Valence quark-stopping and gluon junction-stopping scenarios in electron-nucleus collisions at the forthcoming Electron-Ion Collider: Which one is correct?

Using a multi-source thermal model, this paper argues that the valence quark-stopping scenario is more suitable than the gluon junction scenario for explaining baryon number transport in high-energy collisions, a conclusion that can be further validated by future electron-nucleus collision experiments at the Electron-Ion Collider.

The Gist

Imagine a high-energy particle collision not as a violent crash of cars, but as a chaotic dance party where tiny, invisible dancers (particles) are thrown together at incredible speeds. The big question physicists are trying to answer is: When these dancers collide, who carries the "identity card" (baryon number) that tells us which ones are the original team members (protons/neutrons) and which are just new guests?

This paper tackles two competing theories about how this identity card is passed around during the dance, specifically looking forward to a new, massive dance hall called the Electron-Ion Collider (EIC).

Here is the breakdown using simple analogies:

The Two Competing Theories

Think of a proton (a building block of matter) as a small team of three friends holding hands.

1. The "Valence Quark" Theory (The Team Stays Together):

   • The Idea: The three friends (valence quarks) are the ones carrying the team's identity. If the team gets hit, the friends might get separated, but they still carry the identity.
   • The Prediction: Because these friends are tough and fast, they can punch through the crowd. If they stop, they stop in the middle of the room (the "central" area) because they got hit hard. If they don't stop, they fly to the edges.
   • The Analogy: Imagine three runners in a race. If they get tackled, they fall right in the middle of the track.

2. The "Gluon Junction" Theory (The Invisible Rope):

   • The Idea: The identity isn't carried by the friends, but by a magical, invisible knot (a "gluon junction") in the middle of their hands. This knot is heavy and sticky.
   • The Prediction: When the team collides, the knot gets stuck in the mud. It loses all its energy and stops right in the center of the room, dragging the identity card with it.
   • The Analogy: Imagine the three runners are tied to a heavy anchor in the middle of the track. When they crash, the anchor stops dead in the center, and the runners just spin around it.

The Detective Work: How to Tell Them Apart

The authors of this paper are like detectives trying to figure out which theory is right before the new collider even opens. They used a mathematical tool called the "Multi-Source Thermal Model."

Think of this model as a thermometer and a speedometer for the collision.

• Soft Excitation: This is like a gentle bump in the dance. It happens a lot, involves many people, and creates a "cool" temperature.
• Hard Scattering: This is a violent crash. It happens less often, involves fewer people, and creates a "hot" temperature (high energy).

The Clue:
The researchers looked at where the "identity cards" (net-protons) ended up and how "hot" (fast) they were in different parts of the room.

• If the "Valence Quark" theory is right: The "hot" particles (from the violent crashes) should be found in the center of the room. The "cool" particles should be on the edges.
• If the "Gluon Junction" theory is right: The "hot" particles should be on the edges, and the "cool" particles should be stuck in the center.

What the Paper Found

After analyzing data from previous experiments (like collisions at the Relativistic Heavy Ion Collider), the authors found a pattern:

• The particles in the center of the collision were hotter (moving faster) than the ones on the edges.
• This matches the "Valence Quark" prediction.

The Verdict: The data suggests that the "friends" (valence quarks) are the ones carrying the identity card, not the "invisible knot" (gluon junction). The "knot" theory seems less likely to be the main story.

Why Wait for the EIC?

The authors are excited about the upcoming Electron-Ion Collider (EIC).

• The Setup: Instead of smashing two heavy nuclei together, they will shoot a single electron at a heavy nucleus.
• The Advantage: This is like a "cleaner" experiment. It's easier to see exactly what happens when a single electron hits a nucleus without the noise of a massive crash.
• The Test: By measuring the speed (temperature) of particles in the center vs. the edges of this new setup, they can confirm their prediction with high precision.

The Bottom Line

The paper argues that valence quarks (the three main parts of a proton) are the ones responsible for stopping and carrying the "baryon number" in high-energy collisions.

• Current Evidence: Points strongly to the Valence Quark theory.
• Future Proof: The upcoming Electron-Ion Collider will act as the final referee to confirm this, likely settling the debate once and for all.

In short: The "friends" (quarks) are doing the running and stopping, not the "invisible knot" (gluon junction). The new collider will be the ultimate test to prove it.

Technical Summary

1. Problem Statement

In high-energy nuclear collisions, a fundamental unresolved question concerns the mechanism of baryon number transport (stopping). Two competing theoretical scenarios exist:

• Valence Quark-Stopping Scenario: Based on the standard QCD picture where the three valence quarks of a baryon each carry $1/3$ of the baryon number. In this model, valence quarks possess high penetrability and tend to stop in the central rapidity region during hard scattering, while remaining in the forward/backward regions during soft processes.
• Gluon (Baryon Junction)-Stopping Scenario: Proposes that baryon number is carried by a non-perturbative gluon field configuration (a "junction") in a Y-shaped topology. In this scenario, the junction loses energy rapidly due to strong stopping power, causing baryons to concentrate in the central rapidity region even in soft processes.

Currently, there is no consensus on which scenario is correct. The authors aim to distinguish between these two mechanisms by analyzing net-proton production in electron-nucleus ($eA$) collisions, specifically predicting outcomes for the upcoming Electron-Ion Collider (EIC).

2. Methodology

The authors employ a Multi-Source Thermal Model (MSTM) to analyze particle production. Key methodological components include:

• Two-Component Framework: The model separates collision events into:
  1. Soft Excitation Process: Involving sea quarks, gluons, and leptons. Characterized by low momentum transfer and low emission source temperature.
  2. Hard Scattering Process: Involving principal participating parton pairs. Characterized by high momentum transfer and high emission source temperature.
• Transverse Momentum ($p_T$) Distribution: Modeled using a superposition of two Erlang distributions (derived from the folding of exponential distributions). This allows for the extraction of average transverse momentum ($\langle p_T \rangle$), which serves as a proxy for the temperature of the emission source.
• Rapidity ($y$) Distribution: Modeled using a superposition of Gaussian distributions (specifically, a multi-logarithmic Gaussian distribution for net-baryons) to account for emission sources in backward, central, and forward rapidity regions.
• Data Analysis: The model was first validated against experimental data from $Pb-Pb$ and $Au-Au$ collisions at $\sqrt{s_{NN}} = 17.2, 62.4,$ and $200$ GeV (NA49 and BRAHMS collaborations).
• Prediction: Based on the fitted parameters and trends, the authors predicted net-proton rapidity distributions for $ep$ (electron-proton) collisions at EIC energies ($\sqrt{s} = 7.2, 62.4, 200$ GeV).

3. Key Contributions

• Differentiation Mechanism: The paper establishes a clear experimental signature to distinguish the two stopping scenarios based on the spatial distribution of emission source temperatures (inferred from $\langle p_T \rangle$).
  • Valence Quark Scenario: Soft processes dominate the backward rapidity region (low $T$), while hard processes dominate the central region (high $T$). Result: $\langle p_T \rangle_{central} > \langle p_T \rangle_{backward}$.
  • Gluon Junction Scenario: Soft processes localize baryons in the central region (low $T$), while hard processes shift them to the backward region. Result: $\langle p_T \rangle_{central} < \langle p_T \rangle_{backward}$.
• Reconciliation of Topologies: The authors address the apparent contradiction between lattice QCD (which supports a static Y-shaped flux tube) and their dynamic results. They propose that the $\Delta$-shaped topology (associated with valence quarks) represents a highly excited state or dynamic transfer pathway relevant to high-energy scattering, while the Y-shape represents the static ground state.
• Charge-Baryon Correlation: The paper highlights the strong linear correlation between charge stopping and baryon stopping observed in previous data. This correlation supports the valence quark scenario, as both charge and baryon number are carried by valence quarks, whereas a neutral gluon junction would decouple these transports.

4. Results

• Model Validation: The multi-component distribution (Eq. 11) provided a superior fit to experimental net-proton rapidity data compared to the traditional three-Gaussian distribution (Eq. 5), particularly in the backward and forward rapidity regions where the latter overestimated yields.
• Temperature Trends: Analysis of $Pb-Pb$ and $Au-Au$ data confirmed that the emission source temperature (and $\langle p_T \rangle$) is significantly higher in the central rapidity region than in the backward/forward regions.
• EIC Predictions:
  • In $eA$ collisions, net-baryons are absent in the forward rapidity region (no leading nucleon from the electron projectile).
  • The predicted rapidity distributions show that the central rapidity region exhibits a higher $\langle p_T \rangle$ (higher temperature) compared to the backward region.
  • This trend aligns with the Valence Quark-Stopping Scenario.
• Topology Implications: The results favor the $\Delta$-shaped topology (valence quark dominance) for dynamic high-energy processes, suggesting that valence quarks act as the primary carriers of baryon number in these collisions.

5. Significance

• Experimental Roadmap for EIC: The paper provides a concrete, testable prediction for the Electron-Ion Collider. By measuring the average transverse momentum ($\langle p_T \rangle$) of charged particles (or net-baryons) in the backward versus central rapidity regions, the EIC can definitively determine whether baryon number is transported by valence quarks or gluon junctions.
• Theoretical Clarification: It offers a unified framework that reconciles static lattice QCD findings (Y-shape) with dynamic high-energy phenomenology (Valence Quark/$\Delta$-shape), suggesting that the effective topology depends on the energy scale and excitation state of the system.
• Mechanism of Baryon Transport: The study reinforces the view that valence quarks are the primary carriers of baryon number in high-energy collisions, supported by the observed correlation between charge and baryon stopping. This deepens the understanding of QCD matter evolution in extreme conditions.

In conclusion, the authors argue that current data and their multi-source thermal model strongly support the valence quark-stopping scenario, predicting that future EIC measurements will show higher temperatures (and $\langle p_T \rangle$) in the central rapidity region compared to the backward region.