton distributions and angular momentum in a light-cone spectator model

Gluon generalized parton distributions and angular momentum in a light-cone spectator model

Pion valence-quark generalized parton distribution at physical pion mass

We present the first lattice-QCD x-dependent pion valence-quark generalized parton distribution (GPD) calculated directly at physical pion mass using the Large-Momentum Effective Theory (LaMET) with next-to-next-to-leading order perturbative matching correction. We use clover fermions for the valence action on 2+1+1 flavors of highly improved staggered quarks (HISQ), generated by MILC Collaboration, with lattice spacing a≈0.09 fm and box size L≈5.5 fm; the pion two-point measurements number up to O(106) with boost momentum 1.73 GeV. The pion valence distribution is renormalized in hybrid scheme with Wilson-line mass subtraction at large distances in coordinate space, followed by a procedure to match it to the MS‾ scheme. We focus on the zero-skewness limit, where the GPD has a probability-density interpretation in the longitudinal Bjorken x and the transverse impact-parameter distributions. We take the integral of our GPD functions to generate leading moment so that we can make comparisons with past lattice-QCD and experimental determinations of the pion form factors and found consistent agreement among them. We predict the higher GPD moments and reveal x-dependent tomography of the pion for the first time using lattice QCD.