This document presents a synthesis of the theory contributions and discussions from the 2nd EIC-France Workshop, held at IJCLab (Orsay) on 1-3 December 2025. The workshop brought together members of the French hadron-physics community to review recent theoretical developments relevant to the future Electron-Ion Collider (EIC) and to coordinate national efforts in preparation for its early physics program. The report first summarizes the collider's initial running conditions and luminosity performance, as outlined in the EIC Early Science Matrix. It then provides concise overviews of the theoretical presentations on inclusive, semi-inclusive, exclusive, heavy-flavor, and small-x physics. Based on these discussions, two measurements emerged as especially well suited for early EIC operation and strongly aligned with areas of established French expertise: inclusive diffraction and inclusive quarkonium production. These channels offer clean signatures, robust theoretical interpretability, and direct sensitivity to fundamental QCD phenomena such as gluon saturation, heavy-quark dynamics, and the small-x structure of hadrons and nuclei. In addition, the workshop identified longer-term physics opportunities that will benefit from the full capabilities of the EIC after its ramp-up phase. These include accessing the three-dimensional structure of the pion through the Sullivan process and a broader program of exclusive three-body final states, both of which represent high-impact avenues for exploring hadronic structure and non-perturbative QCD. Together, the elements summarized in this report provide a coherent overview of the strategic priorities and scientific ambitions shaping the French community's contribution to the EIC physics program.

Coherent hard exclusive reactions on light nuclei provide access to their quark and gluon structure and enable three-dimensional tomography of these complex systems. We study deeply virtual Compton scattering on a helium-4 target, including both kinematic twist-3 and twist-4 corrections, as well as next-to-leading-order corrections to the twist-2 amplitude in the strong coupling α_s. We show that these contributions are crucial for achieving a precise description of the data and, as a result, obtain the first tomographic image of the helium-4 nucleus at the quark-gluon level.

QCD collinear factorization allows coherent hard exclusive reactions to reveal the quark-gluon structure of light nuclei, enabling their 3D tomography. We study elastic form factors and deeply virtual Compton scattering on a helium-4 target, achieving theoretical precision unprecedented even in proton studies. Constraining generalized parton distributions at next-to-leading order in $α_s$, incorporating kinematic twist corrections, and using full evolution equations, we provide the first tomography of a light nucleus, revealing distinct transverse spatial distributions of quarks and gluons.

The CEBAF Large Acceptance Spectrometer for operation at 12 GeV (CLAS12) at the Thomas Jefferson National Accelerator Facility has played a central role in advancing the understanding of nucleon and nuclear structure. As increasingly precise data become available, new physics opportunities emerge that extend beyond the current capabilities of CLAS12. In this article, a program to explore the quark and gluon structure of the nucleon through di-muon electro- and photoproduction is presented. Its primary focus is the measurement of beam-spin asymmetries in Double Deeply Virtual Compton Scattering, ep → e^' μ^+ μ^-p^'. By independently varying the incoming and outgoing photon virtualities and momentum transfer, the DDVCS measurement provides access to the Generalized Parton Distributions over their full three-dimensional phase space, extending beyond the kinematic constraints of Deeply Virtual Compton Scattering and Timelike Compton Scattering. In addition, the large acceptance and high luminosity of the μCLAS12 experiment will enable precision measurements of near-threshold J/ψ production and high-statistics studies of Timelike Compton Scattering.

We introduce a new approach to modeling transition distribution amplitudes (TDAs) for the processes ep -> en pi(+) and ep -> ep pi(0). The modeling is flexible, constrained by sparsely available experimental data, and satisfies theoretical requirements, including reduction to nucleon distribution amplitudes in the appropriate limit. We study the sensitivity of observable predictions to various modeling assumptions. We discuss unpolarized cross sections, as well as the three nonvanishing polarization observables at leading twist, namely, the single transverse target spin asymmetry and the two double spin asymmetries that occur with a polarized lepton beam on either a longitudinally or transversely polarized target. The analysis is complemented by a simple Monte Carlo study to provide guidance for exploring exclusive processes in the so-called backward kinematics. Our work aims to highlight the importance of future measurements to better constrain TDAs and to support upcoming experimental proposals.

We calculate the kinematic twist-3 and twist-4 corrections to the leading-order amplitude of timelike Compton scattering (TCS) on a (pseudo)scalar target, in the recently developed framework based on the conformal operator-product expansion. This allows us to compute the complete set of helicity amplitudes of the process, in particular those that vanish at leading twist. We compare the effects of higher-twist contributions to TCS with those in deeply virtual Compton scattering. Our estimates, based on a IT-meson GPD model, indicate that these contributions are sizeable and will play a crucial role in the interpretation of data from current and forthcoming experiments.

Generalized Parton Distributions (GPDs) have emerged as a powerful framework for exploring the internal structure of hadrons in terms of their partonic constituents. Over the past three decades, the field has witnessed significant theoretical and experimental advancements. The interpretation of GPDs in impact parameter space offers a vivid three-dimensional visualization of hadron structure, correlating longitudinal momentum and transverse spatial distributions, thereby enabling tomographic imaging of hadrons. Furthermore, the link between GPDs and the matrix elements of the QCD energy-momentum tensor provides access to fundamental properties of hadrons, including spin decomposition and internal pressure distributions. Notably, recent analyses of Deeply Virtual Compton Scattering (DVCS) data have enabled the empirical extraction of the quark pressure profile inside the proton. Motivated by the rapidly evolving experimental landscape, this white paper provides a timely and focused overview of recent developments in GPD theory, phenomenology, and lattice QCD studies. Its scope is shaped by the needs and opportunities of forthcoming experimental programs, and it highlights advances that are particularly relevant for the next generation of dedicated measurements, including the extended Jefferson Lab 12 GeV program and its potential 22 GeV upgrade, J-PARC, COMPASS/AMBER, LHC ultra-peripheral collisions, and the future electron-ion colliders EIC and EicC.

Double deeply virtual Compton scattering (DDVCS) is a very precise tool for the nucleon tomography. Its measurement requires high luminosity electron beams and precise dedicated detectors, since its amplitude is quite small in the interesting kinematical domain where collinear QCD factorization allows the extraction of quark and gluon generalized parton distributions (GPDs). We analyze the prospects for its study in the JLab energy domain as well as in higher energy electron-ion colliders. Our results are very encouraging for various observables both with an unpolarized and polarized lepton beam. Using various realistic models for GPDs, we demonstrate that DDVCS measurements are indeed very sensitive to their behaviour. Implementing our lowest order cross-section formulae in the EpIC Monte Carlo generator, we estimate the expected number of interesting events.

Generalized parton distributions (GPDs) are off-forward matrix elements of quark and gluon operators that work as a window to the total angular momentum of partons and their transverse imaging (nucleon tomography). To access GPDs one needs to look into exclusive processes which are usually studied in a kinematic regime known as the Björken limit. In this limit, the photon virtualities are much larger than the hadron mass M, and the kick to the hadron measured by the Mandelstam's variable t. It turns out that this is not enough for the purposes of a precise GPD extraction and, in particular, of nucleon tomography for which measurements in a sizable range of t are required. Deviation with respect to the Björken limit induces kinematic higher-twist corrections which enter the amplitudes with powers of |t|/ℚ^2 and M^2/ℚ^2, where ℚ^2 denotes the scale of the process (basically, the sum of photon virtualities in the case of DDVCS). There are also corrections by the name of "genuine" higher twists which are a separate topic and are not the subject of this research study. In this manuscript, we present novel calculations of DDVCS amplitudes off a (pseudo-)scalar target including up to kinematic twist-4 corrections. These results are important for measuring DDVCS, DVCS and TCS through the Sullivan process and off helium-4 target at the future Electron-Ion Collider (EIC) and JLab experiments. Preliminary numerical estimates for the pion target are provided.

This document presents the initial scientific case for upgrading the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab (JLab) to 22 GeV. It is the result of a community effort, incorporating insights from a series of workshops conducted between March 2022 and April 2023. With a track record of over 25 years in delivering the world's most intense and precise multi-GeV electron beams, CEBAF's potential for a higher energy upgrade presents a unique opportunity for an innovative nuclear physics program, which seamlessly integrates a rich historical background with a promising future. The proposed physics program encompass a diverse range of investigations centered around the nonperturbative dynamics inherent in hadron structure and the exploration of strongly interacting systems. It builds upon the exceptional capabilities of CEBAF in high-luminosity operations, the availability of existing or planned Hall equipment, and recent advancements in accelerator technology. The proposed program cover various scientific topics, including Hadron Spectroscopy, Partonic Structure and Spin, Hadronization and Transverse Momentum, Spatial Structure, Mechanical Properties, Form Factors and Emergent Hadron Mass, Hadron-Quark Transition, and Nuclear Dynamics at Extreme Conditions, as well as QCD Confinement and Fundamental Symmetries. Each topic highlights the key measurements achievable at a 22 GeV CEBAF accelerator. Furthermore, this document outlines the significant physics outcomes and unique aspects of these programs that distinguish them from other existing or planned facilities. In summary, this document provides an exciting rationale for the energy upgrade of CEBAF to 22 GeV, outlining the transformative scientific potential that lies within reach, and the remarkable opportunities it offers for advancing our understanding of hadron physics and related fundamental phenomena.

Double deeply virtual Compton scattering (DDVCS) is the process where an electron scatters off a nucleon and produces a lepton pair. The main advantage of this process in contrast with deeply virtual and timelike Compton scatterings (DVCS and TCS) is the possibility of directly measuring GPDs for $x\neq\pm\xi$ at leading order in $\alpha_s$ (LO). We present a new calculation of the DDVCS amplitude based on the methods developed by R. Kleiss and W. J. Stirling in the 1980s. These techniques produce expressions for amplitudes that are perfectly suited for implementation in numerical simulations. Via the PARTONS software, the correctness of this new formulation has been tested by comparing the DVCS and TCS limits of DDVCS with independent calculations of DVCS and TCS.

Double deeply virtual Compton scattering (DDVCS) is the process where an electron scatters off a nucleon and produces a lepton pair. The main advantage of this process in contrast with deeply virtual and timelike Compton scatterings (DVCS and TCS) is the possibility of directly measuring GPDs for $x\neq\pm\xi$ at leading order in $\alpha_s$ (LO). We present a new calculation of the DDVCS amplitude based on spinor techniques which produce expressions for amplitudes that are perfectly suited for their implementation in numerical simulations. Elements of impact studies, including predictions for experiments at JLab12, JLab20+ and the Electron-Ion Collider (EIC), are studied by means of the PARTONS software and the EpIC Monte Carlo event generator.

This White Paper aims at highlighting the important benefits in the science reach of the EIC. High luminosity operation is generally desirable, as it enables producing and harvesting scientific results in a shorter time period. It becomes crucial for programs that would require many months or even years of operation at lower luminosity.

We revisit the phenomenology of the deep exclusive electroproduction of a lepton pair, i.e. double deeply virtual Compton scattering (DDVCS), in view of new experiments planned in the near future. The importance of DDVCS in the reconstruction of generalized parton distributions (GPDs) in their full kinematic domain is emphasized. Using Kleiss-Stirling spinor techniques, we provide the leading order complex amplitudes for both DDVCS and Bethe-Heithler sub-processes. Such a formulation turns out to be convenient for practical implementation in the PARTONS framework and EpIC Monte Carlo generator that we use in simulation studies.

We discuss two collider processes which combine a diffractively produced ρ meson separated by a large rapidity gap from a hard exclusive scattering of a Pomeron on a nucleon, giving rise to a lepton pair or to a second meson. These two processes probe the nucleon quark content described by generalized parton distributions in a very specific way.

We estimate kinematical higher-twist (up to twist 4) corrections to the $\gamma^*(q_1) \gamma(q_2) \to M(p_1) \bar{M}(p_2)$ amplitudes at large $Q^2=-q_1^2$ and small $s=(q_1+q_2)^2$, where $M$ is a scalar or pseudoscalar meson. This process is known to factorize at leading twist into a perturbatively calculable coefficient function and generalized distribution amplitudes (GDAs). The kinematical higher-twist contributions of order $s/Q^2$ and $m^2/Q^2$ turn out to be important in the cross section, considering the kinematics accessible at Belle and Belle II. We present numerical estimates for the cross section for $\gamma^* \gamma \to \pi^0 \pi^0$ with the $\pi \pi$ GDA extracted from Belle measurements and with the asymptotic $\pi \pi$ GDA as inputs to study the magnitude of the kinematical corrections. To see how the target mass corrections of order $m^2/Q^2$ affect the cross section, we also perform the calculation for $\gamma^* \gamma \to \eta \eta$ by using a model $\eta \eta$ GDA.In the range $s> 1$ GeV$^2$, the kinematical higher-twist corrections account for $\sim 15 \%$ of the total cross section, an effect which is not negligible. Since $\pi \pi$ GDAs are the best way to access the pion energy-momentum tensor (EMT), our study demonstrates that an accurate evaluation of EMT form factors requires the inclusion of kinematical higher-twist contributions.

We develop the analysis of diphoton exclusive photoproduction in the kinematics where a collinear QCD factorization framework applies, namely nearly forward large invariant mass diphoton production. We work at the leading twist level and at the next-to-leading order (NLO) in the strong coupling constant alpha(S). We compare our predictions for cross sections with Born order calculations for the experimental conditions accessible to JLab experiments and show the interesting sensitivity of our results to various models of generalized parton distributions (GPDs). The NLO corrections are rather large and negative but do not prevent the studied reaction from being a promising tool for the extraction of C-odd GPDs, which do not contribute to either spacelike or timelike deeply virtual Compton scattering amplitudes.

Exclusive electro-weak processes have peculiar features which make them complementary to usually discussed deeply virtual electroproduction processes such as deep virtual Compton scattering or meson production (and the corresponding crossed reactions). They allow in particular single charmed meson production, which we study in two different contexts : electroproduction at an electron ion collider and neutrino-production at a medium energy neutrino facility. We rely on the QCD collinear factorization framework where generalized parton distributions allow physicists to perform a nucleon tomography.

Deeply virtual Compton scattering (DVCS) and timelike Compton scattering (TCS) leading twist amplitudes are intimately related thanks to their analytic properties as a function of $Q^2$. We exploit this feature to use Compton form factors previously extracted from available DVCS data and derive data-driven predictions for TCS observables to be measured in near future experiments. Our results quantitatively illustrate the complementarity of DVCS and TCS experiments.