Measurement of the near-threshold J$/ψ$ photoproduction cross section with the CLAS12 experiment

This paper presents measurements of near-threshold J/$\psi$ photoproduction cross sections using the CLAS12 detector at Jefferson Lab, providing new experimental constraints on QCD models regarding the proton's gluonic structure and hadronic mass generation.

The Gist

Imagine the proton, the tiny particle at the heart of every atom in your body, not as a solid marble, but as a bustling, chaotic city. Inside this city, there are three main residents (quarks) who are well-known, but the city is actually held together by a massive, invisible cloud of "glue" (gluons) that zips around at the speed of light.

For a long time, scientists could see the residents, but the "glue" was a mystery. We knew it was there, but we couldn't map out exactly how it was distributed or how much "weight" it carried.

This paper is like a team of high-tech detectives (the CLAS12 collaboration) who decided to take a "X-ray" of this proton city to see the glue in action. Here is how they did it, explained simply:

1. The Experiment: A High-Speed Collision

To see the glue, you can't just look at the proton; you have to hit it hard enough to make it reveal its secrets.

• The Weapon: They used a massive particle accelerator at Jefferson Lab (JLab) to fire a beam of electrons at a target of liquid hydrogen (which is just protons).
• The Trick: When these fast electrons fly past the protons, they sometimes spit out a super-energetic photon (a particle of light). This photon then smashes into the proton.
• The Goal: The scientists wanted to create a very specific, heavy particle called a $J/\psi$ (pronounced "J-psi"). Think of the $J/\psi$ as a "heavy gold coin." It's so heavy that it can only be made if the incoming photon hits the proton with just the right amount of energy—specifically, enough energy to tap into that invisible "glue" cloud.

2. The Detective Work: Catching the Evidence

When the photon hits the proton, it creates the $J/\psi$ and knocks the proton backward. The $J/\psi$ is unstable and immediately splits apart into two lighter particles: an electron and a positron (its antimatter twin).

The CLAS12 detector is like a giant, 360-degree camera that takes a snapshot of this explosion.

• The Challenge: The $J/\psi$ is rare. For every million collisions, you might only get one. Plus, there is a lot of "noise" (other particles flying around) that looks like the real thing.
• The Solution: The team used a super-smart computer algorithm (a "Boosted Decision Tree") to filter out the noise. It's like a bouncer at a club who checks IDs so strictly that only the real $J/\psi$ guests get in, while the impostors (pions and other particles) are turned away.

3. The Discovery: Mapping the "Glue"

Once they caught enough $J/\psi$ particles, they started measuring two things:

1. How often it happened: They counted how many $J/\psi$ particles were made at different energy levels.
2. Where they went: They measured the angle at which the particles flew out.

Why does this matter?
The way the $J/\psi$ flies out depends on the "shape" of the glue inside the proton.

• The Analogy: Imagine throwing a ball at a cloud. If the cloud is dense in the middle and thin on the edges, the ball bounces off differently than if the cloud is a hollow shell. By measuring the angles of the $J/\psi$, the scientists could map out the density of the glue.

4. The Big Reveal: The Proton's "Mass Radius"

The most exciting result is that they calculated the mass radius of the proton.

• The Charge Radius: We already knew the "charge radius" (how big the proton is based on its electric charge). It's about 0.84 femtometers (a femtometer is a quadrillionth of a meter).
• The Mass Radius: This new measurement tells us how big the proton is based on where its mass (weight) is located.
• The Result: They found the mass radius is actually smaller (about 0.5 femtometers) than the charge radius!

What does this mean?
It means the "glue" that holds the proton together and gives it most of its weight is packed into a tighter, denser core than the electric charge. It's like finding out that while a city's streetlights (charge) are spread out over a wide area, the actual heavy buildings and people (mass) are packed into a tiny, dense downtown district.

5. Why Should You Care?

This isn't just about tiny particles; it's about understanding the universe.

• Where does mass come from? The atoms in your body get 99% of their mass from the energy of this gluon glue, not from the weight of the quarks themselves. This experiment helps us understand the origin of mass.
• The "Gravitational" Map: They also mapped out the "Gravitational Form Factors." Even though protons are too small to have gravity we can feel, they do have a gravitational structure. This map tells us how the pressure and shear forces are distributed inside the proton, essentially showing us the "stress points" of the universe's building blocks.

Summary

In short, this paper is a successful "X-ray" of the proton's interior. By smashing particles together and using a giant detector to catch the rare debris, the scientists proved that the "glue" holding our universe together is packed into a surprisingly small, dense core. It's a crucial step in understanding why matter has weight and how the strong force builds the world around us.

Technical Summary

1. Problem and Motivation

The photoproduction of heavy vector mesons, specifically the $J/\psi$, is a critical process for probing the gluon content of nucleons. While exclusive $J/\psi$ photoproduction has been measured at high energies (HERA, LHC) and previously at JLab (GlueX, J/$\psi$-007), measurements near the production threshold are essential for several reasons:

• Non-perturbative QCD: Near-threshold interactions are dominated by non-perturbative strong interactions, offering a unique window into the mechanism of hadronic mass generation.
• Gluon Gravitational Form Factors (GFFs): The $t$-dependence (momentum transfer squared) of the cross section is theoretically linked to the proton's gluon GFFs ($A_g(t)$ and $C_g(t)$), which encode the distribution of mass, angular momentum, and internal pressure/shear forces within the proton.
• Reaction Mechanisms: There is ongoing debate regarding the contribution of open-charm intermediate states (e.g., $\Lambda_c D$ thresholds) and potential pentaquark contributions. Previous data (GlueX) suggested a dip in the cross section near 9 GeV, potentially indicating open-charm effects, but higher precision data was needed to confirm or refute this.

2. Methodology

The study utilized data collected by the CLAS12 detector at the Thomas Jefferson National Accelerator Facility (JLab) during the Fall 2018 and Spring 2019 running periods (Run Group A).

• Experimental Setup:

  • Beam: Continuous electron beams with energies of 10.6 GeV (Fall 2018) and 10.2 GeV (Spring 2019).
  • Target: Liquid hydrogen target (5 cm length).
  • Reaction: The process $ep \to e' \gamma p \to e' J/\psi p' \to e' e^+ e^- p'$ was identified. Since CLAS12 does not have a dedicated photon beam, the "photoproduction" regime was selected by identifying events where the scattered electron ($e'$) was undetected (small angle) and the virtuality of the photon ($Q^2$) was low.
  • Detector: Only the Forward Detector (FD) was used. Charged tracks were reconstructed via the Drift Chamber (DC); electrons/positrons were identified using the High Threshold Cherenkov Counter (HTCC) and Electromagnetic Calorimeter (ECAL); protons were identified via Time-of-Flight (FTOF).

• Analysis Procedure:

  • Particle Identification (PID): A Boosted Decision Tree (BDT) algorithm was developed to distinguish leptons from charged pions at momenta $> 4.9$ GeV, where HTCC discrimination fails.
  • Event Selection: Events were selected requiring exactly one proton, one positron, and one electron in the FD. Exclusivity cuts were applied on the missing mass squared ($|M_X^2| < 0.4$ GeV$^2$) and photon virtuality ($Q^2 < 0.5$ GeV$^2$).
  • Background Modeling:
    • Bethe-Heitler (BH) Continuum: Modeled using Monte Carlo (MC) generators (GRAPE, TCSGen).
    • Incoherent Background: A "mixed-event" technique was employed, combining particles from different events and reweighting them using a BDT to match the kinematic distributions of real data.
  • Yield Extraction: The $J/\psi$ signal was extracted by fitting the $e^+e^-$ invariant mass spectrum with a Gaussian signal and an exponential background.
  • Corrections: Cross sections were corrected for detector acceptance (via MC), radiative effects, and efficiency discrepancies between data and simulation (using a factor $\omega_c \approx 0.77$).

3. Key Contributions

• New Kinematic Coverage: Provided simultaneous measurements of total and differential cross sections in the near-threshold region (photon energies $E_\gamma$ from $\sim 8.2$ to $10.6$ GeV), complementing existing GlueX and J/$\psi$-007 data.
• Refined Background Subtraction: Implemented a sophisticated BDT-based reweighting method for incoherent backgrounds, improving the purity of the signal extraction.
• Model-Independent Interpretation: Extracted the slope parameter ($m_S$) of the differential cross section to determine the proton mass radius without relying on specific QCD models initially.
• GFF Extraction: Performed the first extraction of Gluon Gravitational Form Factors ($A_g(t)$ and $C_g(t)$) using CLAS12 data alone and in combination with other experiments, utilizing both Generalized Parton Distribution (GPD) and Holographic-QCD models.

4. Results

• Total Cross Section:

  • Measured 779.9 $\pm$ 40.4 $J/\psi$ events.
  • The cross section rises smoothly with photon energy from the threshold up to 10.6 GeV.
  • Crucial Finding: Unlike the GlueX data which showed a potential dip near 9 GeV (near $\Lambda_c D$ thresholds), the CLAS12 data exhibits a smooth energy dependence. This suggests that open-charm intermediate states may have a smaller contribution to the total cross section than previously hypothesized, or that the dip is an artifact of limited statistics/kinematics in previous measurements.
  • The results are consistent with GlueX and J/$\psi$-007 data within uncertainties.

• Differential Cross Section ($d\sigma/dt$):

  • Measured as a function of $-t$ for three photon energy bins.
  • The $t$-dependence was fitted with a dipole parametrization: $\frac{d\sigma}{dt} \propto (1 - t/m_S^2)^{-4}$.
  • Proton Mass Radius: Derived from the slope parameter $m_S$, the proton mass radius was found to be $\sqrt{\langle r_m^2 \rangle} \approx 0.49 - 0.53$ fm. This is consistent with previous extractions and is significantly smaller than the proton charge radius ($\sim 0.84$ fm).

• Gluon Gravitational Form Factors (GFFs):

  • Using GPD and Holographic-QCD models, the form factors $A_g(t)$ (related to momentum fraction) and $C_g(t)$ (related to pressure/shear) were extracted.
  • The extracted parameters ($m_A$, $m_C$) and the resulting form factors are consistent with previous J/$\psi$-007 results but provide new constraints, particularly at higher gluon momentum skewness ($\xi > 0.4$).
  • The combined analysis (CLAS12 + GlueX + J/$\psi$-007) yielded a scalar radius $\sqrt{\langle r_s^2 \rangle}_g \approx 0.99$ fm (Holographic model) and $1.64$ fm (GPD model).

5. Significance

• Validation of QCD Models: The smooth energy dependence of the cross section challenges models predicting strong open-charm cusp effects near 9 GeV, providing tighter constraints for theoretical descriptions of near-threshold dynamics.
• Probing Proton Structure: The extraction of $A_g(t)$ and $C_g(t)$ offers direct experimental access to the mechanical properties of the proton (mass and pressure distributions) generated by gluons, a fundamental aspect of the Standard Model that remains poorly understood.
• Foundation for Future Physics: These results serve as a benchmark for future high-luminosity experiments at JLab (SoLID, $\mu$CLAS12) and the Electron-Ion Collider (EIC), which will aim to map the 3D gluonic structure of the proton with unprecedented precision.

In summary, this paper provides the most precise near-threshold $J/\psi$ photoproduction measurements to date, resolving ambiguities regarding open-charm contributions and delivering robust experimental constraints on the gluonic gravitational form factors of the proton.