⚛️ phenomenology

Nucleon Stron-Interactions Size From Charmonium Photoproduction

By combining recent high-precision near-threshold $J/\psi$ photoproduction data from Jefferson Lab with quark-sector results, the study reveals that the nucleon's overall strong-interaction spatial extent, which governs mass generation, is approximately $0.94\pm 0.09$ fm and extends beyond its electromagnetic charge and mass distributions.

Original authors: Xiangdong Ji, Sylvester Joosten, Zein-Eddine Meziani, Dimitra A. Pefkou

Published 2026-09-10

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CC BY 4.0

Original authors: Xiangdong Ji, Sylvester Joosten, Zein-Eddine Meziani, Dimitra A. Pefkou

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

For decades, scientists have known the proton is not a solid, indivisible marble, but a bustling city of smaller particles called quarks and gluons. To understand the size of this city, researchers have long relied on a specific kind of map: the electric charge. By bouncing electrons off protons, they have measured how the electric charge is spread out, finding a radius of about 0.84 femtometers. However, this map is incomplete. The proton is held together not by electricity, but by the strong force, a powerful interaction carried by gluons that are electrically neutral. Because these gluons do not carry charge, the traditional electric map misses a vast portion of the proton's true structure. Just as a building's footprint might be defined by its outer walls rather than its electrical wiring, the proton's true physical size is likely defined by the reach of this strong force, a question that has remained difficult to answer because the tools to measure it have been elusive.

A team of researchers has now taken a significant step toward solving this puzzle by using a unique probe to peer inside the proton's strong-force landscape. They focused on a specific particle called the J/psi, which is a compact pair of a charm quark and its antimatter twin. This particle acts like a tiny, dense magnet that is sensitive only to the gluons inside the proton, ignoring the electric charge entirely. By firing high-energy beams of light at protons at the Jefferson Lab in Virginia, the team created these J/psi particles just barely enough to exist, a condition known as near-threshold production. This delicate process allowed them to measure how the proton's internal gluon field responds without destroying the target, providing a direct glimpse into the spatial distribution of the force that gives the proton its mass.

The researchers combined these new, high-precision measurements with existing data and advanced theoretical models to reconstruct the shape of the proton's internal "stress-energy" field. This field describes how the energy and pressure of the gluons are distributed in space. By analyzing this distribution, they were able to calculate the radius of the proton as defined by the strong interaction. Their findings reveal that the proton is larger than previously thought when measured by its electric charge. The strong-interaction size extends to a radius of 0.94 femtometers, with an uncertainty of 0.09 femtometers. This result suggests that the force holding the proton together reaches further out than the electric charge does, creating a kind of "skin" of strong force that surrounds the core of charged particles.

This discovery helps resolve a long-standing mystery about why the proton and its partner, the neutron, have nearly identical masses and strong-force properties despite having very different electric charges. The neutron, for instance, has a net electric charge of zero, making its electric radius difficult to define, yet it is bound by the same strong force as the proton. The study indicates that both particles share a similar overall spatial extent when viewed through the lens of the strong interaction, confirming that the gluon field is the true architect of the nucleon's size. The researchers note that while their current measurement is the most comprehensive to date, it is still limited by statistical uncertainties and the specific models used to interpret the data. They anticipate that future experiments with even more powerful detectors will refine this number, potentially improving the precision by a factor of ten.

The work also highlights a fundamental difference between how mass is generated in the strong force versus the electroweak force. In the strong force, the mass of the proton arises largely from the energy of the gluon field itself, a phenomenon driven by quantum fluctuations that create a scale of interaction. This is distinct from the way other particles get their mass from the Higgs field. By mapping out the distribution of this gluon energy, the team has effectively measured the physical boundary of the proton as it exists in nature, rather than just its electrical boundary. The result is a clearer, more complete picture of the building blocks of matter, showing that the proton is a larger, more complex object than its electric signature alone would suggest.

Technical Summary: Nucleon Strong-Interaction Size From Charmonium Photoproduction

Problem Statement
The spatial extent of the nucleon (proton and neutron) is traditionally defined by its electric charge radius, measured via electromagnetic probes. However, this metric fails to capture the nucleon's true size as a strongly interacting system of quarks and gluons. While protons and neutrons share nearly identical masses and strong-force properties, their charge radii differ significantly (the neutron's is nearly zero due to charge cancellation). Consequently, the electromagnetic radius is an inadequate measure of the nucleon's overall spatial extent. A "strong-interaction microscope" is required to probe the internal color (gluonic) field, which governs the nucleon's mass, spin, and energy distribution. Specifically, the paper addresses the challenge of determining the nucleon's size based on the distribution of the scalar color field ( $G^2$ ), which arises from the QCD trace anomaly and is responsible for the majority of the nucleon's mass.

Methodology
The authors employ a multi-step approach combining experimental data analysis with theoretical frameworks:

Experimental Probe: The study utilizes high-precision measurements of near-threshold $J/\psi$ photoproduction off the proton, conducted at the 12-GeV Jefferson Lab. The $J/\psi$ particle, a compact charm-anticharm color dipole, serves as an ideal probe for gluon distributions.
Theoretical Framework: The analysis is conducted within the holographic QCD framework. In this model, the near-threshold production amplitude is related to the gluonic stress-energy tensor (SET) form factors via the exchange of gluonic modes.
Form Factor Extraction:
- The study focuses on extracting the gluonic SET form factors $A_g(t)$ and $C_g(t)$ (where $t$ is the squared momentum transfer). The form factor $B_g(t)$ is neglected as it is found to be small.
- A global fit of available differential cross-section data is performed. The form factors are modeled as a dipole ( $A_g$ ) and a tripole ( $C_g$ ) function, consistent with perturbative QCD behavior at large momentum transfer.
- The authors assume $B_g(t) = 0$ , consistent with lattice QCD calculations.
Integration with Quark Sector: To determine the total properties of the nucleon, the extracted gluon form factors are combined with recent global Bayesian extractions of the quark sector form factors ( $A_q, B_q, C_q$ ) derived from experimental and lattice QCD data.
Definition of Radii: Using the total SET form factors ( $A = A_q + A_g$ , $C = C_q + C_g$ ), the authors define the scalar color field radius ( $r_s$ ) and the mass radius ( $r_m$ ) in the Breit frame. These are derived from the derivatives of the form factors at $t=0$ and the value of $C(0)$ .

Key Contributions

Global Data Synthesis: The paper presents a comprehensive global analysis of world data on near-threshold $J/\psi$ photoproduction, overcoming limitations of previous studies that were restricted by specific model ranges or partial datasets.
Indirect Measurement of Scalar Field: The work establishes a rigorous connection between the measurable gluonic SET form factors and the scalar color field distribution ( $G^2$ ) via the energy-momentum conservation law and the trace anomaly. This allows for the indirect determination of the scalar color field radius, a quantity previously difficult to access directly.
Unified Nucleon Size Definition: By combining gluon and quark contributions, the study provides a unified definition of the nucleon's strong-interaction size, distinct from its electromagnetic size.

Results

Strong-Interaction Radius: The analysis yields a strong-interaction (scalar) radius for the nucleon of $0.94 \pm 0.09$ fm.
Comparison with Other Radii: This value is larger than both the proton's electric charge radius ( $\approx 0.84$ fm) and its mass radius.
Density Profiles: The derived scalar and mass energy density profiles in the Breit frame show that the scalar color field extends further than the charge distribution.
The "Scalar Skin": The difference between the square root of the mean square scalar radius and the charge radius indicates the existence of a "scalar color-field skin," analogous to the neutron skin in heavy nuclei. This highlights that the gluonic field defines the outer boundary of the nucleon's strong interaction.
Model Stability: The result remains stable even when specific datasets (such as the lowest-energy GlueX bin) are excluded, suggesting robustness against statistical fluctuations.

Significance and Claims
The paper claims to provide the first comprehensive study of the nucleon's strong-interaction radius derived from a proper experimental probe ( $J/\psi$ photoproduction) combined with theoretical constraints.

Physical Insight: The finding confirms that the nucleon's overall spatial extent is governed by the scalar color field generated by the QCD trace anomaly, rather than just the distribution of electric charge or mass. This validates phenomenological expectations from bag models where a scalar potential confines quarks.
Precision and Future: While the current result ( $0.94 \pm 0.09$ fm) is limited by statistical and model uncertainties, it achieves accuracy comparable to lattice QCD and other theoretical analyses. The authors anticipate that future high-precision experiments at Jefferson Lab (using the SoLID detector) and the Electron-Ion Collider (using the ePIC detector) will improve the precision of this determination by up to an order of magnitude.
Modesty: The authors acknowledge that the interpretation relies on the holographic QCD framework and that alternative production mechanisms (e.g., open-charm intermediate states) exist, though the current framework provides a consistent extraction of the gluonic form factors. The result is presented as a significant step toward a precise definition of the nucleon's size in the context of the strong force.

Technical Summary: Nucleon Strong-Interaction Size From Charmonium Photoproduction

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