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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Open database for GPD analyses

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.

Burkert, V. D. [Thomas Jefferson National Accelera↗
DOE OSTI2025

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↗
DOE OSTI2023

A multidimensional study of the structure function ratio $\sigma_{LT'}$/$\sigma_0$ from hard exclusive $\pi^+$ electro-production off protons in the GPD regime

A multidimensional extraction of the structure function ratio σ LT' /σ 0 from the hard exclusive $\vec{e}$p → e'nπ+ reaction above the resonance region has been performed. The study was done based on beam-spin asymmetry measurements using a 10.6 GeV incident electron beam on a liquid-hydrogen target and the CLAS12 spectrometer at Jefferson Lab. The measurements focus on the very forward regime (t/Q 2 $\ll$ 1) with a wide kinematic range of x B in the valence regime (0.17 < x B < 0.55), and virtualities Q 2 ranging from 1.5 GeV 2 up to 6 GeV 2 . The results and their comparison to theoretical models based on Generalized Parton Distributions demonstrate the sensitivity to chiral-odd GPDs and the directly related tensor charge of the nucleon. In addition, the data is compared to an extension of a Regge formalism at high photon virtualities. It was found that the Regge model provides a better description at low Q 2 , while the GPD model is more appropriate at high Q 2 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

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 (DV⁢𝐽/𝜓⁢P) 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 DV⁢𝐽/𝜓⁢P 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↗
DOE OSTI2026

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↗
DOE OSTI2022

Hard exclusive $\pi^{+}n$ electro production beam spin asymmetries off the proton in the GPD and TDA regimes

Hard exclusive \pi^{+} π + n electro-production can be used to gain access to the 3D nucleon structure. The QCD factorisation mechanism in the “nearly forward region” ( t/Q^{2} t / Q 2 small) allows a description by Generalized Parton Distributions (GPDs), while for the “nearly backward” kinematic region ( u/Q^{2} u / Q 2 small) a description based on nucleon to pion transitions (TDAs) is available. The paper presents a measurement of single beam spin asymmetries to extract the A^{\sin\phi}_{LU} A L U sin ϕ moments and the related cross section ratio \sigma_{LT^\prime}/\sigma_{0} σ L T ′ / σ 0 from the hard exclusive \pi^{+} π + channel off the unpolarized hydrogen target in a wide range of kinematics based on data taken with the CLAS spectrometer at Jefferson Lab. In addition, under forward angles a detailed multidimensional study will be presented based on CLAS12 data and compared to theoretical predictions.

Diehl, Stefan↗
DOE OSTI2025

Generalized parton distributions and gravitational form factors at large momentum transfer

Within the soft collinear effective theory (SCET), we derive a factorization theorem which resums Sudakov logarithms (α s ln 2 ( –t)) n to all orders in the quark-in-quark generalized parton distribution (GPD) at large momentum transfer t, and perform a consistency check to one-loop. We show that the same Sudakov factor appears in the ‘Feynman’ contribution to the GPDs of the nucleon. Our result enables the resummation of all the large logarithms ln Q 2 and ln 2 t in exclusive processes with two hard scales Λ$^{2}_{QCD}$ ≪ |t| ≪ Q 2 . We also present a SCET power counting analysis of the Feynman contributions to the GPDs and show that the x-dependence of GPDs factorizes at large-t with controlled corrections. This in particular implies that any ratio of GPD moments such as the electromagnetic and gravitational form factors (GFF) is perturbatively calculable in this approximation. Furthermore, we identify a novel order α s power-law t-dependence in the GPD and the D-type GFF that will dominate over the standard order α$^{2}_{s}$ ‘leading twist’ asymptotic contribution in the phenomenologically relevant region of t.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Lattice QCD calculation of the pion generalized parton distribution

We present the results of a Lattice QCD computation of pion generalized parton distribution (GPD), employing perturbative matching up to next-to-next-to-leading order (NNLO). The computations are based on an ensemble of Nf=2+1 highly improved staggered quarks (HISQ) with a pion mass of 300 MeV and a lattice spacing of 0.04 fm. Centered on the zero-skewness limit, we utilize a recently proposed Lorentz-invariant definition of GPD, which is derived from Lorentz-invariant amplitudes. We analyze and compare these amplitudes in both Breit and non-Breit kinematic frames at comparable momentum transfers, validating their frame-independent nature. To obtain light-cone GPD, we integrate hybrid scheme renormalization with the large momentum effective theory (LaMET). Moreover, we determine the first three iso-vector generalized form factors (GFFs) of the pion using the ratio scheme renormalization and leading-twist factorization, achieving NNLO accuracy.

Ding, Heng-Tong↗
DOE OSTI2025

Unexpected Breakdown of Collinear Factorisation at Leading Twist in Exclusive π 0 γ Photoproduction Due to Glauber Pinch

We demonstrate the breakdown of collinear factorisation for the exclusive photoproduction at leading twist of a pair, sensitive to both quark and gluon GPD channels. For the very first time in the case of an exclusive process, we demonstrate the breakdown of collinear factorisation through soft-to-collinear Glauber exchanges. We show that the amplitude fails to factorise due to the presence of a Glauber pinch, which has the same power counting as the standard collinear pinch. The Glauber pinch that occurs here is peculiar, since the mechanism that produces it involves two-loop integrals. This is corroborated by an explicit calculation of the gluon GPD channel to pair photoproduction, which leads to a divergent amplitude already at leading twist-2 and at leading order in . On the other hand, for processes where the gluon GPD channel is forbidden, for example when the outgoing meson is a charged pion or a rho meson, collinear factorisation works without any issues.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Parton distribution function for topological charge at one loop

We present results for the gg-part of the one-loop corrections to the recently introduced “topological charge” GPD F~(x, q 2 ). In particular, we give expression for its evolution kernel. To enforce strict compliance with the gauge invariance requirements, we have used on-shell states for external gluons, and have obtained identical results both in Feynman and light-cone gauges. No “zero mode” δ(x) terms were found for the twist-4 gluon GPD F~(x, q 2 ).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Three-dimensional imaging of pion using lattice QCD: generalized parton distributions

In this work, we report a lattice calculation of x-dependent valence pion generalized parton distributions (GPDs) at zero skewness with multiple values of the momentum transfer −t. The calculations are based on an N f = 2 + 1 gauge ensemble of highly improved staggered quarks with Wilson-Clover valence fermion. The lattice spacing is 0.04 fm, and the pion valence mass is tuned to be 300 MeV. We determine the Lorentz-invariant amplitudes of the quasi-GPD matrix elements for both symmetric and asymmetric momenta transfers with similar values and show the equivalence of both frames. Then, focusing on the asymmetric frame, we utilize a hybrid scheme to renormalize the quasi-GPD matrix elements obtained from the lattice calculations. After the Fourier transforms, the quasi-GPDs are then matched to the light-cone GPDs within the framework of large momentum effective theory with improved matching, including the next-to-next-to-leading order perturbative corrections, and leading renormalon and renormalization group resummations. We also present the 3-dimensional image of the pion in impact-parameter space through the Fourier transform of the momentum transfer −t.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Resummation for lattice QCD calculation of generalized parton distributions at nonzero skewness

Large-momentum effective theory (LaMET) provides an approach to directly calculate the x-dependence of generalized parton distributions (GPDs) on a Euclidean lattice through power expansion and a perturbative matching. When a parton’s momentum becomes soft, the corresponding logarithms in the matching kernel become non-negligible at higher orders of perturbation theory, which requires a resummation. But the resummation for the off-forward matrix elements at nonzero skewness ξ is difficult due to their multi-scale nature. In this work, we demonstrate that these logarithms are important only in the threshold limit, and derive the threshold factorization formula for the quasi-GPDs in LaMET. We then propose an approach to resum all the large logarithms based on the threshold factorization, which is implemented on a GPD model. We demonstrate that the LaMET prediction is reliable for [−1 + x 0 , −ξ − x 0 ] ∪ [−ξ + x 0 , ξ − x 0 ] ∪ [ξ + x 0 , 1 − x 0 ], where x 0 is a cutoff depending on hard parton momenta. Through our numerical tests with the GPD model, we demonstrate that our method is self-consistent and that the inverse matching does not spread the nonperturbative effects or power corrections to the perturbatively calculable regions.

hadronic spectroscopy↗
DOE OSTI2021

Nucleon helicity generalized parton distribution at physical pion mass from lattice QCD

The generalized parton distributions (GPDs) offer a window on three-dimensional imaging of the nucleon, providing understanding of how the fundamental properties of the nucleon, such as its mass and spin, arise from the underlying quark and gluon degrees of freedom. In this work, we present the first lattice calculation of the nucleon isovector helicity GPD at physical pion mass, using an a≈0.09 fm lattice ensemble with 2+1+1 flavors of highly improved staggered quarks generated by MILC Collaboration. We perform the GPD calculation in Breit frame using averaged nucleon boost momentum P z ≈2.2 GeV with nonzero momentum transfers in [0.2,1.0] GeV 2 . Nonperturbative renormalization in RI/MOM scheme is used to obtain the quasi-distribution before matching to the lightcone GPDs. The three-dimensional distribution $\tilde{H}$(x, Q 2 ) is presented, along with the three-dimensional nucleon tomography and impact-parameter-dependent distribution for selected Bjorken x at μ=3 GeV in $\overline{MS}$ scheme.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Rosenbluth-like separation of the $J/ψ$ near-threshold photoproduction: An access to the gluon gravitational form factors at high t

Here, we perform analysis of the near-threshold $J/\psi $ photoproduction data off the proton based on two theoretical approaches, GPD \cite{Guo3} and holographic \cite{Zahed2}, that represent the differential cross sections as powers of the skewness parameter with coefficients that depend only on the momentum transfer $t$. This allows to separate kinematically the corresponding coefficient functions, in much the same way as this is done for the electric and magnetic form factors using the Rosenbluth separation. We examine the independence of the extracted functions with the photon beam energy. These functions, under additional assumptions, are related to the proton's gluon Gravitational Form Factors (gGFFs). We compare the extracted functions with lattice calculations of the gGFFs in the region of $0.5<|t|<2$~GeV$^{2}$, where they overlap. Such analysis demonstrates the possibility of extracting some combinations of the gGFFs from the data at high $t$, complementary to the lattice calculations available in the low $t$ region. However, higher statistics are needed to more accurately check the predicted scaling behavior of the data and compare with the lattice results, thus testing and comparing the theoretical assumptions used in the GPD and holographic models.

Pentchev, Lubomir [Thomas Jefferson National Accel↗
DOE OSTI2025

Nonlocal chiral anomaly and generalized parton distributions

We discuss the nonlocal generalization of the QCD chiral anomaly along the light cone and derive relations between twist-two, twist-three, and twist-four generalized parton distributions (GPDs) mediated by the anomaly. We further establish the connection to the “anomaly pole” in the GPD E ˜ recently identified in the perturbative calculation of the Compton scattering amplitudes, and demonstrate its cancellation at the GPD level. Our work helps elucidate the previously unexplored connection between GPDs, the chiral anomaly, and the mass generation of the η ′ meson. Published by the American Physical Society 2025

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Extraction of Beam-Spin Asymmetries from the Hard Exclusive π + Channel off Protons in a Wide Range of Kinematics

We have measured beam-spin asymmetries to extract the $\sin\phi$ moment $A_{LU}^{\sin\phi}$ from the hard exclusive $\vec{e} p \to e^\prime n \pi^+$ reaction above the resonance region, for the first time with nearly full coverage from forward to backward angles in the center-of-mass. The $A_{LU}^{\sin\phi}$ moment has been measured up to 6.6 GeV$^{2}$ in $-t$, covering the kinematic regimes of Generalized Parton Distributions (GPD) and baryon-to-meson Transition Distribution Amplitudes (TDA) at the same time. The experimental results in very forward kinematics demonstrate the sensitivity to chiral-odd and chiral-even GPDs. In very backward kinematics where the TDA framework is applicable, we found $A_{LU}^{\sin\phi}$ to be negative, while a sign change was observed near 90$^\circ$ in the center-of-mass. The unique results presented in this paper will provide critical constraints to establish reaction mechanisms that can help to further develop the GPD and TDA frameworks.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗