Electro- and photoproduction of muon pairs with $\mu$CLAS12: Double Deeply Virtual Compton Scattering, Timelike Compton Scattering, and $J/\psi$ production

This paper outlines a proposed physics program using the upgraded $\mu$CLAS12 detector to explore the three-dimensional quark and gluon structure of the nucleon through precision measurements of Double Deeply Virtual Compton Scattering, Timelike Compton Scattering, and near-threshold $J/\psi$ production via di-muon electro- and photoproduction.

The Gist

Imagine the atom's core, the proton, not as a solid marble, but as a bustling, three-dimensional city made of tiny, energetic particles called quarks and gluons. For decades, scientists have tried to map this city, but they've mostly been looking at it from just two angles. This paper proposes a new, high-tech expedition to finally see the city in full 3D, using a massive, upgraded microscope called µCLAS12 at the Thomas Jefferson National Accelerator Facility (JLab).

Here is the story of that expedition, explained simply.

The Problem: A Blurry, Flat Picture

Think of the proton's internal structure as a complex 3D object. Scientists use a mathematical tool called Generalized Parton Distributions (GPDs) to describe it. However, the current methods are like trying to understand a 3D sculpture by only looking at its shadow on a wall.

• The Old Way (DVCS and TCS): Scientists have been firing electrons or photons at protons and watching what bounces off. This gives them a "shadow" that depends on two variables (like width and height), but it misses the third dimension (depth). It's like trying to guess the shape of a sphere by only seeing a circle.
• The Ambiguity: Because they are missing that third dimension, different theories about the proton's interior can look exactly the same in the data. It's like trying to solve a puzzle where you can't see all the pieces; you might fit the pieces together, but you aren't sure if you have the right picture.

The Solution: The "Double" Deep Dive

The paper proposes a new experiment called Double Deeply Virtual Compton Scattering (DDVCS).

• The Analogy: Imagine you are trying to see inside a dark room. The old method was like shining a flashlight in and seeing what reflects off the back wall. The new method is like shining a flashlight in and having a second, different light source appear on the other side of the room.
• How it works: In this experiment, an electron hits a proton. The proton absorbs a "virtual" photon (a flash of energy that exists only for a split second) and then spits out a different virtual photon. This second photon immediately decays into a pair of muons (heavy cousins of electrons).
• The Magic: By measuring both the incoming and outgoing energy, scientists can vary three different knobs at once. This allows them to map the proton's interior in full 3D, finally resolving the "shadow" ambiguity and seeing the true shape of the quark and gluon city.

The Machine: µCLAS12

To do this, the scientists are upgrading their giant detector, CLAS12, into µCLAS12.

• The Shield: The experiment is so intense that it creates a storm of background noise (like trying to hear a whisper in a hurricane). To fix this, they are building a massive lead shield (like a thick, heavy wall) in front of the detector. This blocks the "noise" but lets the precious muons pass through.
• The Muon Spectrometer: The detector is being reconfigured to act like a specialized muon catcher. Muons are tricky; they are hard to spot because they look a lot like pions (another type of particle). The team is using advanced "AI-like" algorithms (Machine Learning) to act as a super-smart bouncer, letting only the muons in and kicking out the impostors.
• The Target: They will smash an 11 GeV electron beam into a tank of liquid hydrogen (pure protons) at a rate so high it's like a continuous stream of bullets hitting a target.

The Three Big Goals

The paper outlines three main "treasures" they hope to find with this setup:

1. The 3D Map (DDVCS)
This is the main event. By measuring how the muon pairs are scattered, they will create the first high-resolution, 3D map of the proton's internal structure. This will tell us exactly how the quarks and gluons are arranged in space and how they move, solving the "shadow" problem mentioned earlier.

2. The Heavyweight Champion (J/ψ Production)
They will also look for the creation of a heavy particle called the J/ψ meson right at the edge of where it can be created (near-threshold).

• Why it matters: The J/ψ is made of heavy "charm" quarks. Creating it requires a huge amount of energy, which means it acts like a probe for the gluons (the glue holding the proton together).
• The Mystery: They want to see if there are hidden "pentaquarks" (particles made of five quarks) hiding in the data. Previous experiments hinted at these, but the data was too fuzzy. With µCLAS12's high precision, they hope to either confirm these exotic particles exist or rule them out.

3. The Mirror Image (Timelike Compton Scattering)
This is a process that is the "mirror image" of the first one. Instead of a virtual photon going in and a real one coming out, a real photon goes in and a virtual one comes out.

• The Goal: They will measure this with much higher precision than ever before. This helps cross-check the 3D map and provides a different angle on how the proton's internal forces work.

The Bottom Line

This paper is a proposal and a plan. It doesn't present new data yet; instead, it argues that by upgrading the CLAS12 detector with heavy shielding and muon-tracking technology, they can run an experiment that is 1,000 times more powerful than previous attempts.

They claim that with 200 days of running this machine, they will collect enough data to:

• Finally see the proton in 3D.
• Understand how the "glue" (gluons) holds the proton together.
• Solve the mystery of whether strange, five-quark particles (pentaquarks) exist.

It's essentially a blueprint for building a better camera to take the sharpest possible picture of the universe's most fundamental building block.

Technical Summary

Technical Summary: Electro- and Photoproduction of Muon Pairs with µCLAS12

Problem Statement
The primary challenge in the experimental investigation of Generalized Parton Distributions (GPDs) is the "deconvolution problem." Current measurements of Deeply Virtual Compton Scattering (DVCS) and Timelike Compton Scattering (TCS) provide access to only two of the three kinematic variables ($x, \xi, t$) upon which GPDs depend. Specifically, these processes constrain the GPDs to the ridge $x = \pm \xi$, leaving the dependence on the longitudinal momentum fraction $x$ integrated out in the Compton Form Factors (CFFs). This leads to an inherent ambiguity in GPD extraction, as "shadow GPDs" (SGPDs)—functions that vanish in the forward limit and at specific scales but contribute to the inverse problem—cannot be ruled out by DVCS or TCS data alone. Furthermore, existing measurements of near-threshold $J/\psi$ production and TCS at Jefferson Lab (JLab) are statistically limited, hindering precise extractions of Gluon Gravitational Form Factors (GFFs) and the search for hidden-charm pentaquark states.

Methodology
The paper proposes a comprehensive experimental program using the upgraded µCLAS12 detector in Hall B at the Thomas Jefferson National Accelerator Facility (JLab). The core methodology involves the electro- and photoproduction of muon pairs ($ep \to e'\mu^+\mu^-p'$) to access Double Deeply Virtual Compton Scattering (DDVCS), TCS, and near-threshold $J/\psi$ production.

• Detector Configuration: The CLAS12 Forward Detector (FD) is modified to function as a high-efficiency muon spectrometer capable of operating at luminosities up to $10^{37} \text{ cm}^{-2}\text{s}^{-1}$. Key modifications include:
  • Shielding: Installation of a 60-cm-thick lead shield and a new PbWO$_4$ electromagnetic calorimeter (wECal) to replace the High Threshold Čerenkov Counter (HTCC). This suppresses electromagnetic and hadronic backgrounds (primarily Møller scattering and pion pairs) while detecting scattered electrons.
  • Tracking: Replacement of the Forward Micromegas with a Forward Vertex Tracker (FVT) based on triple-GEM technology to ensure precise vertex reconstruction for tracks traversing the shield.
  • Recoil Detection: Implementation of a new Recoil Detector (RD) comprising a Micro-Resistive Well (µRWELL) tracker and a Scintillation Hodoscope (SH) to detect recoil protons in the angular range of $40^\circ$ to $70^\circ$.
• Simulation and Analysis: The study utilizes the µGEMC simulation package (a modified GEANT4 model of CLAS12) and the COATJAVA reconstruction framework. Particle identification (PID) relies on Boosted Decision Trees (BDT) and machine learning algorithms to distinguish muons from pions, leveraging energy deposition profiles in the calorimeter. Backgrounds from inelastic muon pair production, pion pair production, and accidental coincidences are rigorously estimated.

Key Contributions and Planned Measurements
The paper outlines three primary physics goals enabled by the µCLAS12 configuration:

1. Double Deeply Virtual Compton Scattering (DDVCS):

   • Objective: Measure beam-spin asymmetries ($A_{LU}$) in the reaction $ep \to e'\mu^+\mu^-p'$.
   • Kinematics: By independently varying the spacelike virtuality of the incoming photon ($Q^2$) and the timelike virtuality of the outgoing photon ($Q'^2$), the experiment accesses the full three-dimensional phase space of GPDs, specifically the region $-\xi < x < \xi$.
   • Significance: This allows for the mapping of GPDs as a function of $x$ and $\xi$, potentially resolving the SGPD ambiguity that plagues DVCS and TCS extractions. The study projects the collection of over $0.5 \times 10^6$ events, sufficient to observe the expected sign change of the asymmetry between spacelike and timelike regions.

2. Near-Threshold $J/\psi$ Production:

   • Objective: Measure the exclusive photoproduction of $J/\psi$ mesons decaying into muon pairs ($J/\psi \to \mu^+\mu^-$).
   • Kinematics: The experiment will cover initial photon energies ($E_\gamma$) from the production threshold up to 10.5 GeV, including the critical region for open-charm contributions (8.7–9.4 GeV).
   • Significance: With an expected yield of $\sim 3 \times 10^4$ events (40 times the current CLAS12 statistics), the measurement aims to precisely determine the $t$-dependence of the cross section. This is essential for extracting Gluon GFFs (specifically $A_g(t)$ and $C_g(t)$), which relate to the proton's mass radius, scalar radius, and internal pressure distributions. The high statistics also enable a search for hidden-charm pentaquark states ($P_c$) in the $J/\psi p$ invariant mass spectrum.

3. Timelike Compton Scattering (TCS):

   • Objective: Measure photon beam-polarization asymmetries ($A_{\odot U}$) and forward-backward asymmetries ($A_{FB}$) in the reaction $\gamma p \to \mu^+\mu^- p'$.
   • Significance: The projected statistics ($7.7 \times 10^6$ events) represent a three-order-of-magnitude increase over previous CLAS12 results. This will allow for precision extraction of CFFs in finer kinematic bins, providing new constraints on the real part of the Compton amplitude and testing the universality of GPDs.

Results and Projections
The paper presents detailed feasibility studies based on Monte Carlo simulations:

• Background Suppression: The lead shield and wECal are projected to reduce pion contamination in the muon sample by a factor of at least $2 \times 10^4$. The estimated background contamination for DDVCS is approximately 12% (dominated by inelastic muon pairs), while accidental coincidences contribute less than 5%.
• Resolution: The inclusion of the FVT significantly improves the missing mass resolution for the $e'\mu^+\mu^-X$ system, sharpening the proton peak.
• Statistical Precision: The study projects that the statistical uncertainties for $A_{LU}$ in DDVCS and $A_{FB}$ in TCS will be sufficiently small to distinguish between different GPD models (e.g., VGG, GK19) and to detect the presence of SGPDs. For $J/\psi$ production, the precision is expected to be sufficient to differentiate between holographic QCD, GPD-based, and Regge-based models.

Significance
The paper claims that the µCLAS12 experiment represents a unique opportunity to advance the understanding of nucleon structure. By enabling the measurement of DDVCS, it offers the first experimental pathway to map GPDs over their full three-dimensional phase space, directly addressing the deconvolution problem and the SGPD ambiguity. Furthermore, the high-luminosity, high-statistics dataset for $J/\psi$ and TCS will provide unprecedented constraints on the gluonic structure of the proton, including its mechanical properties (pressure, shear forces) and the potential existence of exotic pentaquark states. The experiment is designed to operate at the luminosity frontier, leveraging the unique capabilities of JLab's 12 GeV electron beam to explore physics regimes inaccessible to other facilities.