Lattice QCD pseudo-distributions at m_π=358 MeV are inverted via multidimensional Gaussian process regression to reconstruct the full kinematic dependence of GPDs H^{u-d} and E^{u-d} while directly extracting double distributions.
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Unraveling hadron structure with generalized parton distributions
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abstract
The generalized parton distributions, introduced nearly a decade ago, have emerged as a universal tool to describe hadrons in terms of quark and gluonic degrees of freedom. They combine the features of form factors, parton densities and distribution amplitudes--the functions used for a long time in studies of hadronic structure. Generalized parton distributions are analogous to the phase-space Wigner quasi-probability function of non-relativistic quantum mechanics which encodes full information on a quantum-mechanical system. We give an extensive review of main achievements in the development of this formalism. We discuss physical interpretation and basic properties of generalized parton distributions, their modeling and QCD evolution in the leading and next-to-leading orders. We describe how these functions enter a wide class of exclusive reactions, such as electro- and photo-production of photons, lepton pairs, or mesons. The theory of these processes requires and implies full control over diverse corrections and thus we outline the progress in handling higher-order and higher-twist effects. We catalogue corresponding results and present diverse techniques for their derivations. Subsequently, we address observables that are sensitive to different characteristics of the nucleon structure in terms of generalized parton distributions. The ultimate goal of the GPD approach is to provide a three-dimensional spatial picture of the nucleon, direct measurement of the quark orbital angular momentum, and various inter- and multi-parton correlations.
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representative citing papers
Conformal moments of the two-loop DVCS coefficient functions have been computed with a new technique.
Quantum algorithm for GPDs in Schwinger model using Wilson fermions, with polynomial resource scaling and exact-diagonalization benchmarks matching theory.
The paper derives factorization of fixed-spin conformal moments of unpolarized gluon GTMDs into a universal staple-worldsheet soft factor and a target-dependent Witten amplitude, with UV/IR reductions and Reggeization via the holographic Pomeron.
Derives t/P_z² and m_N²/P_z² kinematic corrections to the short-distance expansion of quasi-GPD matrix elements for lattice QCD applications.
Computes LO amplitudes for di-meson photoproduction channels sensitive to quark GPDs and reports high cross sections suitable for GPD studies at JLab energies.
Computes kinematic twist-3, twist-4 and NLO alpha_s corrections to coherent DVCS on He-4 and extracts the first 3D quark-gluon tomography of the nucleus.
Fixed-j holographic DDVCS and DVCS structurally match the singlet conformal-OPE Wilson-kernel family of QCD via open- and closed-string Witten vertices.
Analytical expressions for quark gravitational TMDs are derived in the LFQDM, verified against standard TMD relations, and linked to transverse pressure and shear-force distributions.
A vacuum-normalized holographic photon profile in a fixed-j Witten diagram reproduces the QCD conformal hard kernel for DVCS/DDVCS, with the Mellin exponent fixed by z-power counting.
Using NJL density-dependent quark masses in a light-front dressed-quark model, the paper predicts O(10–40%) medium modifications of GTMDs linked to quark OAM, spin, and spin–orbit correlation, and defines eA/eP GTMD ratios as nuclear-density probes.
A neural network framework informed by lattice QCD uses all-order dispersion relations to significantly constrain both real and imaginary parts of Compton Form Factors extracted from DVCS proton data.
Presents leading-order calculations of exclusive dijet electroproduction cross sections via GPDs in double distribution model, highlighting valence contributions at large x_P and azimuthal modulations consistent with ZEUS data for beta greater than or equal to 0.4.
The authors use the two-flavor NJL model to obtain medium-modified constituent quark masses and then compute the in-medium pion electromagnetic form factor, distribution amplitude, and parton distribution function via light-cone wave functions, with DGLAP evolution applied.
σ-pole residues in gluon D-form factors for π, N, ρ and Δ are consistent with dilaton effective theory predictions within large uncertainties.
T-odd leading-twist GTMDs in σ-space exhibit -t-dependent oscillations with transverse-longitudinal interference, while Sivers and Boer-Mulders Wigner distributions encode proton spin-transverse momentum correlations.
A neural network trained solely on integral observables from a known GPD model recovers the main features of the underlying distributions in a closure test.
Replacing the rapidity argument of the dipole amplitude with ln min{1/|x|, 1/|ξ|} and refining initial conditions for non-linear evolution can eliminate two R-factors in small-x shockwave calculations.
Light-front quark model calculations with two Gaussian wave functions yield transverse mechanical distributions for pseudoscalar charmonium and bottomonium, showing a nodal pressure and positive force.
In the chiral quark-soliton model with 1/N_c corrections, the isoscalar tensor charge is 0.81, the isovector anomalous tensor magnetic moment is 1.97, and the isoscalar tensor quadrupole moment is 5.98, completing the flavor decomposition.
In the bag model, GTMD calculations are consistent, orbital angular momentum is tied to F_{1,4}^q through the Ji sum rule, and a deeper link to pretzelosity TMD is established.
Pion unpolarized quark GPDs at zero skewness are extracted from a data-driven fit to the electromagnetic form factor and PDFs using a parameterized form factor embedded in a PDF-plus-profile GPD framework.
Quantum advantage in hadronic tomography should be evaluated selectively for CFFs, GPDs, TMDs, and GTMDs because their light-front and real-time correlation functions create ill-posed inverse problems that quantum algorithms may address at algorithmic, computational, and inference levels.
citing papers explorer
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Reconstructing the full kinematic dependence of GPDs from pseudo-distributions
Lattice QCD pseudo-distributions at m_π=358 MeV are inverted via multidimensional Gaussian process regression to reconstruct the full kinematic dependence of GPDs H^{u-d} and E^{u-d} while directly extracting double distributions.
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Conformal moments of the two-loop coefficient functions in DVCS
Conformal moments of the two-loop DVCS coefficient functions have been computed with a new technique.
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Quantum Simulation of Generalized Parton Distributions in the Schwinger Model
Quantum algorithm for GPDs in Schwinger model using Wilson fermions, with polynomial resource scaling and exact-diagonalization benchmarks matching theory.
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Gluon GTMD at strong coupling: fixed-spin saddle factorization and Reggeization
The paper derives factorization of fixed-spin conformal moments of unpolarized gluon GTMDs into a universal staple-worldsheet soft factor and a target-dependent Witten amplitude, with UV/IR reductions and Reggeization via the holographic Pomeron.
-
Finite-$t$ and target mass corrections for the short-distance expansion of quasi(pseudo) GPDs
Derives t/P_z² and m_N²/P_z² kinematic corrections to the short-distance expansion of quasi-GPD matrix elements for lattice QCD applications.
-
Exclusive photoproduction of a di-meson pair with large invariant mass
Computes LO amplitudes for di-meson photoproduction channels sensitive to quark GPDs and reports high cross sections suitable for GPD studies at JLab energies.
-
Coherent deeply virtual Compton scattering on helium-4 beyond leading power
Computes kinematic twist-3, twist-4 and NLO alpha_s corrections to coherent DVCS on He-4 and extracts the first 3D quark-gluon tomography of the nucleus.
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Holographic Open/Closed Exchange in Double Deeply Virtual Compton Scattering: Fixed-$j$ Structural Matching to the $\pm$-Basis Wilson Kernels
Fixed-j holographic DDVCS and DVCS structurally match the singlet conformal-OPE Wilson-kernel family of QCD via open- and closed-string Witten vertices.
-
Gravitational transverse momentum distribution of proton
Analytical expressions for quark gravitational TMDs are derived in the LFQDM, verified against standard TMD relations, and linked to transverse pressure and shear-force distributions.
-
From Vacuum to Nucleon: Fixed-$j$ Kernel Matching of Holographic Current Correlators to QCD
A vacuum-normalized holographic photon profile in a fixed-j Witten diagram reproduces the QCD conformal hard kernel for DVCS/DDVCS, with the Mellin exponent fixed by z-power counting.
-
Electron-Ion Collision Environment: Distribution of Quark Spin and Orbital Angular Momentum
Using NJL density-dependent quark masses in a light-front dressed-quark model, the paper predicts O(10–40%) medium modifications of GTMDs linked to quark OAM, spin, and spin–orbit correlation, and defines eA/eP GTMD ratios as nuclear-density probes.
-
Constraining DVCS Compton Form Factors Using Lattice QCD informed Neural Network
A neural network framework informed by lattice QCD uses all-order dispersion relations to significantly constrain both real and imaginary parts of Compton Form Factors extracted from DVCS proton data.
-
Probing GPDs in exclusive electroproduction of dijets
Presents leading-order calculations of exclusive dijet electroproduction cross sections via GPDs in double distribution model, highlighting valence contributions at large x_P and azimuthal modulations consistent with ZEUS data for beta greater than or equal to 0.4.
-
Valence quark distribution of the pion inside a medium with finite baryon density: A Nambu--Jona-Lasinio model approach
The authors use the two-flavor NJL model to obtain medium-modified constituent quark masses and then compute the in-medium pion electromagnetic form factor, distribution amplitude, and parton distribution function via light-cone wave functions, with DGLAP evolution applied.
-
Gluon Gravitational $ D$-Form Factor: The $\sigma$-Meson as a Dilaton Confronted with Lattice Data II
σ-pole residues in gluon D-form factors for π, N, ρ and Δ are consistent with dilaton effective theory predictions within large uncertainties.
-
T-odd Wigner Distributions in boost-invariant longitudinal position space and Spin-momentum correlation in proton
T-odd leading-twist GTMDs in σ-space exhibit -t-dependent oscillations with transverse-longitudinal interference, while Sivers and Boer-Mulders Wigner distributions encode proton spin-transverse momentum correlations.
-
Neural Network Representation of Generalized Parton Distributions (NNGPD)
A neural network trained solely on integral observables from a known GPD model recovers the main features of the underlying distributions in a closure test.
-
On the Two $R$-Factors in the Small-$x$ Shockwave Formalism
Replacing the rapidity argument of the dipole amplitude with ln min{1/|x|, 1/|ξ|} and refining initial conditions for non-linear evolution can eliminate two R-factors in small-x shockwave calculations.
-
Mechanical distribution of the pseudoscalar charmonium and bottomonium on the light-front
Light-front quark model calculations with two Gaussian wave functions yield transverse mechanical distributions for pseudoscalar charmonium and bottomonium, showing a nodal pressure and positive force.
-
Multipole structure of the nucleon tensor form factors
In the chiral quark-soliton model with 1/N_c corrections, the isoscalar tensor charge is 0.81, the isovector anomalous tensor magnetic moment is 1.97, and the isoscalar tensor quadrupole moment is 5.98, completing the flavor decomposition.
-
GTMDs, orbital angular momentum, and pretzelosity
In the bag model, GTMD calculations are consistent, orbital angular momentum is tied to F_{1,4}^q through the Ji sum rule, and a deeper link to pretzelosity TMD is established.
-
Extraction of Pion Unpolarized Quark Generalized Parton Distribution from Charge Form Factors
Pion unpolarized quark GPDs at zero skewness are extracted from a data-driven fit to the electromagnetic form factor and PDFs using a parameterized form factor embedded in a PDF-plus-profile GPD framework.
-
Toward selective quantum advantage in hadronic tomography:explicit cases from Compton form factors, GPDs, TMDs, and GTMDs
Quantum advantage in hadronic tomography should be evaluated selectively for CFFs, GPDs, TMDs, and GTMDs because their light-front and real-time correlation functions create ill-posed inverse problems that quantum algorithms may address at algorithmic, computational, and inference levels.