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DOE OSTI2025

Exploring the Nucleon Structure via Deep Electroproduction Processes

Understanding the internal structure of the nucleon is a fundamental goal of modern physics, which aims at a comprehensive framework describing the internal dynamics of quarks and gluons. Among other structure functions, Generalized Parton Distributions (GPDs) offer a powerful framework for describing the nucleon dynamics by correlating the longitudinal momentum and the transverse position of its internal partons. Such a correlation provides a three-dimensional picture of the nucleon and enables access to fundamental properties, including the internal pressure distributions and the parton’s angular momentum contribution to the nucleon's total spin, thereby playing a central role in resolving the nucleon spin puzzle. At the Thomas Jefferson National Facility (JLab), polarized electron beam experiments allow for probing GPDs through the measurement of hard exclusive processes. Among the cleanest experimental channels, we find the electro-production of a real photon through the Deeply Virtual Compton Scattering (DVCS) mechanism. The first data-taking period of the CLAS12 program, taking place in 2018, allowed for unique DVCS Beam Spin Asymmetry (BSA) measurements in the phase space covered by a 10.6 GeV polarized electron beam impinging on an unpolarized liquid hydrogen target. Although detecting all final-state particles ensures exclusivity of the process, conservation laws indicate that it is not mandatory. I adopt an approach omitting the direct detection of the recoil proton, providing a simplified yet effective event selection strategy that boosts statistics and gives access to a larger phase space sensitive to the underlying GPD dynamics through BSA and cross section measurements. The Double DVCS (DDVCS) process promises a dedicated mapping of GPDs. Contributing to the electro-production of a lepton pair cross-section, the DDVCS reaction extends DVCS by allowing the final-state photon to be virtual, enriching the kinematic phase space and providing unique access to the internal correlations encoded by GPDs. A feasibility study is conducted to assess the potential of future DDVCS measurements at Jefferson Lab and the future Electron-Ion Collider (EIC). While Jefferson Lab will provide DDVCS measurements in the valence region through the SoLID$\mu$ and $\mu$CLAS12 experimental projects, in the long term, the EIC will provide complementary measurements in the sea region, both accessing unprecedented information about GPDs in a phase space region otherwise inaccessible. Taken together, these investigations demonstrate both the current capabilities and future opportunities for probing GPDs through exclusive processes. The experimental analysis of DVCS at CLAS12 provides precise measurements within an established framework, while the phenomenological study of DDVCS opens the door to richer and more comprehensive explorations with future detectors and facilities.

Alvarado, Juan [Université Paris-Saclay: Gif-sur-Y↗
DOE OSTI2023

Generalized parton distributions through universal moment parameterization: non-zero skewness case

We present the first global analysis of generalized parton distributions (GPDs) combing lattice quantum chromodynamics (QCD) calculations and experiment measurements including global parton distribution functions (PDFs), form factors (FFs) and deeply virtual Compton scattering (DVCS) measurements. Following the previous work where we parameterize GPDs in terms of their moments, we extend the framework to allow for the global analysis at non-zero skewness. Together with the constraints at zero skewness, we fit GPDs to global DVCS measurements from both the recent JLab and the earlier Hadron-Electron Ring Accelerator (HERA) experiments with two active quark flavors and leading order QCD evolution. With certain choices of empirical constraints, both sea and valence quark distributions are extracted with the combined inputs, and we present the quark distributions in the proton correspondingly. We also discuss how to extend the framework to accommodate more off-forward constraints beyond the small ξ expansion, especially the lattice calculated GPDs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

On extraction of twist-two Compton form factors from DVCS observables through harmonic analysis

We investigate the exercise of locally extracting the real and imaginary parts of the four twist-2 Compton form factors (CFFs) {$\mathcal{H,E,\tilde H,\tilde E}$} which arise in the deeply virtual Compton scattering (DVCS) process e + p → e + p + y. Neglecting dynamical higher-twist contributions, we find that there are a sufficient number of DVCS observables and degrees of freedom to extract all 8 leading quantities model-independently, exploiting the azimuthal dependence of the absolute cross sections across all possible beam and target polarizations at a common kinematical point in {Q, t,x b , y}. As an example, for typical JLab lab-frame kinematics, we simplify the reduced DVCS observables to their dominant terms, providing a sufficient number of equations for local determination of the twist-2 CFFs. We demonstrate the feasibility using harmonic fitting to both cross sections and beam spin asymmetries with both real and pseudo-data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Novel Rosenbluth extraction framework for Compton form factors from deeply virtual exclusive experiments

We use a generalization of the Rosenbluth separation method for a model independent simultaneous extraction of the Compton Form Factors $\mathscr{H}$ and $\mathscr{E}$ from virtual Compton scattering data on an unpolarized target. A precise evaluation of $\mathscr{H}$ and $\mathscr{E}$ enabled by the proposed method, is the first step towards pinning down the distribution of angular momentum inside the proton.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Shedding light on shadow generalized parton distributions

The feasibility of extracting generalized parton distributions (GPDs) from deeply virtual Compton scattering (DVCS) data has recently been questioned because of the existence of an infinite set of so-called “shadow GPDs” (SGPDs). These SGPDs depend on the process and manifest as multiple solutions (at a fixed scale 𝑄 2 ) to the inverse problem that needs to be solved to infer GPDs from DVCS data. SGPDs therefore pose a significant challenge for extracting GPDs from DVCS data. With this motivation we study the extent to which QCD evolution can provide constraints on SGPDs. This is possible because the known classes of SGPDs begin to contribute to observables after evolution, and can then be constrained (at the input scale 𝑄$^{2}_{0}$) by data that has a finite 𝑄 2 range. The impact that SGPDs could have on determining the total angular momentum, pressure and sheer force distributions, and tomography is also discussed. We find that 𝑄 2 evolution, given empirical data over a wide range of skewness (𝜉 ) and 𝑄 2 scales, constrains the SGPDs studied at low 𝑥 and low 𝜉. If this finding generalizes to all SGPDs—and we have not been able to find any SGPDs with qualitatively different behavior—then this potentially makes extraction of GPDs from DVCS possible over a limited range of 𝑥 and 𝜉.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Gravitational form factors and mechanical properties of quarks in protons: A basis light-front quantization approach

We compute the gravitational form factors (GFFs) and study their applications for the description of the mechanical properties such as the pressure, shear force distributions, and the mechanical radius of the proton from its light-front wave functions (LFWFs) based on basis light-front quantization (BLFQ). The LFWFs of the proton are given by the lowest eigenvector of a light-front effective Hamiltonian that incorporates a three-dimensional confining potential and a one-gluon exchange interaction with fixed coupling between the constituent quarks solved in the valence Fock sector. We find acceptable agreement between our BLFQ computations and the lattice QCD for the GFFs. Our D -term form factor also agrees well with the extracted data from the deeply virtual Compton scattering experiments at Jefferson Lab, and the results of different phenomenological models. The distributions of pressures and shear forces are similar to those from different models. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2025

First Global Extraction of Generalized Parton Distributions from Experiment and Lattice Data with Next-to-Leading-Order Accuracy

We report the first global extraction of generalized parton distributions, GUMP 1.0, by combining deeply virtual Compton scattering and 𝜌-meson production data from Jefferson Lab and the Hadron-Electron Ring Accelerator with global fits of parton distribution functions, charge form factors, and lattice quantum chromodynamics simulations. Using a conformal moment space parametrization, we achieve a unified description across low- and high-𝑥 regions at next to leading order accuracy in perturbative corrections. The results provide state-of-the-art generalized parton distributions consistent with almost all known facts, enabling three-dimensional nucleon imaging in impact parameter space and, at the same time, establishing a benchmark for future theoretical and experimental studies of the nucleon structure.

Form factors↗
DOE OSTI2025

Exploring baryon resonances with transition generalized parton distributions: status and perspectives

QCD gives rise to a rich spectrum of excited baryon states. Understanding their internal structure is important for many areas of nuclear physics, such as nuclear forces, dense matter, and neutrino-nucleus interactions. Generalized parton distributions (GPDs) are an established tool for characterizing the QCD structure of the ground-state nucleon. They are used to create 3D tomographic images of the quark/gluon structure and quantify the mechanical properties such as the distribution of mass, angular momentum, and forces in the system. Transition GPDs extend these concepts to N → N* transitions and can be used to characterize the 3D structure and mechanical properties of baryon resonances. They can be probed in high-momentum-transfer exclusive electroproduction processes with resonance transitions e + N → e' + M + N*, such as deeply-virtual Compton scattering (M = γ) or meson production (M = π, K, etc.), and in related photon/hadron-induced processes. This White Paper describes a research program aiming to explore baryon resonance structure with transition GPDs. This includes the properties and interpretation of the transition GPDs, theoretical methods for structures and processes, first experimental results from JLab 12 GeV, future measurements with existing and planned facilities (JLab detector and energy upgrades, COMPASS/AMBER, EIC, EicC, J-PARC, LHC ultraperipheral collisions), and the theoretical and experimental developments needed to realize this program.

Experimental Nuclear Physics↗
DOE OSTI2024

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

Abstract 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 $$\xi $$ ξ which has only been brushed in the literature so far, paving the way for a joint extraction of GPDs.

Physics↗
DOE OSTI2023

The EIC on a Table Top (Final Report)

A research collaboration between JLab and the Atomic and Molecular Optics group of Olivier Pfister at UVA was established to adapt and enhance their optics-based Quantum Computing (QC) system for the calculation of Doubly-Deeply Virtual Compton Scattering amplitudes relevant for JLab12 and the EIC program. The formalism and simulation infrastructure for computing matrix elements of such Compton amplitudes was established. In partnership with UVA, JLab has provided the technical expertise to enhance the current system, and explored significantly scaling it to become a unique and powerful resource.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Theoretical Studies in Hadronic Physics and Fundamental Symmetries

The nucleons (protons and neutrons) are at the center of every atom, the fundamental building blocks of matter in our Universe. Their structure and properties have been actively studied at DOE’s Thomas Jefferson Lab as well as the future US electron-ion collider at Brookhaven National Lab, and are believed to be described by a mathematical theory known as quantum chromodynamics (QCD). In this project, the PI and collaborators invented a theoretical approach called “Generalized parton distributions through Universal Moment Parametrization” (GUMP) to construct the 3D structure of the nucleon from experimental data on Deeply virtual compton scattering and Deep-Exclusive meson production, and semi-inclusive jet or meson productions. The PI and collaborators have also explored the full power of a theory called the large- momentum effective theory (LaMET) to calculate the 3D structure of the nucleon from the first principles known as lattice QCD. In particular, the work paved the way for unprecedented precision calculations which are coming in next decade.

3D Structure↗
DOE OSTI2025

Nucleon structure studies: DVCS on polarised protons with the CLAS12 experiment, and development of Micromegas detectors for EIC

The quark and gluon structure of nucleons is crucial for understanding the origin of their mass and spin. This information is encoded in structure function such as Generalised Parton Distributions (GPDs), which provide a three-dimensional picture of the nucleon in terms of its constituents. Deeply Virtual Compton Scattering (DVCS) offers the most direct access to GPDs, but their extraction requires high-precision measurements of multiple observables over a wide kinematic range. In 2022 and 2023 the CLAS12 experiment at Jefferson Lab (JLab) collected data from polarised electron scattering on a longitudinally polarised proton target, enabling the first measurement of polarised DVCS asymmetries at JLab 12GeV kinematics. This thesis will present preliminary measurement of the beam, target and double spin DVCS asymmetries from the CLAS12 polarised proton target data. Nucleon structure studies will also constitute a major part of the physics program at the future Electron Ion Collider (EIC). The development of the first detector at the EIC is ongoing and it requires light Micro-Pattern Gaseous Detectors (MPGDs) for its tracking system. This thesis further reports initial tests of Micromegas MPGDs with a two-dimensional readout developed for EIC.

Polcher, Samy [Univ. Paris-Saclay, Gif-sur-Yvette ↗
DOE OSTI2021

Neutral Pion Electroproduction Cross sections from 12 GeV Jefferson Lab for x B > 0 . 3

Nuclear physics aims at understanding structure of the building blocks of the atom, the protons and neutrons in terms of their constituents, the quarks and gluons. Traditionally, this was accomplished through studies of their static properties and the underlying one-dimensional quark and gluon momentum distributions. Over the last few decades, realization has grown that the true study of the proton dynamical structure has to come from more exclusive reactions. These deep exclusive processes describe a subset of unique inelastic processes in which all particles in their final state are detected. Such processes can allow access to Generalized Parton Distributions, or GPDs, a conceptual mechanism that lies at the root of three-dimensional spatial imaging of the proton?s quark-gluon substructure. In particular, photon electroproduction as well as meson electroproduction are two kinds of deep inelastic processes that can allow access to GPDs. Deeply Virtual Compton Scattering (DVCS) is a type of deep inelastic process, and is known as one of the cleanest ways to access GPDs.

Ali, Salina↗
DOE OSTI2023

The Future Electron-Ion Collider

Generalized Parton Distributions include rich information and became a powerful tool for studying hadron structure. Deeply Virtual Compton Scattering is the golden channel to access GPDs. The development of high luminosity and high-acceptance detectors (Electron-Ion Collider) allows physicists to overcome the difficulty of DVCS measurements. The outstanding performance of the accelerator performs the eA collisions at the center of mass energy from 20 to 140 GeV, while the luminosity at the scale of 1034 cm?2s?1. The new type of high-density crystal, PWO-II, produced by CRYTUR in 2×2×20 cm3 will be utilized in the calorimeter. The transparency of PWO-II crystals is > 70% at 620 nm, > 60% at 420 nm, and >35% at 360 nm. The crystals also show good radiation hardness under 30 Gy radiation exposure. Ten PWO-II crystals have a uniform light yield at 30 p.e./MeV, providing sufficient light yield to reduce the fluctuation of the energy measurements. Near 3000 crystals were constructed inside the 12-sided polygon supporting structure in the simulation. The island clustering algorithm was used for reconstructed the energy. The energy resolution study by the particle gun shows the stochastic term and constant term are 1.8% and 1.2%, respectively. The spatial resolution of NEEMC varies from 5% to 15% of the crystal?s width depending on the particle?s incident angle. The pion rejection of NEEMC can reach 103 with electron efficiency > 85% when the particle?s energy is larger than 1GeV. The Pi0- identified efficiency study can be interpreted as finding the local maxima in the single cluster caused by two high energy close photons. The study results show that efficiency is nearly 100% for pi0 energy is smaller than 10 GeV, and efficiency drops to 30% with 20 GeV pi0. The new type of 3x3 pixelated AC-LGAD were wire bonded to ALTIROC for performance test. The cross-talk between the adjacent channels is about 20% for VPA and 10% for TZ. A series of the TDC characteristic measurements show that the jitter for both preamplifiers is about 20 ps, and the time-walk effect is mild for inject charge > 12 pF. Furthermore, the beta source radiation results quantify the sharing scale of the 3x3 pixels AC-LGAD (? 20%). The electronics simulation study results show no significant changes in the spatial resolution, whether ADC resolution is 8, 10, or 12 bits. The 8-bit ADC is decided to use in the EICROC as it has a smaller size and power consumption than the 10-bit and 12-bit ADC. The ECCE is one of the full detector proposals for EIC. The new type of DVCS generator, called TOPEG, is used to generate the high acceptance beam configurations of 18×110 GeV2 electron and 4He. The acceptance study shows a -1.8 < ? < -1.4 gap between the BEMC and EEMC. The 10?x,y geometry cut is applied on the Roman Pots, so the acceptance of Roman Pots quickly drops to 0% when the polar angle of the recoiled 4He < 2 mrad. This primary ECCE simulation study suggests extending the acceptance of BEMC longitudinally as the structure limits the radial size of EEMC. The acceptance of the Roman Pots is still challenging. In 2023, The overall design of ePIC was finalized by merging two full detector proposals (ECCE and ATHENA) after a series of intensive simulation studies.

Wang, Pu-Kai↗
DOE OSTI2024

Nucleon Structure Studies at Jefferson Lab and the Electron Ion Collider

The research programs of Thomas Jefferson Laboratory (JLab) and the future Electron- Ion Collider (EIC) focus on one of the main goals of strong interaction studies : understanding the structure of nucleons in terms of the quarks and gluons composing them. Their structure is encoded in functions such as Generalized Parton Distributions (GPDs), which describe how quarks and gluons’ transverse position and longitudinal momentum are distributed inside nucleons. GPDs allow to obtain three-dimensional pictures of nucleons and to understand some of their fundamental properties, such as their internal pressure or the emergence of their spin from the dynamics of the partons composing them. At JLab and the EIC, electron beams are used to probe nucleons. Measurement of reactions such as Deeply Virtual Compton Scattering (DVCS) allows access to GPDs. The first longitudinally polarized-target experiment of the CLAS12 program at Jlab took place in 2022-2023. Combining polarized electron beams and nucleon targets, this experiment offers unique access to observables that allow the measurement of different types of GPDs. In particular, the DVCS beam- and target-spin asymmetries for protons and neutrons in deuterium will be measured for the first time. They give access to kinds of GPDs that are still poorly known, and the comparison between proton and neutron data will allow the extraction of the flavor dependence of the structure of nucleons. Specific analysis methods have been implemented to work with a polarized nuclear target and are presented in this thesis. These methods allow to obtain preliminary results for the asymmetries, waiting for the complete statistics to be available. In the long term, the experimental program for the EIC has been established with a strong emphasis on the measurement of the structure of nucleons at high energy. Measurements of reactions such as DVCS impose strict requirements on the electromagnetic calorimeter that will allow to measure the energy of the scattered electrons and photons. This calorimeter, which is under development, will be based on scintillating crystals read by Silicon Photomultipliers (SiPMs). A new type of glass-based scintillating material was tested, evaluating the possibilities to meet the technical requirements concerning their light yield and resistance to radiation damage in particular. Several models of SiPMs have been characterized, demonstrating they can operate over the vast energy range necessary to address the physics case at the EIC and providing guidelines for developing their readout electronics.

Pilleux, Noemie↗
DOE OSTI2026

EXCLUSIVE NEUTRAL PION ELECTROPRODUCTION CROSS SECTION MEASUREMENTSWITHANEUTRALPARTICLE SPECTROMETER

Deep Virtual Compton Scattering (DVCS), the exclusive electron-proton scattering process ep ¿e'p'¿, provides access to generalized parton distributions (GPDs), which correlate information about the longitudinal momentum and transverse spatial structure of quarks inside the nucleon. Experiment E12-13-010 in Hall C at Jefferson Lab was designed to take high-precision measurements of the DVCS cross section over an extended kinematic range using the newly commissioned Neutral Particle Spectrometer (NPS). The NPS features a high-resolution electromagnetic calorimeter and a streaming data acquisition system optimized for operation at high luminosities. This thesis presents the detector and analysis work carried out to support the NPS DVCS program. In particular, it focuses on the hardware design, calibration, and performance of the calorimeter. A development of a waveform reconstruction analysis of the calorimeter signals enabled improved extraction of pulse amplitudes and times. The waveform analysis was also extended to operate in a multithreaded environment, substantially reducing processing time for large datasets. Analysis of exclusive neutral pion electroproduction events in the calorimeter gives a strong validation of the calorimeter’s performance and resolution. Together these developments establish a foundation for future analyses and extraction of the DVCS cross section and its use in constraining the GPDs.

Kerver, Mitchell [Old Dominion Univ., Norfolk, VA ↗
DOE OSTI2024

Bayesian Neural Network Variational Autoencoder Inverse Mapper (BNN-VAIM) and its application in Compton Form Factors extraction

Abstract We extend the Variational Autoencoder Inverse Mapper (VAIM) framework for the inverse problem of extracting Compton Form Factors (CFFs) from deeply virtual exclusive reactions, such as the unpolarized Deeply virtual exclusive scattering (DVCS) cross section. VAIM is an end-to-end deep learning framework to address the solution ambiguity issue in ill-posed inverse problems, which comprises of a forward mapper and a backward mapper to simulate the forward and inverse processes, respectively. In particular, we incorporate Bayesian Neural Network (BNN) into the VAIM architecture (BNN-VAIM) for uncertainty quantification. By sampling the weights and biases distributions of the BNN in the backward mapper of the VAIM, BNN-VAIM is able to estimate prediction uncertainty associated with each individual solution obtained for an ill-posed inverse problem. We first demonstrate the uncertainty quantification capability of BNN-VAIM in a toy inverse problem. Then, we apply BNN-VAIM to the inverse problem of extracting 8 CFFs from the unpolarized DVCS cross section.

Instruments & Instrumentation↗