⚛️ nuclear theory

Separating non-collective effects in d-Au collisions

This study utilizes the PYTHIA8/Angantyr model to demonstrate that non-collective effects can account for charged hadron multiplicities and baryon enhancement in central d-Au collisions at $\sqrt{s_{NN}}= 200$ GeV without requiring a thermalized medium, while highlighting the model's underprediction of invariant yields and the absence of high- $p_T$ suppression.

Original authors: Satya Ranjan Nayak, Akash Das, B. K. Singh

Published 2026-07-23

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CC BY 4.0

Original authors: Satya Ranjan Nayak, Akash Das, B. K. Singh

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 the universe as a giant, cosmic kitchen where the ingredients are the tiniest building blocks of matter. For most of its life, this kitchen has been cool enough to bake these ingredients into solid particles like protons and neutrons. But right after the "Big Bang," the oven was turned up so high that these particles melted into a soupy, chaotic state called the Quark-Gluon Plasma (QGP). Think of it like a super-hot soup where the individual ingredients have lost their shape and are swimming freely. Scientists at massive particle accelerators, which are like giant cosmic slingshots, smash heavy atoms together at nearly the speed of light to recreate this ancient soup. They look for specific "flavors" or signals in the debris—like an increase in strange particles or a change in how particles flow—to prove they've actually made the soup. However, there's a tricky problem: sometimes, the ingredients can clump together or push against each other in ways that look like soup, even if no actual soup was ever made. It's like seeing a crowd of people pushing and shoving in a hallway; it might look like a chaotic riot, or it might just be people trying to get through a narrow door.

This paper tackles that exact confusion in a specific type of experiment: smashing a deuteron (a tiny particle made of a proton and a neutron) into a gold atom. This is a "small system" collision, much smaller than the usual heavy-ion crashes, yet it still shows some of those mysterious "soup-like" signals. The authors wanted to know: Is this a tiny drop of the primordial soup, or is it just a bunch of particles bumping into each other without forming a collective medium? To find out, they used a sophisticated computer simulation called PYTHIA8/Angantyr. Think of this simulation as a "control group" that assumes no soup is formed. It only calculates what happens when particles bounce off each other like billiard balls, using complex rules about how they connect and break apart. By comparing this "no-soup" simulation to real experimental data, the authors tried to separate the effects of simple particle bumps from the effects of a real, hot medium.

The researchers ran their simulation on 50 million d-Au collisions at an energy of $\sqrt{s_{NN}} = 200$ GeV. They found that their "no-soup" model was surprisingly good at predicting the total number of particles produced and how they were spread out across different angles, without needing to assume a hot medium existed. However, when they looked at the specific types of particles, the simulation started to diverge from reality. In the most violent, central collisions, the model predicted fewer particles than what the experiments actually saw, especially for pions and protons. The paper notes that the model underpredicts the invariant yield in central collisions. The interesting twist is that the model did include a mechanism (spatially constrained color reconnection) designed to enhance baryon production. While this mechanism boosted proton production within the simulation, the model still fell short of the experimental data. Consequently, when comparing the data to the model, the ratio showed a signal that looks like baryon enhancement, but this is actually because the real data is higher than the model's prediction, not because the model perfectly reproduced the effect.

When the authors compared their simulation to the real data using a ratio called "Data/MC" (Data divided by Model Calculation), they saw a pattern that looked very similar to what is seen in massive gold-gold collisions where a QGP is definitely formed. The ratio showed a bump in the middle range of particle speeds and a rise in the number of protons and kaons. This suggests that even in these tiny d-Au collisions, there are signals that look like strangeness and baryon enhancement. However, there was one major difference: in the big gold-gold collisions, high-speed particles get "quenched" or suppressed because they get stuck in the thick soup. In these d-Au collisions, the authors found no high $p_T$ suppression. This is a crucial clue; it suggests that while there are some collective effects happening, the "soup" might not be thick enough to stop fast-moving particles, or perhaps no soup was formed at all.

Furthermore, the authors compared their results to a "thermal model," which is a calculation that assumes the system is a perfect, hot soup. They found that the actual yield of particles in the d-Au collisions was much smaller than what a thermal model would predict for a system with the same number of participants. This implies that if a thermal medium exists, it is very different from what standard models predict, or that the thermal model simply doesn't apply to these small systems. The paper concludes that while the d-Au collisions show some signals that mimic a QGP (like baryon enhancement), they lack the "smoking gun" of high-momentum suppression. The authors suggest that the "Data/MC" ratio from their simulation can be used as a new tool to check for in-medium effects, acting as a baseline to see if the "no-soup" explanation is enough to explain the data. In short, the study suggests that the mysterious signals in these small collisions might be explained by complex particle interactions without needing to invoke a full-blown Quark-Gluon Plasma, though the question remains open for further investigation.

Technical Summary: Separating Non-Collective Effects in d-Au Collisions

Problem Statement
The identification of Quark-Gluon Plasma (QGP) formation in small collision systems, such as deuteron-gold (d-Au) and helium-gold (He-Au), remains a subject of debate. While these systems exhibit signatures traditionally associated with QGP—such as strangeness enhancement, baryon enhancement, and anisotropic flow—recent theoretical developments suggest that non-collective mechanisms (e.g., rope hadronization, string shoving, and color reconnection) can mimic these signals. Consequently, there is a critical need to distinguish between collective medium effects and non-collective phenomena arising from the complex dynamics of wounded nucleon interactions. The primary challenge lies in establishing a reliable baseline that describes heavy-ion collisions without assuming QGP formation, thereby allowing for the isolation of genuine in-medium effects.

Methodology
This study utilizes the PYTHIA8/Angantyr event generator to simulate minimum-biased d-Au collisions at a center-of-mass energy of $\sqrt{s_{NN}} = 200$ GeV. The Angantyr model simulates heavy-ion events based on the interactions of wounded nucleons using a modified Glauber model that incorporates Glauber-Gribov color fluctuations, explicitly without assuming the formation of a thermalized medium.

Key methodological components include:

Spatially Constrained Color Reconnection (SC CR): The authors employ a newly added mechanism where color reconnections are performed across the entire event but constrained spatially. This allows strings from different sub-collisions to interact if they are within a specific spatial range, addressing the limitation of standard models that treat sub-collisions independently.
Parameter Tuning: The default PYTHIA tunes (Monash, QCD CR) were insufficient for describing identified particle spectra at 200 GeV. The authors modified specific parameters to better reproduce experimental data for $pp$ collisions at this energy. Notable adjustments included increasing BeamRemnants:primordialKTsoft and BeamRemnants:primordialKThard to improve mid- $p_T$ yields, and adjusting StringFlav:ProbStoUD and StringFlav:ProbQQtoQ to enhance kaon and proton yields, respectively.
Centrality Definition: Rather than relying on the number of participant nucleons ( $N_{part}$ ), which is sensitive to the Glauber model used, centrality was assigned based on the final-state charged hadron multiplicity ( $N_{ch}$ ) in the pseudo-rapidity interval $-3.8 < \eta < -2.8$ , mirroring experimental procedures.
Comparative Analysis: The study compares Angantyr results with experimental data from STAR, PHOBOS, and PHENIX. It also contrasts the Angantyr baseline with thermal model calculations (using HYDJET++) for peripheral Au-Au collisions that share a similar $N_{part}$ with central d-Au collisions.

Key Results

Multiplicity and Pseudo-rapidity: The Angantyr model with SC CR successfully reproduces the charged particle multiplicity ( $N_{ch}$ ) distribution and the high-multiplicity tail in minimum-biased d-Au collisions without further tuning. The model provides a good description of the pseudo-rapidity distribution ( $dN_{ch}/d\eta$ ) across the entire $\eta$ range, outperforming QGP-based models like AMPT and jet-based models like HIJING at backward rapidities.
Invariant Yields and Spectra:
- Pions and Protons: The model agrees well with experimental data in peripheral collisions but underpredicts the invariant yields in central collisions.
- Kaons: The model underpredicts the kaon spectra across all centrality classes.
- Ratios: The $p/\pi^+$ and $K^+/\pi^+$ ratios deviate from experimental data, a limitation attributed to PYTHIA's lack of partonic coalescence mechanisms essential for describing these ratios.
Data/MC and Nuclear Modification: The ratio of experimental data to the Angantyr Monte Carlo (Data/MC) exhibits trends analogous to the nuclear modification factor ( $R_{AA}$ $R_{AA}$ ) observed in Pb-Pb collisions.
- Enhancement: In central d-Au collisions, the Data/MC shows a mid- $p_T$ enhancement for protons and kaons, suggesting signals similar to baryon and strangeness enhancement.
- Suppression: Unlike Pb-Pb collisions, the d-Au Data/MC does not exhibit high- $p_T$ suppression, indicating the absence of jet quenching in these small systems.
Thermal Model Comparison: When comparing the invariant yield of central d-Au collisions to thermal model calculations (HYDJET++) for peripheral Au-Au collisions with equivalent $N_{part}$ , the d-Au yields are significantly smaller. This suggests that the particle production in d-Au collisions is lower than what a thermal model would predict for a system of similar size.

Significance and Claims
The paper posits that the PYTHIA8/Angantyr model, particularly with spatially constrained color reconnection, serves as a robust non-hydrodynamic baseline for d-Au collisions at RHIC energies. Its significance lies in its ability to:

Reproduce multiplicity and pseudo-rapidity distributions without invoking a thermalized medium.
Provide a model-dependent observable (Data/MC) that complements the traditional $R_{AA}$ . This observable can help distinguish between modifications caused by the separation of sub-collisions (non-collective) and those caused by a strong collective medium.
Demonstrate that while central d-Au collisions exhibit signals resembling baryon enhancement, they lack the high- $p_T$ suppression characteristic of jet quenching.
Highlight that the observed yields in d-Au collisions are inconsistent with thermal model predictions for similar $N_{part}$ , reinforcing the view that these systems do not form a QGP in the same manner as large A-A systems.

The authors conclude that while the model has limitations in describing specific particle ratios and central collision yields, it offers a crucial tool for isolating non-collective effects, thereby aiding in the rigorous assessment of QGP formation in small collision systems.

Technical Summary: Separating Non-Collective Effects in d-Au Collisions

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