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Studying baryon number transport dynamics via hyperon-kaon correlations in $p + \mathrm{Au}$ collisions at $\sqrt{s_{_{\rm NN}}}=20$ , $39$ and $62$ GeV

This paper utilizes AMPT and UrQMD models to simulate hyperon-kaon correlations in $p + \mathrm{Au}$ collisions at 20, 39, and 62 GeV, establishing a baseline without baryon junction mechanisms to test theories of baryon number transport and strange quark pair correlations.

Original authors: Siyuan Ping, Xiaozhou Yu, Long Ma

Published 2026-07-07

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CC BY 4.0

Original authors: Siyuan Ping, Xiaozhou Yu, Long Ma

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

Imagine a high-speed crash between a single proton (a tiny particle) and a massive gold nucleus. In this chaotic collision, particles are smashed apart and reassembled into new forms. One of the most puzzling things physicists want to understand is how "baryon number" (a fundamental property that makes matter, like protons and neutrons, what they are) travels from the incoming proton to new particles that appear far away in the collision.

This paper is like a detective story trying to figure out how that property gets transported across the "crime scene" of the collision.

Here is the breakdown of their investigation using simple analogies:

1. The Mystery: How does the "Soul" travel?

When the proton hits the gold nucleus, it breaks apart. Usually, the "soul" of the proton (its baryon number) stays with the pieces that were originally part of it. But sometimes, this "soul" travels a long distance across the collision zone and ends up inside a new, strange particle called a hyperon (which contains "strange" quarks).

The scientists want to know: Does the soul travel on a specific "highway" or does it just drift randomly?

There are two main theories about the "highway":

The Standard Theory (Valence Quarks): The soul travels attached to the three main building blocks (quarks) of the proton. It's like a backpack carried by a hiker.
The Exotic Theory (Gluon Junction): The soul travels on a special, Y-shaped "glue" field (a gluon junction) that connects the three building blocks. It's like a hiker dropping their backpack and sending it flying on a separate, invisible drone.

2. The Clue: The "Dance Partners"

To figure out which theory is right, the scientists look at hyperons and kaons (another type of particle).

The Rule: In these collisions, strange particles are always made in pairs. If a hyperon is born, a kaon is usually born with it, like dance partners.
The Clue: If the "soul" travels via the standard backpack method, the hyperon and its kaon partner should stay relatively close together in speed and direction. If the "soul" travels via the exotic "drone" (gluon junction), the hyperon might end up far away from its partner, or moving at a very different speed.

3. The Experiment: The "Mixing Bowl"

The researchers used powerful computer simulations (AMPT and UrQMD) to crash protons into gold nuclei at different speeds (energies). They didn't just look at the crashes; they used a clever trick called "Event Mixing."

The Analogy: Imagine you have a bowl of soup with real ingredients (the actual collision). To see what is special about the real soup, you take ingredients from different bowls and mix them together randomly. This "fake soup" represents what you would see if there were no special connection between the ingredients.
The Comparison: By subtracting the "fake soup" (random mix) from the "real soup" (actual collision), they isolated the true connection between the hyperons and kaons. This revealed the "dance" they were doing together.

4. The Measurement: The "Wasserstein Distance"

To measure how far apart the dance partners were, they used a mathematical tool called the Wasserstein distance (or Earth Mover's Distance).

The Analogy: Imagine you have a pile of dirt (the hyperons) in one spot and a hole (the kaons) in another. The "distance" is how much work it takes to move the dirt to fill the hole.
The Result: If the partners are tightly linked, the "work" is low (they are close). If they are loosely linked, the "work" is high (they are far apart).

5. What They Found

The paper presents a "baseline" prediction. This means they calculated what the results should look like if only the standard "backpack" theory is true (without the exotic "drone" mechanism).

The Direction Matters: They found that hyperons flying in the same direction as the incoming proton (the "proton-going" side) showed a clearer pattern of connection with their kaon partners than those flying the other way. This side is the best place to look for the truth.
The Energy Matters: As the collision energy increased, the connection between the hyperons and kaons changed. In their standard models, the partners tended to move at different speeds as energy went up.
The Conclusion: The paper does not claim to have found the "drone" (gluon junction) yet. Instead, it says: "Here is exactly what the data should look like if the standard theory is the only thing happening."

Why This Matters

This paper is like drawing a map of a "normal" forest. If future experiments (real-life crashes in big machines) show a path that doesn't match this map, scientists will know that something exotic (like the gluon junction) is happening.

In short: The authors built a computer model to predict how particles should behave if the "soul" of the proton travels in the standard way. They found that looking at particles moving in the direction of the incoming proton gives the clearest view. This map serves as a reference point for future experiments to see if they discover something new and exotic.

Technical Summary: Studying Baryon Number Transport Dynamics via Hyperon-Kaon Correlations in p + Au Collisions

Problem Statement
In heavy-ion collisions at RHIC and LHC energies, a baryon-to-antibaryon ratio greater than unity is observed at mid-rapidity. Since initial baryons reside at beam rapidity and baryon number is conserved, this implies a transport mechanism moving baryon number across a large rapidity gap ( $\delta y \sim y_{beam}$ ) to mid-rapidity. While the Standard Model conserves baryon number, the specific mechanism of this transport remains a subject of investigation. One proposed framework is the gluon junction (or baryon junction) model, where a Y-shaped gluonic field carries the baryon number, distinct from the valence-quark picture where baryon number is carried solely by three valence quarks.

The paper posits that hyperon-kaon correlations can serve as a sensitive probe for this transport mechanism. Since initial nucleons carry no net strangeness, strange quark pairs ( $s-\bar{s}$ ) are produced from the vacuum. Depending on the fragmentation process, these pairs can generate correlations between hyperons (carrying the transported baryon number) and kaons. Specifically, the authors aim to distinguish between scenarios where baryon number is transported via valence quarks versus a gluon junction, and to establish a baseline for future experimental tests in the absence of the junction mechanism.

Methodology
The study utilizes proton-gold (p + Au) collisions at center-of-mass energies $\sqrt{s_{NN}} = 20, 39,$ and $62$ GeV. Two theoretical models are employed to simulate these collisions:

AMPT (A Multi-Phase Transport) model with string melting (SM) mechanism.
UrQMD (Ultra-relativistic Quantum Molecular Dynamics) model (version 4.0).

Both models generate over 100 million events. The analysis focuses on two production scenarios for hyperons:

Scenario 1 (General Associated Production): Baryon number is transported from the incident proton to the hyperon; $s-\bar{s}$ pairs are produced to conserve strangeness, linking the hyperon to specific kaons.
Scenario 2 (General Pair Production): Hyperons and kaons are produced from the vacuum without baryon number transport from the incident beam.

To isolate the genuine correlation signal from Scenario 1, the authors develop a combinatorial background subtraction method:

They construct same-event and mixed-event distributions for hyperon-kaon pairs ( $\Lambda K$ , $\Xi K$ ).
By leveraging charge symmetry and the fact that anti-hyperons are produced only via Scenario 2, they derive a correlation function, $CCBS_{HK^+}(\Delta y)$ , which removes contributions from uncorrelated pairs and Scenario 2.
The relative rapidity difference, $\Delta y$ , is defined to analyze the kinematic relationship between the hyperon and the associated kaon.

To quantify the correlation strength and directionality, the authors introduce two metrics based on the Wasserstein distance (Energy Mover's Distance, EMD):

EMD: Quantifies the average transport distance required to map the "excess" distribution (correlated signal) from negative regions to the positive region, representing the overall correlation strength.
EMD $_p$ (Energy-Mover's Displacement): Retains directional information, indicating whether correlated kaons are preferentially emitted at larger or smaller relative rapidities compared to the hyperon.

Key Results

Correlation Function Shape: The $CCBS_{HK^+}(\Delta y)$ functions exhibit a characteristic shape where correlated kaons preferentially populate a specific relative rapidity interval ( $\Delta y \in [-2, 1]$ for full acceptance; narrower for detector acceptance).
Proton-Going vs. Au-Going: Hyperons emitted in the proton-going direction ( $y > 0$ ) show distinct correlation patterns compared to those in the Au-going direction ( $y < 0$ ). The difference is more pronounced for $\Lambda$ hyperons than for $\Xi$ hyperons.
Energy Dependence: In the full acceptance range, the EMD $_p$ values for proton-going hyperons decrease as collision energy increases. This suggests that at higher energies, hyperons carrying baryon number from the incident proton correlate with relatively slower kaons. Conversely, the EMD (correlation strength) increases with energy.
Hyperon Species Dependence: Multi-strange hyperons ( $\Xi$ ) exhibit different stopping behaviors compared to $\Lambda$ . In the valence-quark picture (implemented in AMPT and UrQMD), $\Xi$ hyperons experience stronger stopping, correlating with slower kaons.
Model Dependence: While AMPT and UrQMD show consistency in full acceptance for proton-going hyperons, discrepancies arise in the Au-going direction and within specific detector acceptance ranges ( $|\eta| < 1.5$ ). UrQMD predicts a larger shift of kaons to higher $\Delta y$ for $\Lambda$ hyperons in the Au-going direction compared to AMPT.
Detector Acceptance: Applying a pseudo-rapidity cut ( $|\eta| < 1.5$ ) reduces the observable differences between proton-going and Au-going hyperons, particularly for $\Lambda$ , consistent with the expected suppression of baryon number transport effects in the mid-rapidity region under the valence-quark picture.

Significance and Claims
The paper claims to provide a baseline without the baryon junction mechanism for future experimental measurements. By establishing the expected hyperon-kaon correlations based on standard valence-quark fragmentation and string melting models, the authors offer a reference prediction against which experimental data can be tested.

The study concludes that:

Hyperon-kaon correlations are a viable probe for baryon number transport dynamics.
Proton-going hyperons provide a cleaner and more reliable probe for observing these effects in p + A collisions compared to Au-going hyperons.
If the gluon junction mechanism exists, it would likely manifest as a deviation from the baseline established here—specifically, an opposite trend in energy dependence (e.g., hyperons becoming slower relative to kaons at higher energies due to stronger gluonic field stopping) or a larger separation between proton-going and Au-going correlation patterns than predicted by current models.

The work does not claim to have observed the baryon junction; rather, it establishes the theoretical framework and quantitative baseline necessary for future experiments with large rapidity coverage to test for its presence.