Near-Threshold J/$ψ\to μ^+μ^-$ Photoproduction and the Gluonic Gravitational Form Factors of the Proton

This paper reports the measurement of near-threshold $J/\psi \to \mu^+\mu^-$ photoproduction cross sections from the J/$\psi$-007 experiment at Jefferson Lab, which, when combined with electron decay data and analyzed via Holographic QCD, yields precise constraints on the proton's gluonic gravitational form factor $\mathcal{C}_g(t)$ that agree with lattice QCD calculations and support a spatial picture of gluon dominance at larger radii with confining inward pressure.

The Gist

Imagine the proton not as a tiny, solid marble, but as a bustling, invisible city made of energy. Inside this city, there are two main groups of workers: quarks (the heavy-duty construction crews) and gluons (the super-fast delivery trucks and the glue holding everything together).

For a long time, scientists have known that gluons are responsible for most of the proton's mass. But a big mystery remained: How do these gluons push and pull to keep the proton from falling apart? Do they act like a spring pushing outward, or a vacuum sucking inward?

This paper is like a new, high-resolution X-ray that finally lets us see the "mechanical blueprint" of this invisible city. Here is the story of how they did it, explained simply.

1. The Experiment: Catching a Ghost with a New Net

The scientists at Jefferson Lab wanted to study the proton by firing high-energy photons (packets of light) at it. When a photon hits a proton, it can sometimes knock out a heavy particle called a J/ψ (pronounced "J-psi").

Think of the J/ψ as a special "messenger" that only appears when the photon hits the gluons just right. Once created, this messenger immediately decays (breaks apart) into two smaller particles.

• The Old Way: In a previous experiment, they looked for the messenger breaking into electrons (like finding a pair of tiny, fast mice).
• The New Way: In this paper, they looked for the messenger breaking into muons (like finding a pair of slightly heavier, but very similar, mice).

By adding the muon data to the old electron data, they doubled their sample size. It's like going from taking a blurry photo of a crowd to taking a high-definition video of the whole event. This gave them much better statistics to work with.

2. The Big Question: Is There an "Open Door"?

Before they could map the proton, they had to make sure they weren't looking at something else. There was a worry that at these energy levels, the proton might be "opening the door" to a different kind of particle production called open charm (creating new, heavy particles that aren't the J/ψ).

If this were happening, it would be like trying to map the interior of a house, but realizing there's a secret tunnel to a different building nearby. That would mess up the map.

• The Result: They checked their data very carefully. They found no evidence of this "open door." The proton stayed closed, and they were looking at exactly what they thought they were: pure J/ψ production. This confirmed their map would be accurate.

3. The Discovery: The Gluonic "Pressure Map"

Now that they had clean data, they used a sophisticated mathematical tool (called Holographic QCD) to translate the collision data into a picture of forces.

They were looking for something called the Gravitational Form Factor. Don't let the name scare you; it doesn't mean they are studying black holes. In this context, "gravitational" just means they are measuring how the proton responds to forces, similar to how gravity pulls on mass.

They mapped out the pressure inside the proton:

• The Quarks: Near the very center of the proton (the "city center"), the quarks are dominant. They create a pressure that pushes outward, like a balloon trying to expand.
• The Gluons: As you move further out from the center (the "suburbs" of the proton), the gluons take over. But here is the twist: instead of pushing out, the gluons create a massive inward pressure.

The Analogy: The Cosmic Spring

Imagine the proton is a giant, invisible spring.

• The quarks in the middle are trying to push the spring apart (expansion).
• The gluons on the outside are acting like a tight rubber band, squeezing the spring inward (confinement).

The paper confirms that the gluons are the "glue" in the truest sense. They provide the crushing inward force that keeps the quarks from flying apart. Without this inward pressure from the gluons, the proton would explode.

Why Does This Matter?

This is the first time scientists have measured this specific "gluon pressure" with such precision.

1. It matches the theory: Their experimental map looks almost identical to predictions made by "Lattice QCD," which is a super-computer simulation of the universe's rules. This proves our understanding of how the strong force works is correct.
2. It explains the mass: It shows us exactly where the mass and the holding force come from. It's not just a blob of stuff; it's a dynamic balance between outward push and inward squeeze.

The Bottom Line

This paper is a major step forward in understanding the "mechanics" of matter. By catching more particles (muons) and combining them with old data, the scientists have drawn a clearer picture of the proton's internal engine. They confirmed that gluons are the heavy lifters that squeeze the proton together, holding the universe's building blocks in place.

It's like finally seeing the blueprint of a skyscraper and realizing that the steel beams (gluons) on the outside are doing the heavy lifting to keep the whole structure from collapsing.

Technical Summary

1. Problem Statement and Motivation

The internal structure and mass of the proton are predominantly determined by gluon dynamics within Quantum Chromodynamics (QCD). A critical tool for probing the mechanical properties of the proton (such as mass distribution and internal forces) is the Gluonic Gravitational Form Factor (GFF).

• Context: Near-threshold $J/\psi$ photoproduction is a unique process sensitive to these gluonic GFFs.
• Previous Work: The J/ψ–007 experiment previously measured this process using the electron decay channel ($J/\psi \to e^+e^-$), providing the first high-resolution 2D cross-section data.
• Open Questions:
  1. Open Charm Contamination: Recent GlueX data suggested fluctuations near the threshold (around 9.5 GeV) that might indicate contributions from open-charm production (e.g., $\bar{D}^*\Lambda_c$). Such contributions would complicate the extraction of pure $J/\psi$ GFFs.
  2. Statistical Limitations: The existing data had limited statistics, restricting the precision of GFF extraction.
  3. Decay Channel Validation: It was necessary to verify that the muon decay channel ($J/\psi \to \mu^+\mu^-$) yields consistent results with the electron channel to double the available statistics.

2. Methodology

The study utilized data from the J/ψ–007 experiment conducted in 2019 at the Thomas Jefferson National Accelerator Facility (Jefferson Lab) in Hall C.

• Experimental Setup:

  • Beam: High-intensity electron beam incident on a copper radiator to produce bremsstrahlung photons.
  • Target: Liquid hydrogen target.
  • Detection: Exclusive $J/\psi$ events were detected using the High Momentum Spectrometer (HMS) and Super High Momentum Spectrometer (SHMS).
  • Kinematics: Four kinematic settings provided 2D coverage in photon energy ($E_\gamma$) and momentum transfer ($t$) near the threshold (9.1–10.6 GeV).

• Analysis Strategy:

  • Muon Selection: Unlike the electron channel, muon detection in Hall C is challenging. The analysis relied on the longitudinal segmentation of electromagnetic calorimeters to identify Minimum Ionizing Particles (MIPs). Coincident MIP signals in both spectrometers were required.
  • Background Subtraction: The primary background consisted of $\pi^+\pi^-$ pairs mimicking MIPs. This was subtracted by selecting di-pion events where at least one pion showered in the calorimeter and normalizing to the signal sidebands.
  • Efficiency Corrections: Corrections were applied for trigger electronics, live-time, tracking, and Particle Identification (PID). The PID efficiency for di-muons was determined to be $90.5\% \pm 1.8\%$.
  • Unfolding: Detector effects and acceptance were corrected using an iterative unfolding procedure validated by Monte Carlo simulations (using the lAger generator and SIMC).

• Theoretical Framework:

  • Holographic QCD (hQCD): The primary extraction method modeled the photoproduction via graviton and dilaton exchanges in Anti-de Sitter space.
  • Generalized Parton Distributions (GPD): An alternative approach was attempted but found to be poorly constrained due to a lack of precise measurements at high $t$.
  • Fit Shapes: A dipole shape was used for the form factor $A_g(t)$ and a tripole shape for $C_g(t)$.

3. Key Contributions

1. First Muon Channel Measurement: This paper reports the first measurement of near-threshold $J/\psi \to \mu^+\mu^-$ photoproduction, effectively doubling the statistics available from the J/ψ–007 experiment.
2. Validation of Decay Channels: The study confirms that the muon channel results are statistically consistent with the previously published electron channel results, validating the use of both channels for combined analysis.
3. Exclusion of Open Charm: By integrating the combined data and analyzing the cross-section as a function of photon energy, the authors found no evidence for the threshold cusps or fluctuations associated with open-charm production, resolving a discrepancy suggested by other datasets.
4. Improved GFF Constraints: The combined dataset allowed for a more precise extraction of the gluonic gravitational form factor $C_g(t)$, which is directly related to the internal pressure and shear forces of the proton.

4. Results

• Cross-Section Consistency: The differential cross-section measurements ($d\sigma/dt$) for the muon channel agree with the electron channel within statistical uncertainties across ten photon energy slices.
• Integrated Cross Section: The integrated cross-section as a function of $E_\gamma$ shows a smooth behavior consistent with GlueX and Cornell data but lacks the fluctuations near 9.5 GeV that would imply significant open-charm contributions.
• Gluonic Gravitational Form Factors ($C_g(t)$):
  • The combined data yielded a $\chi^2$ per degree of freedom close to unity for the hQCD fit.
  • The extracted $C_g(t)$ agrees with recent Lattice QCD calculations.
• Spatial Pressure Distribution:
  • Using the extracted $C_g(t)$, the authors calculated the gluonic pressure distribution in the Breit frame.
  • Key Finding: The results support a spatial picture where quarks dominate at small radii, while gluons dominate at larger radii.
  • Confining Pressure: The gluon distribution exhibits a strong inward (confining) pressure, balancing the outward pressure from quarks.

5. Significance

• Proton Structure: This work provides the most precise experimental constraints to date on the gluonic mechanical properties of the proton. It confirms the theoretical prediction that gluons are responsible for the confining force at larger radii within the proton.
• Methodological Benchmark: The agreement between experimental data (muon and electron channels) and Lattice QCD predictions validates both the experimental techniques and the theoretical frameworks (hQCD and Lattice) used to interpret proton structure.
• Future Impact: These results serve as a crucial input for future high-statistics measurements at Jefferson Lab (SoLID–J/ψ) and the Electron-Ion Collider (EIC), which aim to reduce model uncertainties and achieve a complete understanding of the proton's mechanical structure.

In summary, this paper successfully doubles the statistical power of near-threshold $J/\psi$ photoproduction data, rules out significant open-charm contamination in the threshold region, and provides robust experimental evidence for the spatial distribution of gluonic pressure inside the proton, aligning closely with Lattice QCD predictions.