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Light hadron production measurements with Au+Au Collisions from $\sqrt{s_{NN}} = 3.2$ --$4.5$ GeV with STAR

This paper presents light hadron production measurements ( $\pi^{\pm}$ , $K^{\pm}$ , p) from Au+Au collisions at fixed-target energies of $\sqrt{s_{NN}} = 3.2$ --$4.5$ GeV using the STAR detector, utilizing blast-wave model analysis of transverse momentum spectra to study kinetic freeze-out properties and constrain the QCD equation of state in the high baryon density region.

Original authors: Mathias C. Labonté

Published 2026-07-28

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Mathias C. Labonté

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. In the very first moments after the Big Bang, this kitchen was so hot and crowded that the basic building blocks of matter—protons and neutrons—couldn't even form. Instead, everything was a swirling, super-hot soup of even smaller pieces called quarks and gluons. Scientists call this the "quark-gluon plasma." As the universe cooled down, this soup froze into the solid matter we see today, like the protons in your body. But here's the mystery: we know exactly how this happens when the universe is empty and cool, but we don't know what happens when you squeeze that soup incredibly hard and hot, like in the center of a neutron star. Does it just melt smoothly? Or does it snap into a new state of matter, like water turning instantly to ice? To find out, physicists build giant particle accelerators that smash heavy atoms together, recreating that tiny, super-dense moment of the early universe to see how the "soup" behaves under extreme pressure.

This paper is a report from a team of scientists at the STAR experiment, part of a massive project called the Beam Energy Scan. They are playing with the "knobs" on their particle collider to see what happens when they smash gold atoms together at different speeds. Specifically, they are looking at the lower end of the speed range, where the collisions are slower but create a much denser, more crowded environment. Think of it like a dance floor: if you spin the dancers fast, they fly apart; if you slow the music down but pack the room tighter, they bump into each other more, creating a different kind of chaos. The scientists want to map out this "dance floor" to see if there is a special spot—a "critical point"—where the rules of matter change completely. They are focusing on the lightest particles that fly out of these collisions, like tiny messengers carrying news about the temperature and speed of the explosion inside.

The researchers took data from gold atom collisions at four specific speeds: 3.2, 3.5, 3.9, and 4.5 GeV (a unit of energy). To understand what happened, they used a clever tool called a "blast-wave model." Imagine the collision as a firework exploding in slow motion. The firework creates a hot, expanding shell of gas. The scientists looked at the speed and direction of the particles (pions, kaons, and protons) flying out of this explosion to figure out two things: how hot the "firework" was when it stopped expanding (the temperature at kinetic freeze-out) and how fast the surface of the explosion was moving outward (the surface velocity).

What they found is quite interesting. The temperature of the explosion didn't change much depending on where you looked or how fast the atoms were moving; it stayed fairly steady across the different speeds they tested. However, the speed of the expanding surface was very sensitive to where you looked. It was fastest in the middle of the collision and slowed down as you looked toward the edges. When they compared these new, slower-speed results to previous experiments done at higher speeds, the numbers started to line up, suggesting a smooth transition as the energy changes.

The team also measured something called "baryon stopping." This is a fancy way of asking: "How much did the colliding atoms slow down when they hit each other?" When two fast-moving cars crash, they might bounce off or crumple, losing their forward speed. In these collisions, the scientists tracked how much the protons (which are like the heavy passengers in the atoms) lost their forward momentum. They found that in the most violent, head-on collisions, the protons lost about two-thirds of their original speed. In less violent, side-swipe collisions, they didn't slow down as much. This makes sense because in a side-swipe, there are fewer atoms hitting each other to share the braking force.

The paper suggests that these measurements are crucial for building better computer models of how heavy ions collide. By knowing exactly how hot and fast the matter gets at these specific energies, scientists can refine their theories about the "equation of state" of dense matter—basically, the rulebook for how matter behaves when squeezed tight. While the data shows a smooth trend so far, the scientists note that they need even more precise measurements at higher energies to see if there is a sudden dip or change in the stopping power, which would be the "smoking gun" for that mysterious phase transition they are hunting for. For now, they have successfully mapped out the behavior of this dense matter at four new energy levels, providing a clearer picture of the universe's most crowded moments.

Technical Summary: Light Hadron Production in Fixed-Target Au+Au Collisions at $\sqrt{s_{NN}} = 3.2\text{--}4.5$ GeV

Problem and Motivation
The primary physics objective of the Beam Energy Scan (BES) program at the Relativistic Heavy Ion Collider (RHIC) is to map the Quantum Chromodynamics (QCD) phase diagram, specifically the region of high baryon chemical potential ( $\mu_B$ ). While lattice QCD calculations indicate a smooth crossover between the Quark-Gluon Plasma (QGP) and hadronic phases at vanishing $\mu_B$ , theoretical models suggest a first-order phase transition line terminating in a critical point at higher $\mu_B$ . This critical point remains experimentally unconfirmed.

BES Phase-I previously mapped the chemical freeze-out line up to $\mu_B \approx 420$ MeV using collider-mode Au+Au collisions ( $\sqrt{s_{NN}} = 7.7\text{--}62.4$ GeV). BES Phase-II extends this investigation by introducing a fixed-target (FXT) configuration, enabling collisions at lower center-of-mass energies ( $\sqrt{s_{NN}} = 3.0\text{--}13.7$ GeV) corresponding to higher $\mu_B$ (up to 720 MeV). This energy regime is critical for exploring the dense baryonic matter region where the QCD critical point may reside. However, the FXT configuration presents experimental challenges, notably the shift of mid-rapidity outside the nominal STAR acceptance at lower energies.

Methodology
This study presents bulk property measurements for Au+Au collisions at four specific FXT energies: $\sqrt{s_{NN}} = 3.2, 3.5, 3.9,$ and $4.5$ GeV. The analysis utilizes data from the STAR experiment, leveraging the upgraded endcap Time-of-Flight (eTOF) and inner Time Projection Chamber (iTPC) to recover mid-rapidity coverage.

Particle Identification (PID): The Time Projection Chamber (TPC) measures energy loss ($dE/dx$) for low-momentum identification, while the Time-of-Flight (TOF) system extends PID to higher momenta.
Corrections: Identified particle yields for $\pi^\pm$ , $K^\pm$ , and $p$ are corrected for detector efficiency, geometric acceptance, and energy loss in experimental material. Notably, feed-down corrections from weak decays (e.g., $\Lambda \to \pi^- + p$ ) are not applied in this specific analysis; the contribution of feed-down protons is estimated at roughly 5% at 3.2 GeV and 20% at 4.5 GeV.
Modeling: Transverse momentum ( $p_T$ ) spectra are fitted simultaneously using a blast-wave model. This model assumes a thermalized source with a transverse flow velocity profile $\beta_T(r) = \beta_s(r/R)^n$ , where the exponent $n$ is fixed to 1. The $\pi^\pm$ spectra are fitted for $p_T > 0.3$ GeV/c to minimize resonance decay contributions.
Parameters Extracted: The fitting procedure yields the kinetic freeze-out temperature ( $T_{kin}$ ) and the surface velocity of the expanding medium ( $\beta_s$ ). Additionally, proton rapidity distributions ($dN/dy$) are analyzed to quantify baryon stopping.

Key Results

Kinetic Freeze-out Parameters:
- Temperature ( $T_{kin}$ ): Across the FXT energy range, $T_{kin}$ exhibits only a weak dependence on both rapidity ( $y_{cm}$ ) and collision energy.
- Surface Velocity ( $\beta_s$ ): In contrast to temperature, the transverse flow velocity $\beta_s$ shows a strong dependence on rapidity, decreasing away from mid-rapidity, while exhibiting only a weak dependence on collision energy.
- Trends: When averaged over $0 < y_{cm} < 0.5$ and compared to BES-I results, the FXT measurements show a trend toward the values observed in collider-mode collisions at $\sqrt{s_{NN}} = 7.7$ GeV as energy increases.
Baryon Stopping:
- Proton rapidity distributions are modeled using two symmetric Gaussians to represent stopped projectile and target participants. The stopping observable is defined as $\Delta y = y_{beam} - |\mu|$ .
- The extracted $\Delta y$ values follow the smooth energy dependence established by previous AGS measurements (specifically E895 at 3.2 and 3.9 GeV). The result at 4.5 GeV lies between E895 and E917 measurements.
- Centrality Dependence: For the most central collisions (0-5%), $\Delta y$ is approximately two-thirds of the beam rapidity across all measured energies. Less central collisions (5-10%, 10-20%) exhibit reduced stopping, consistent with fewer binary nucleon-nucleon interactions and lower longitudinal momentum loss per participant.

Significance and Claims
The paper asserts that these results provide essential input for transport models of heavy-ion collisions in the low-energy, high-baryon-density regime. Specifically, the measurements of $T_{kin}$ , $\beta_s$ , and baryon stopping help constrain the equation of state (EoS) of dense baryonic matter.

The authors note that while a dip in the baryon stopping trend has been theoretically associated with a softening of the EoS and a possible first-order phase transition, the current data does not definitively confirm such a feature. The paper concludes that more precise measurements at higher FXT energies are required to determine if such a feature is present. Future work is planned to extract chemical freeze-out parameters using thermal models (Thermal-FIST, THERMUS) and to include additional particle species to achieve a system-wide characterization of bulk particle production across the full STAR FXT energy range.

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