Generalized Parton Distributions Research Articles

Deciphering twist-3 chiral-even GPDs in the light-front quark-diquark model

We investigate quantum chromodynamics (QCD) in this study by computing chiral-even generalized parton distributions (GPDs) at twist-3 in the framework of the light-front quark-diquark model, particularly in the zero skewness scenario. We provide a detailed examination of twist-3 chiral-even GPDs, illustrating their behavior through extensive two-dimensional (2-D) and three-dimensional (3-D) visualizations, which demonstrate their dependence on the longitudinal momentum fraction (x) and the momentum transfer (t). Our investigation also reveals the intricate relationships between these GPDs and other distribution functions such as generalized transverse-momentum dependent distributions, transverse momentum-dependent parton distributions, and parton distribution functions (PDFs). Our study also includes the connected form factors at this twist, which are crucial in understanding the internal structure of hadrons. Additionally, we provide impact parameter-dependent PDF plots to offer insights into the spatial distribution of partons. Published by the American Physical Society 2024

Heavy flavor-asymmetric pseudoscalar mesons on the light front

We extract the leading Fock-state light front wave functions of heavy flavor-asymmetric pseudoscalar mesons D, B, and Bc from their Bethe-Salpeter wave functions, based on the Dyson-Schwinger equations approach. We then study their leading-twist parton distribution amplitudes, generalized parton distribution functions, and transverse momentum-dependent parton distributions. The spatial distributions of the quark and antiquark on the transverse plane are presented, along with their charge and energy distributions on the light front. We find that in the considered mesons, the heavier quarks carry most of the longitudinal momentum fraction, resulting in narrow x distributions, while the lighter quarks play an active role in shaping the transverse distributions in both spatial and momentum space, exhibiting a duality that embodies characteristics of both light mesons and heavy quarkonium. Published by the American Physical Society 2024

Exclusive vector-quarkonium photoproduction at NLO in αs in collinear factorisation with evolution of the generalised parton distributions and high-energy resummation

We perform the first complete one-loop study of exclusive photoproduction of vector quarkonia off protons in Collinear Factorisation (CF) including the scale evolution of the Generalised Parton Distributions (GPDs). We confirm the perturbative instability of the cross section at high photon-proton-collision energies (Wγp) at Next-to-Leading Order (NLO) in αs and solve this issue by resumming higher-order QCD corrections, which are enhanced by a logarithm of the parton energies, using High-Energy Factorisation (HEF) in the Doubly-Logarithmic Approximation (DLA) matched to CF. Our NLO CF ⊕ DLA HEF results are in agreement with the latest HERA data, show a smaller sensitivity to the factorisation and renormalisation scales compared to Born-order results. Quark-induced channels via interference with gluon ones are found to contribute at most 20% of the cross section for Wγp>100 GeV. Our results also show that such exclusive cross sections cannot be accurately obtained from the square of usual Parton Distribution Functions (PDFs) and clearly illustrate the importance of quarkonium exclusive photoproduction to advance our understanding of the 3D content of the nucleon in terms of gluons. Our work provides an important step towards a correct interpretation of present and future experimental data collected at HERA, the EIC, the LHC and future experiments.

Study of gluon GPDs in exclusive J/ψ production in electron-proton scattering

Exclusive photoproduction of heavy J/ψ meson is performed within the handbag factorization method. The general parton distributions (GPDs) for gluons, which are an essential ingredient here, are constructed using double distribution (DD) representation. The calculated cross section for few sets of gluon GPDs Hg describe fine J/ψ production experimental data from HERA to LHC energies. Based on this approach we estimate J/ψ spin asymmetries determined by Eg and H˜g. The GPDs factorization approach can be employed to analyze heavy vector meson production in electron-proton scattering. Investigations of this reactions at future electron-ion colliders in USA and China can give essential information on gluon GPDs. Published by the American Physical Society 2024

Chiral-even twist-3 GPDs for the proton in a spectator diquark model

We investigate the chiral-even twist-3 generalized parton distributions (GPDs) of valence quarks in the proton at nonzero skewness ξ, using a spectator model with scalar and axial-vector diquarks. We consider the exponential form factor for the nucleon-quark-diquark vertex and the axial-vector diquark with light-cone transverse polarization. We analyze the dependence of GPDs on the longitudinal momentum fraction x at different ξ, and on the square of the transverse momentum transfer ΔT2 at different x. Our numerical results reveal distinct discontinuities in all twist-3 GPDs except G1 and G˜1. By taking the forward limit, we obtain the twist-3 parton distribution function gT, which encodes the transverse spin distribution of quarks. We also compare the kinetic orbital angular momentum and the spin-orbit correlations of quarks defined by the twist-2 and twist-3 GPDs, respectively. Published by the American Physical Society 2024

Pion-production cross sections in neutrino reactions for studying generalized parton distributions of the nucleon

Pion-production cross sections in neutrino reactions for studying generalized parton distributions of the nucleon

Higher-twist generalized parton distributions of the pion and kaon at zero skewness in the light-cone quark model

We investigate the higher-twist generalized parton distributions (GPDs) of the pion and kaon at zero skewness by adopting the overlap representation within the light-cone formalism. Using the wave functions of pion and kaon deduced from a light-cone quark model (LCQM), we calculate the twist-3 and twist-4 GPDs E2(x,0,t), G2(x,0,t), F3(x,0,t), and H3(x,0,t) of valence quarks inside the pion and kaon mesons. Numerical results for these higher-twist GPDs of valence quark and antiquark are presented. By taking the forward limit, we also present the numerical results for the corresponding twist-3 and twist-4 parton distribution functions (PDFs) e(x) and f3(x) of pion and kaon. We further study the relations between e(x) or f3(x) and the twist-2 unpolarized PDF f1(x). Published by the American Physical Society 2024

Nonlocal chiral contributions to generalized parton distributions of the proton at nonzero skewness

We compute the one-loop contributions to spin-averaged generalized parton distributions (GPDs) in the proton from pseudoscalar mesons with intermediate octet and decuplet baryon states at nonzero skewness. Our framework is based on nonlocal covariant chiral effective theory, with ultraviolet divergences regularized by introducing a relativistic regulator derived consistently from the nonlocal Lagrangian. Using the splitting functions calculated from the nonlocal Lagrangian, we find the nonzero skewness GPDs from meson loops by convoluting with the phenomenological pion GPD and the generalized distribution amplitude, and verify that these satisfy the correct polynomiality properties. We also compute the lowest two moments of GPDs to quantify the meson loop effects on the Dirac, Pauli, and gravitational form factors of the proton. Published by the American Physical Society 2024

Exclusive photoproduction of ηcγ pairs with large invariant mass

In this manuscript, we analyze the exclusive photoproduction of ηcγ pairs in the collinear factorization framework and evaluate its cross section in leading order in the strong coupling αs. We found that this channel is mostly sensitive to the behavior of the unpolarized gluon generalized parton distributions Hg in the Efremov-Radyushkin-Brodsky-Lepage kinematics. We estimated numerically the cross section and the expected counting rates in the kinematics of middle-energy photoproduction experiments, which can be realized at the future Electron-Ion Collider or in the ultraperipheral collisions at LHC. We found that the cross section is sufficiently large for dedicated experimental study. We also estimated the role of this process as a potential background to ηc photoproduction, which is considered as one of the possible gateways for studies of t-channel odderons. We found that the contribution of ηcγ (with undetected photon) is on par with expected contributions of odderons in the kinematics of small momentum transfer |t|≲0.5 GeV2, though decreases rapidly at larger |t|. Published by the American Physical Society 2024

Chiral-odd GPDs in the bag model

A study of chiral-odd generalized parton distributions (GPDs) of the nucleon is presented in the bag model demonstrating that in this model all four chiral-odd GPDs are nonzero contrary to other claims in literature. The bag model results for the GPDs HTq(x,ξ,t), ETq(x,ξ,t), H˜Tq(x,ξ,t) agree with other models within a typical quark model accuracy. We present one of the few quark model calculations where polynomiality is satisfied and the sum rule ∫dxE˜Tq(x,ξ,t)=0 holds. We confront our results with predictions from the large-Nc limit, and with lattice QCD calculations. We conclude that the bag model successfully catches the main features of chiral-odd GPDs. Published by the American Physical Society 2024

Spin-orbit correlations in the nucleon in the large- Nc limit

We study the twist-3 spin-orbit correlations of quarks described by the nucleon matrix elements of the parity-odd rank-2 tensor QCD operator (the parity-odd partner of the QCD energy-momentum tensor). Our treatment is based on the effective dynamics emerging from the spontaneous breaking of chiral symmetry and the mean-field picture of the nucleon in the large-Nc limit. The twist-3 QCD operators are converted to effective operators, in which the QCD interactions are replaced by spin-flavor-dependent chiral interactions of the quarks with the pion field. We compute the nucleon matrix elements of the twist-3 effective operators and discuss the role of the chiral interactions in the spin-orbit correlations. We derive the first-quantized representation in the mean-field picture and develop a quantum-mechanical interpretation. The chiral interactions give rise to new spin-orbit couplings and qualitatively change the correlations compared to the quark model picture. We also derive the twist-3 matrix elements in the topological soliton picture where the quarks are integrated out (skyrmion). The methods used here can be extended to other QCD operators describing higher-twist nucleon structure and generalized parton distributions. Published by the American Physical Society 2024

Generalized parton distributions from the pseudodistribution approach on the lattice

Generalized parton distributions (GPDs) are key quantities for the description of a hadron’s three-dimensional structure. They are the current focus of all areas of hadronic physics—phenomenological, experimental and theoretical, including lattice QCD. Synergies between these areas are desirable and essential to achieve precise quantification and understanding of the structure of, particularly, nucleons, as the basic ingredients of matter. In this paper, we investigate, for the first time, the numerical implementation of the pseudodistribution approach for the extraction of zero-skewness GPDs for unpolarized quarks. Pseudodistributions are Euclidean parton correlators computable in lattice QCD that can be perturbatively matched to the light-cone parton distributions of interest. Although they are closely related to the quasidistributions and come from the same lattice-extracted matrix elements, they are, however, subject to different systematic effects. We use the data previously utilized for quasi-GPDs and extend it with other momentum transfers and nucleon boosts, in particular a higher one (P3=1.67 GeV) with eightfold larger statistics than the largest one used for quasidistributions (P3=1.25 GeV). We renormalize the matrix elements with a ratio scheme and match the resulting Ioffe time distributions to the light cone in coordinate space. The matched distributions are then used to reconstruct the x dependence with a fitting . We investigate some systematic effects related to this procedure, and we also compare the results with the ones obtained in the framework of quasi-GPDs. Our final results involve the invariant four-momentum transfer squared (−t) dependence of the flavor nonsinglet (u−d) H and E GPDs. Published by the American Physical Society 2024

Investigating the timelike Compton scattering in photon–proton interactions at the EIC

Information about the three-dimensional description of the quark and gluon content of hadrons, described by the generalized parton distributions (GPDs), can be probed by exclusive processes in electron–proton (ep) collisions. In this letter, we investigate the timelike Compton scattering (TCS) in ep collisions at the future electron-ion collider (EIC). Such process is characterized by the exclusive dilepton production through the subprocess γp→γ∗p→l+l-p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma p \\rightarrow \\gamma ^*p \\rightarrow l^+ l^- p$$\\end{document}, with the real photon in the initial state being emitted by the incoming electron. Assuming a given model for the GPDs, the TCS differential cross-section is estimated, as well the contribution associated to the interference between the TCS and Bethe–Heitler (BH) amplitudes. Predictions for the TCS, BH and interference contributions are presented considering the kinematical range expected to be covered by the EIC detectors. Moreover, the polarized photon asymmetry is also studied. Our results indicated that a future experimental analysis, considering photon circular polarizations, can be useful to probe the interference contribution and constrain the description of the GPDs for the proton.

Towards unpolarized GPDs from pseudo-distributions

We present an exploration of the unpolarized isovector proton generalized parton distributions (GPDs) Hu−d(x, ξ, t) and Eu−d(x, ξ, t) in the pseudo-distribution formalism using distillation. Taking advantage of the large kinematic coverage made possible by this approach, we present results on the moments of GPDs up to the order x3 — including their skewness dependence — at a pion mass mπ = 358 MeV and a lattice spacing a = 0.094 fm.

Chiral-odd generalized parton distributions of sea quarks at ξ=0 in the light-cone quark model

We study the chiral-odd generalized parton distributions (GPDs) of the u¯ and d¯ quarks inside the proton at zero skewness using the overlap representation within the light-cone formalism. Utilizing the light-cone wave functions of the proton obtained from the baryon-meson fluctuation model in terms of the |qq¯B⟩ Fock states, we provide expressions for the GPDs H˜Tq¯/P(x,0,t), HTq¯/P(x,0,t), and ETq¯/P(x,0,t) where q¯=u¯ and d¯. Numerical results for these GPDs in momentum space as well as in impact parameter space are presented. Additionally, we investigate specific combinations of the chiral-odd GPDs in impact parameter space, focusing on the spin-orbit correlation effect of the sea quarks. Published by the American Physical Society 2024

Quark spin-orbit correlations in spin-0 and spin-1 mesons using the light-front quark model

We investigate the spin-orbital angular momentum correlations for the active quark inside the light and heavy mesons for both the spin-0 and spin-1 cases. These correlations can be derived from the generalized transverse-momentum-dependent distributions as well as the generalized parton distributions. We employ the overlap representation of light-front wave functions in the light-front quark model to calculate our analytical results. The dependence of spin-orbit correlations (SOCs) on the longitudinal momentum fraction x as well as the transverse-momentum-dependence k⊥ is graphically presented. Even though the SOCs have already been studied for the spin-0 pions and kaons in other approaches, no calculations for the other light and heavy spin-0 mesons have been reported in the literature. Further, the correlations for any of the light and heavy spin-1 mesons are studied for the first time in the present work. Published by the American Physical Society 2024

Systematic improvement of x -dependent unpolarized nucleon generalized parton distributions in lattice-QCD calculation

We present a first study of the effects of renormalization-group resummation (RGR) and leading-renormalon resummation (LRR) on the systematic errors of the unpolarized isovector nucleon generalized parton distribution in the framework of large-momentum effective theory. This work is done using lattice gauge ensembles generated by the MILC Collaboration, consisting of 2+1+1 flavors of highly improved staggered quarks with a physical pion mass at lattice spacing a≈0.09 fm and a box width L≈5.76 fm. We present results for the nucleon H and E generalized parton distributions (GPDs) with average boost momentum Pz≈2 GeV at momentum transfers Q2=[0,0.97] GeV2 at skewness ξ=0 as well as Q2∈0.23 GeV2 at ξ=0.1, renormalized in the modified minimal subtraction (MS¯) scheme at scale μ=2.0 GeV, with two- and one-loop matching, respectively. We demonstrate that the simultaneous application of RGR and LRR significantly reduces the systematic errors in renormalized matrix elements and distributions for both the zero and nonzero skewness GPDs, and that it is necessary to include both RGR and LRR at higher orders in the matching and renormalization processes. Published by the American Physical Society 2024

GPDs and Gravitational Form Factors of Nucleons (Quark and Gluon Contributions)

Taking into account the recent parameterizations of parton distribution functions (PDFs), the momentum transfer dependence of generalized parton distributions (GPDs) of nucleons is obtained in the limit \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi\ o 0$$\\end{document}. The gravitational quark and gluon form factors of nucleons are calculated. It is shown that the gluon gravitational radius of the nucleon is comparable to the electromagnetic radius of the proton. The power dependence of form factors is investigated. As a result, it was obtained that the quark gravitational form factor is reproduced by the dipole form, while the form of the gluon gravitation form factor corresponds to the triple form.

Reconstructing generalized parton distributions from the lattice off-forward Compton amplitude

We present a determination of the structure functions of the off-forward Compton amplitude H1 and E1 from the Feynman-Hellmann method in lattice QCD. At leading twist, these structure functions give access to the generalized parton distributions (GPDs) H and E, respectively. This calculation is performed for an unphysical pion mass of mπ=412 MeV and four values of the soft momentum transfer, t≈0,−0.3,−0.6,−1.1 GeV2, all at a hard momentum scale of Q¯2≈5 GeV2. Using these results, we test various methods to determine properties of the real-time scattering amplitudes and GPDs: (1) we fit their Mellin moments, and (2) we use a simple GPD ansatz to reconstruct the entire distribution. Our final results show promising agreement with phenomenology and other lattice results and highlight specific systematics in need of control. Published by the American Physical Society 2024

Gluon GTMDs at nonzero skewness and impact parameter dependent parton distributions

We investigate the leading twist generalized transverse momentum dependent parton distributions (GTMDs) of the unpolarized and longitudinally polarized gluons in the nucleon. We adopt a light-front gluon-triquark model for the nucleon motivated by soft-wall AdS/QCD. The gluon GTMDs are defined through the off-forward gluon-gluon generalized correlator and are expressed as the overlap of light-cone wave functions. The GTMDs can be employed to provide the generalized parton distributions (GPDs) by integrating out the transverse momentum. The Fourier transform of the GPDs encodes the parton distributions in the transverse position space, namely, the impact parameter dependent parton distributions (IPDs). We also calculate the three gluon IPDs corresponding to the GPDs Hg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H^g$$\\end{document}, Eg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E^g$$\\end{document} and H~g\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{H}^g$$\\end{document}, and present their dependence on x and b⊥\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$b_\\perp $$\\end{document}, respectively.