Gluon skewed generalized parton distributions of proton from a light-front Hamiltonian approach
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Zhang, Pengxiang↗
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Generalized parton distributions from symbolic regression
AI/ML informed Symbolic Regression is the next stage of scientific modeling. We utilize a highly customizable symbolic regression package “PySR” to model the x and t dependence of the flavor isovector combination Hu-d(x, t, ) at = 0. These PySR models were trained on GPD results provided by both Lattice QCD and phenomenological sources GGL, GK, and VGG. We demonstrate, for the first time, the consistency and systematic convergence of Symbolic Regression by quantifying the disparate models through their Taylor expansion coefficients. In addition to PySR penalizing models with higher complexity and mean-squared error, we implement schemes that test specific physics hypotheses, including force-factorized x and t dependence and Regge behavior in PySR GPDs. We show that PySR can identify factorizing GPD sources based on their response to the Force-Factorized model. Here, knowing the precise behavior of the GPDs, and their uncertainties in a wide range in x and t, crucially impacts our ability to concretely and quantitatively predict hadronic spatial distributions and their derived quantities.
Dotson, Andrew [New Mexico State University, Las C↗
Unpolarized GPDs at small x and non-zero skewness
We study the small-x asymptotics of unpolarized generalized parton distributions (GPDs) and generalized transverse momentum distributions (GTMDs). Unlike the previous works in the literature, we consider the case of non-zero (but small) skewness while allowing for non-linear contributions to the evolution equations. We first show that unpolarized GPDs and GTMDs at small x are related to the eikonal dipole amplitude N, whose small-x evolution is given by the BK/JIMWLK evolution equations, and to the odderon amplitude $\mathscr{O}$, whose evolution is also known in the literature. We then show that the effect of non-zero skewness ξ ≠ 0 is to modify the value of the evolution parameter (rapidity) in the arguments for the dipole amplitudes N and $\mathscr{O}$ from Y = ln(1/x) to Y = ln min{1/|x|, 1/|ξ|}.
Generalized parton distributions (GPDs)↗
Small-𝑥 gluon GPD constrained from deeply virtual 𝐽/𝜓 production and gluon PDF through universal-moment parametrization
We phenomenologically constrain the small-𝑥 and small-𝜉 gluon generalized parton distributions (GPDs) with the deeply virtual 𝐽/𝜓 production (DV𝐽/𝜓P) in the framework of GPDs through universal moment parameterization (GUMP). We use a hybrid cross-section formula combining collinear factorization to the next-to-leading order (NLO) accuracy of the strong coupling 𝛼 𝑠 , with corrections from nonrelativistic QCD to account for the power corrections due to the heavy 𝐽/𝜓 mass. We reach reasonable fit to the measured differential cross sections of DV𝐽/𝜓P by H1 at the Hadron-Electron Ring Accelerator as well as forward gluon parton distribution functions (PDFs) from JAM22 global analysis. We find that both NLO and nonrelativistic corrections are significant for heavy vector meson productions. Of course, the gluon GPD we obtain still contains considerable freedom in need of inputs from other constraints, particularly in the distribution-amplitude-like region.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
A unified neural-network framework for nucleon imaging from numerical simulations of QCD
Parton distributions encode the momentum-space structure and, in their generalizations, the spatial tomography of quarks and gluons inside hadrons, the building blocks of visible matter. We present a unified neural-network approach that learns these distributions directly from matrix elements calculated via numerical simulations of quantum chromodynamics (QCD) on the lattice by fitting two complementary inputs simultaneously: data matched to physical quantities via known momentum-space and coordinate-space formalisms. Utilizing data from both methods stabilizes the extraction and mitigates biases that can arise when either is used alone. We validate the method on controlled mock data and apply it to lattice-QCD matrix elements to extract parton distribution functions (PDFs). We show benefits of such an approach for determining the physical quantities. We further extend the framework to zero-skewness generalized parton distributions and demonstrate nucleon tomography within the same neural-network parameterization. Our results provide an adaptable and systematically improvable approach for extracting partonic distributions from Euclidean correlators. It can incorporate polarization, additional channels, and future experimental constraints from current and future facilities, such as the Electron-Ion Collider.
Hadronic Spectroscopy↗
Nonlocal Effective Field Theory and Its Applications
We review recent applications of nonlocal effective field theory, particularly focusing on nonlocal chiral effective theory and nonlocal quantum electrodynamics (QED), as well as an extension of nonlocal effective theory to curved spacetime. For the chiral effective theory, we discuss the calculation of generalized parton distributions (GPDs) of the nucleon at nonzero skewness, along with the corresponding gravitational (or mechanical) form factors, within the convolution framework. In the QED application, we extend the nonlocal formulation to construct the most general nonlocal QED interaction, in which both the propagator and fundamental QED vertex are modified due to the nonlocal Lagrangian, while preserving the Ward–Green–Takahashi identities. For consistency with the modified propagator, a solid quantization is proposed, and the nonlocal QED is applied to explain the lepton g−2 anomalies without the introduction of new particles beyond the standard model. Finally, with an extension of the chiral effective action to curved spacetime, we investigate the nonlocal energy–momentum tensor and gravitational form factors of the nucleon with a nonlocal pion–nucleon interaction.
chiral effective field theory↗
Tensor-polarized parton density in the 𝑁 → Δ transition from the large-𝑁 𝑐 light-cone wave function
The tensor-polarized parton density is defined by the forward matrix element of a partonic operator in the 𝑁 → Δ transition. In this work, we investigate it by employing the large-𝑁 𝑐 light-cone wave function derived from the mean-field approach. The mean-field picture is based on low-energy effective dynamics in the large-𝑁 𝑐 limit, where the baryon wave function is formulated in the rest frame. By exploiting the covariance of the mean-field solution, we derive the corresponding large-𝑁 𝑐 light-cone wave function—decomposed unambiguously into 3𝑄 , 5𝑄 , 7𝑄 , and higher Fock components—in the infinite momentum frame. Evaluating the overlap of these wave functions, we derive an overlap representation of the tensor-polarized parton density in the 𝑁 → Δ transition and find that the leading contribution arises from the 5𝑄 Fock sector. This indicates that the tensor-polarized parton density directly probes the genuine 5𝑄 component and is governed by chiral dynamics. Our numerical analysis shows that the 𝑁 → Δ tensor-polarized parton density is suppressed, consistent with standard large-𝑁 𝑐 expectations. Finally, we establish connections among the tensor-polarized parton density, the generalized parton distribution 𝐻 𝑋 , and the energy-momentum tensor form factor 𝐹 4 .
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
String-based parametrization of nucleon GPDs at any skewness: A comparison to lattice QCD
We introduce a string-based parametrization for nucleon quark and gluon generalized parton distributions (GPDs) valid at all skewness values. The conformal moments of the GPDs are expressed as sums of the spin-j nucleon A-form factor and the skewness-dependent spin-j nucleon D-form factor. This representation, which fulfills the polynomiality condition (due to Lorentz invariance) and does not rely on model-specific assumptions, is derived from t-channel string exchanges in anti-de Sitter spaces. The spin-j nucleon D-form factor is closely related to the spin-j nucleon A-form factor. We use the Mellin moments from empirical parton distributions to model the spin-j nucleon A-form factors. Using only five Regge slope parameters, fixed from the electromagnetic and gravitational form factors, our string-based parametrization generates accurate singlet, nonsinglet, isovector, and flavor-separated nucleon quark GPDs, along with symmetric nucleon gluon GPDs from their Mellin-Barnes integral representations. Our isovector nucleon quark GPD is in agreement with existing lattice data. Our string-based parametrization should facilitate the empirical extraction and global analysis of nucleon GPDs in exclusive processes, bypassing the deconvolution challenge.
Electron-ion collisions↗
Rapidity-dependent spin decomposition of the nucleon
We revisit the two-dimensional Fourier transform of generalized parton distributions (GPDs) at nonzero skewness. At 𝜂 = 0 it reduces to the standard impact-parameter density, while at 𝜂 ≠ 0 it is an off-forward amplitude that we interpret as a genuine parton–nucleon correlation. Its overall strength (the transverse-plane integral of the density) is fixed by the GPD at the kinematic point 𝑡 =−𝑐 𝜂 =−4𝜂 2 𝑚$^{2}_{𝑁}$/(1 − 𝜂 2 ) and decreases monotonically with the rapidity gap Δ𝑦 = ln[(1+𝜂)/(1−𝜂)] = 2 artanh(𝜂). This rapidity dependence implies rapidity-modified Ji identities that connect helicity, orbital, and total angular momenta of the correlation in closed form. To quantify these effects, we construct leading-twist quark and gluon GPDs in a string-based conformal framework: conformal moments are parametrized by linear open- and closed-string Regge trajectories with slopes constrained by parton distribution functions (PDFs), hadron/glueball spectroscopy, and form-factor data, and GPDs are reconstructed over the full (𝑥,𝜂,𝑡) domain by Mellin-Barnes inversion with next-to-leading order evolution. We find qualitative agreement (and fair quantitative agreement within quoted uncertainties) for several moments and selected nonsinglet 𝑥-space channels at 𝜇 = 2 GeV when compared with lattice QCD, while we also identify channels with visible tension and discuss likely sources (PDF priors and 𝑡-slope systematics).
Gauge-gravity dualities↗
String-based axial and helicity-flip GPDs: A comparison to lattice QCD
We construct an analytic, string-based representation of the nucleon’s axial and helicity-flip conformal moments of generalized parton distributions (GPDs) that holds for skewness and for both the quark and gluon channels. The starting point is the Mellin-Barnes resummation of the conformal partial-wave expansion, where the moments are parametrized by open- (Reggeon) and closed-string (Pomeron) trajectories with slopes determined by experimental form factors and meson/glueball spectroscopy. The forward limits are fixed by the empirical unpolarized and polarized parton distributions. Polynomiality, crossing symmetry, and support are satisfied by construction. After next-to-leading order Dokshitzer-Gribov-Lipatov-Altarelli-Parisi/Efremov-Radyushkin-Brodsky-Lepage evolution to μ = 2 GeV our analytic framework (i) reproduces some of the currently available lattice moments of E and H˜ in the nonsinglet sector, (ii) predicts sea-quark and gluon polarized moments that will be testable by forthcoming simulations and experiments at Jefferson Lab and the future Electron-Ion Collider, and (iii) yields axial and helicity-flip GPDs in x-space in reasonable agreement with lattice QCD.
Gauge-gravity dualities↗
Skewness-dependent moments of the pion GPD from nonlocal quark-bilinear correlators
We present lattice QCD calculations of the odd Mellin moments of pion valence-quark generalized parton distribution up to fifth order ⟨𝑥 4 ⟩ and for the skewness range [−0.33, 0] using operator product expansion of bilocal quark-bilinear operators. The calculations are performed on an ensemble with lattice spacing 𝑎 = 0.04 fm and valence pion mass 300 MeV, employing boosted pion states with momenta up to 2.428 GeV and momentum transfers reaching 2.748 GeV 2 . We employ ratio-scheme renormalization and next-to-leading logarithmic resummed perturbative matching. At zero skewness, our results are consistent with previous lattice studies. By combining matrix elements at multiple values of skewness and momentum transfer, skewness-dependent moments are obtained through simultaneous polynomiality-constrained fits.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Tensor-polarized parton density in the $N → Δ$ transition
The generalized parton distributions for transitions between baryon states with different masses have a forward limit in which they behave as parton densities (light-front momentum transfer Δ + , Δ T = 0, energy transfer Δ - ≠ 0). These "transition parton densities" can realize spin/isospin quantum numbers not accessible in the ground-state nucleon. The N → Δ transition gives rise to a new parton density proportional to the 1/2 → 3/2 spin transition tensor. Its properties are derived, and its magnitude is estimated in the chiral quark-soliton model based on the large-N c limit of QCD.
Delta isobar↗
Probing hard/soft factorization via beam-spin asymmetry in exclusive pion electroproduction from the proton
Deep exclusive meson production (DEMP) reactions, such as $p(\vec{e}, e' π^+)n$, provide opportunities to study the three-dimensional structure of the nucleon through differential cross section and beam- and target-spin asymmetry measurements. This work aims to probe the onset of the hard/soft factorization regime through the exclusive $p(\vec{e}, e' π^+)n$ reaction, as measured in the KaonLT experiment at Jefferson Lab Hall C. A 10.6 GeV longitudinally polarized electron beam was incident on an unpolarized liquid hydrogen target, and the scattered electron and produced meson were detected in two magnetic focusing spectrometers, enabling precision cross section measurements. The cross section ratio $σ_{LT'}/σ_0$ was extracted from the beam-spin asymmetry $A_{LU}$. The t -dependence of $σ_{LT'}/σ_0$ was determined at fixed $Q^2$ and $x_B$ over a range of kinematics from 2 < $Q^2$ < 6 GeV$^2$ above the resonance region ($W$ > 2 GeV). Furthermore, these data are combined with recent results from CLAS/CLAS12 to determine the $Q^2$-dependence of at two $(x_B, t)$ settings. This was fairly flat, with $Q^2$ not having a measurable effect on the value of in the range explored. Results are compared to predictions from the generalized parton distribution (GPD) formalism, which relies explicitly on hard/soft factorization, and Regge formalism. The Regge models better predict $σ_{LT'}/σ_0$, which suggests that the factorization regime is not yet reached.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Transverse orbital angular momentum in the proton
Using the equations of motion of QCD and Lorentz invariance relations, we show a new, more direct way of obtaining the decomposition of the proton's quark transverse angular momentum into its spin and orbital components. The new decomposition can be understood as a twist-three relation, with the quark transverse spin described by the parton distribution g T . We find that the orbital component can be expressed in terms of a moment in the quark transverse momentum, k T , of the generalized transverse momentum-dependent distribution F 12 , or alternatively in terms of the twist-three generalized parton distributions H 2T and $\tilde{E}$ 2T .
Lorentz invariance relations↗
Moments of axial-vector GPD from lattice QCD: quark helicity, orbital angular momentum, and spin-orbit correlation
In this work, we present a lattice QCD calculation of the Mellin moments of the twist-2 axial-vector generalized parton distribution (GPD), $\overset{\sim }{H}\left(x,\xi, t\right)$ , at zero skewness, ξ, with multiple values of the momentum transfer, t. Our analysis employs the short-distance factorization framework on ratio-scheme renormalized quasi-GPD matrix elements. The calculations are based on an N f = 2 + 1 + 1 twisted mass fermions ensemble with clover improvement, a lattice spacing of a = 0.093 fm, and a pion mass of m π = 260 MeV. We consider both the iso-vector and iso-scalar cases, utilizing next-to-leading-order perturbative matching while omitting the disconnected contributions and gluon mixing in the iso-scalar case. For the first time, we determine the Mellin moments of $\overset{\sim }{H}$ up to the fifth order. From these moments, we discuss the quark helicity and orbital angular momentum contributions to the nucleon spin, as well as the spin-orbit correlations of the quarks. Additionally, we perform a Fourier transform over the momentum transfer, which allows us to explore the spin structure in the impact-parameter space.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
New framework for extracting GPDs from exclusive photon electroproduction
Recently, a new framework for studying generic 2 → 3 hard exclusive reactions, referred to as single-diffractive hard exclusive processes, has been introduced to provide a cleaner separation of the underlying physical mechanisms. In this work, we expand this formalism to the case of exclusive real-photon electroproduction off a nucleon, 𝑒(ℓ) +𝑁(𝑝) →𝑒(ℓ′) +𝑁(𝑝′) + 𝛾(𝑞′), which represents the classical channel for accessing generalized parton distributions (GPDs) in nucleons and nuclei. This extension enables a more systematic and physically transparent formulation of the reaction dynamics, paving the way for improved extractions of GPDs from experimental data as compared to existing approaches.
Qiu, Jian-Wei [Thomas Jefferson National Accelerat↗
Bayesian Inferring Nucleon Gravitational Form Factors via Near-Threshold 𝐽/𝜓 Photoproduction
With Bayesian inference, we investigate the impact of recent near-threshold 𝐽/𝜓 production measurements by the 𝐽/𝜓007 experiment and GlueX Collaboration on the extraction of proton gravitational form factors. We apply the generalized parton distribution framework at the next to leading order and demonstrate a stable expansion for the near-threshold kinematics. We find that the experimental constraints are in good agreement with the state-of-the-art lattice simulations, where negative 𝐶 𝑞 (𝑡) and 𝐶 𝑔 (𝑡) are strongly preferred. This highlights a great potential to extract them from future high-precision experiments.
QCD phenomenology↗
Off forward non- s -channel helicity conserving contributions to exclusive vector quarkonium production from the spin dependent BFKL Pomeron
A novel contribution to off forward, exclusive vector quarkonium production, γ(*)+p → V+p, at high energy is derived which corresponds to a t-channel exchange of a Balitsky-Fadin-Kuraev-Lipatov (BFKL) hard Pomeron, with a helicity flip of the proton. This “spin-dependent BFKL Pomeron” is required in a consistent expansion in powers of the momentum transfer t ≈−Δ$^{2}_{⊥}$ beyond first order. The spin-dependent Pomeron violates s-channel helicity conservation at O(Δ$^{2}_{⊥}$), and beyond. Expanding to leading twist only, it corresponds to generalized parton distributions E g (x,t) for vanishing skewness. We derive explicit expressions for the eikonal BFKL amplitudes, to all orders in dipole size times momentum transfer, for all helicity configurations of the particles in the initial and final states. We also provide numerical estimates of the helicity flip two gluon exchange amplitude at moderate x from a light cone quark model of the proton. The spin dependent BFKL Pomeron could, in principle, be discovered via double spin asymmetries in e+p → e+p+J/ψ with a transversely polarized proton and longitudinally polarized electron in the initial state.
Deep inelastic scattering↗