2025 EIC-France Workshop: Physics Highlights and Perspectives

This report synthesizes the outcomes of the 2025 EIC-France Workshop, outlining theoretical advancements and strategic priorities for the French hadron-physics community, with a specific focus on immediate opportunities in inclusive diffraction and quarkonium production alongside longer-term goals in pion structure and exclusive three-body final states.

The Gist

Imagine the Electron-Ion Collider (EIC) as the world's most powerful "3D camera" for the subatomic world. Its job is to take incredibly sharp pictures of protons and atomic nuclei to see how they are built from the inside out.

This document is a report from a meeting of French physicists who are getting ready to use this camera. They are figuring out exactly what to photograph first, what to save for later, and how to make sure their French team is ready to lead the way.

Here is a breakdown of their plan, using simple analogies:

1. The Big Picture: The "Construction Site"

Think of the EIC as a massive construction site that is just opening its gates.

• The Early Years (Years 1–3): The site isn't fully built yet. The cranes are smaller, and the lighting isn't perfect. But, the French team says, "We don't need the whole building finished to start doing great work!" They have a plan to use the early, simpler conditions to get some amazing first shots.
• The Later Years (Years 4+): Once the machine is fully upgraded and running at full power, they will tackle the most difficult, high-definition projects.

2. The "Must-Do" Early Projects (The Highlights)

The French team identified two specific things they want to photograph right away because they are perfect for the early camera settings and match their team's special skills.

A. Inclusive Diffraction: The "Ghostly Pass-Through"

• The Analogy: Imagine throwing a ball at a wall. Usually, it bounces back or breaks the wall. But in "diffraction," the ball passes right through the wall, leaving the wall completely intact, and a giant empty space (a "rapidity gap") appears between the ball and the wall.
• Why it matters: This is a rare trick of nature that happens when the "glue" holding the wall together (gluons) is so thick and crowded that it acts like a single, solid sheet.
• The Goal: By studying this "ghostly pass-through," the French team wants to prove that at very high speeds, protons and nuclei become so dense with gluons that they form a new state of matter called the Color Glass Condensate. It's like seeing if a crowd of people can suddenly turn into a solid wall just by running fast enough.

B. Inclusive Quarkonium: The "Heavyweight Hunters"

• The Analogy: Think of a proton as a busy city. Inside, there are tiny, heavy "VIPs" called quarkonia (heavy particles like the J/ψ). These VIPs are hard to make because they are heavy.
• Why it matters: Making these heavy VIPs requires a lot of energy and a lot of "glue" (gluons). By counting how many of these heavy VIPs appear, the physicists can map out exactly how much "glue" is in the city.
• The Goal: This helps them understand the "traffic" of gluons inside the nucleus. It's like counting how many heavy trucks are on a highway to figure out how congested the road is. This is crucial for understanding how the heavy particles in the universe are formed.

3. The "Dream Projects" (Long-Term Goals)

Once the EIC is fully upgraded and the "camera" is super sharp, the French team wants to tackle two even harder challenges.

A. The Sullivan Process: The "Pion Proxy"

• The Analogy: Imagine you want to take a photo of a pion (a tiny particle), but you can't get a camera close enough to it because it's too small and unstable. However, you notice that a proton (a larger particle) is wearing a "pion hat" (a cloud of pions) on its head.
• The Strategy: Instead of trying to photograph the pion directly, the team will shoot the proton, but aim specifically at the "pion hat." By analyzing how the light scatters off the hat, they can reconstruct a 3D image of the pion itself.
• The Goal: This will finally let us see the internal 3D structure of the pion, which is a fundamental building block of matter that we haven't been able to map in 3D before.

B. Exclusive Three-Body Final States: The "Complex Dance"

• The Analogy: Most physics experiments look at a collision where two things hit and two things fly out (like a billiard ball hitting another). This project is about a three-body dance: A photon hits a proton, and three things fly out (a proton and two new particles).
• The Goal: This is a much more complex dance. By watching how these three particles move and spin, the team can map out the "twist" and "turn" of the particles inside the proton. It's like trying to understand the choreography of a dance troupe by watching the shadows they cast. This helps explain how the fundamental parts of matter stick together to form the solid world we see.

4. Why This Matters

The French physicists are saying, "We have the right tools, the right maps, and the right team."

• Short term: They will use the early EIC to prove that gluons get crowded (saturation) and to map the "glue" inside nuclei.
• Long term: They will use the full power of the machine to see the 3D shape of the pion and the complex dances of particles.

In a nutshell: This report is a roadmap. It tells us that the French team is ready to use the new EIC microscope to take the first clear pictures of how the universe's "glue" works, starting with the easiest shots and saving the most complex masterpieces for when the machine is fully ready.

Technical Summary

1. Problem and Context

The paper addresses the strategic preparation of the French hadron-physics community for the upcoming Electron–Ion Collider (EIC). While the EIC is designed to revolutionize the understanding of Quantum Chromodynamics (QCD), specifically regarding the 3D structure of hadrons, gluon saturation, and the proton spin, there is a need to prioritize physics goals for the early operational phase versus long-term goals.

The core challenges identified include:

• Optimizing Early Science: Determining which measurements can be performed immediately upon the EIC's commissioning (Years 1–3) given specific beam species, energies, and luminosities, before the machine reaches full design capabilities.
• Theoretical Precision: Bridging the gap between experimental observables and theoretical frameworks (e.g., Color Glass Condensate, Generalized Parton Distributions) to extract fundamental QCD parameters with Next-to-Leading Order (NLO) precision.
• Community Coordination: Aligning French theoretical expertise (small-$x$ physics, quarkonium, GPDs) with the EIC's technical capabilities to maximize scientific impact.

2. Methodology

The document is a synthesis report based on the 2nd EIC-France Workshop held in December 2025. The methodology involved:

• Workshop Synthesis: Aggregating presentations and discussions from theorists, phenomenologists, and instrumentation specialists from French institutions (e.g., IJCLab, CEA, IP Paris) and international partners.
• Scenario Analysis: Utilizing the EIC Early Science Matrix (Table 1) to map specific physics channels against projected beam configurations (e.g., $e+p$, $e+D$, $e+Au$) and integrated luminosities (ranging from $0.9$ to $13.1 \text{ fb}^{-1}$ in early years).
• Theoretical Frameworks: Evaluating physics channels using established QCD frameworks:
  • Collinear Factorization: For inclusive and semi-inclusive processes.
  • Color Glass Condensate (CGC): For small-$x$ dynamics and gluon saturation.
  • Generalized Parton Distributions (GPDs) & Transverse Momentum Dependent (TMD) distributions: For 3D hadron structure.
  • Non-perturbative Models: Including the Sullivan process for pion structure.
• Simulation and Prediction: Using tools like ePIC (simulation framework) and HELAC-Onia to predict cross-sections, event rates, and statistical significance for specific channels (e.g., $J/\psi$ production, diffractive structure functions).

3. Key Contributions

The paper categorizes the French community's contributions into Early Physics Priorities and Longer-Term Opportunities.

A. Early Physics Priorities (Years 1–3)

Two specific measurements were identified as high-priority targets due to their clean signatures, theoretical robustness, and alignment with French expertise:

1. Inclusive Diffraction:
   • Goal: Probe gluon saturation and non-linear QCD dynamics.
   • Mechanism: Measuring the diffractive structure function $F_2^D$ where the target remains intact or dissociates into a low-mass system, separated by a large rapidity gap.
   • Significance: This is the first facility to measure inclusive diffraction on nuclei. It tests the CGC framework by looking for the enhancement of diffraction in nuclei versus protons (geometric scaling) and mapping the transition between dilute and dense QCD regimes.
2. Inclusive Quarkonium Production:
   • Goal: Constrain nuclear gluon distributions and heavy-quark dynamics.
   • Mechanism: Measuring inclusive photoproduction of $J/\psi$, $\Upsilon$, and associated channels (e.g., $J/\psi + c$).
   • Significance: Dominated by photon-gluon fusion, these measurements provide direct sensitivity to the gluon PDF at small $x$. They allow for the separation of prompt vs. non-prompt yields and the potential first observation of C-even states ($\eta_c, \chi_c$) and intrinsic charm.

B. Longer-Term Physics Opportunities

These goals require full detector performance and higher luminosity (Years 4+):

1. Pion Structure via the Sullivan Process:
   • Mechanism: Electron scattering off the pion cloud of the nucleon (pion exchange) to treat the pion as a virtual target.
   • Goal: Perform Deeply Virtual Compton Scattering (DVCS) off virtual pions to extract 3D GPDs of the pion.
   • Key Prediction: A predicted sign inversion of the beam-spin asymmetry at low $Q^2$, driven by gluon dominance, serving as a signature of gluon-led dynamics in the pion.
2. Exclusive Three-Body Final States:
   • Mechanism: Processes like $\gamma N \to N' P_1 P_2$ (e.g., $\rho\rho$, $\pi\gamma$ production).
   • Goal: Access both chiral-even and chiral-odd GPDs and study factorization breaking effects (e.g., Glauber gluon exchanges in $\pi^0\gamma$ production).
   • Significance: These processes offer richer kinematics than standard DVCS, allowing for better mapping of the $x$-dependence of GPDs.

4. Results and Projections

• Luminosity Impact: The projected early luminosities (up to $\sim 13 \text{ fb}^{-1}$ for $e+D$) already exceed the total integrated luminosity of the entire HERA operational lifetime within a single year.
• Quarkonium Reach: With $10 \text{ fb}^{-1}$, the EIC can measure prompt $J/\psi$ photoproduction up to $p_T > 10 \text{ GeV}$, surpassing HERA limits. The associated production of $J/\psi + c$ is predicted to be measurable up to $p_T \approx 8 \text{ GeV}$, offering unique constraints on intrinsic charm.
• Diffraction Signatures: Theoretical models predict a distinct enhancement in the ratio of diffractive structure functions ($F_2^D$) for nuclei compared to protons, which will serve as a decisive test for the Color Glass Condensate.
• Event Rates: For exclusive three-body states (e.g., $\rho^0\rho^0$), simulations predict event counts up to $10^6$ in early years, providing sufficient statistics for multidimensional measurements.

5. Significance

This report serves as a strategic roadmap for the French contribution to the EIC. Its significance lies in:

• Strategic Alignment: It successfully identifies physics channels that leverage existing French theoretical strengths (small-$x$, saturation, heavy flavor, GPDs) while addressing the most critical open questions in QCD.
• Scientific Readiness: It demonstrates that the French community is prepared to lead in developing predictive frameworks, simulation tools, and analysis strategies for the EIC's early science phase.
• QCD Advancement: By prioritizing gluon saturation (via diffraction) and gluon density mapping (via quarkonia), the proposed program directly targets the transition from linear to non-linear QCD.
• Future Vision: The identification of the Sullivan process and three-body final states outlines a path toward a complete 3D tomography of hadrons (protons and pions), bridging the gap between perturbative partonic descriptions and non-perturbative hadronic structure.

In conclusion, the paper establishes that the French hadron-physics community is poised to play a leading role in the EIC physics program, with a clear, phased strategy moving from immediate, high-impact measurements of gluon dynamics to long-term, transformative studies of hadron structure.