Glauber predictions for oxygen and neon collisions at energies available at the LHC

This paper presents an updated version of the TGlauberMC Monte Carlo code (v3.3) with improved nuclear density profiles and nucleon substructure treatments to provide precise predictions for initial-state observables and centrality-dependent multiplicity in upcoming oxygen-oxygen, neon-neon, and proton-oxygen collisions at the LHC.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle smasher. Usually, scientists crash together massive "boulders" made of lead atoms to study a super-hot, liquid-like state of matter called the Quark-Gluon Plasma (QGP), which existed just after the Big Bang.

But recently, scientists have started smashing together much smaller "pebbles"—specifically, Oxygen and Neon atoms. The question is: Can you make this special plasma with such tiny rocks? To answer this, we need to know exactly what happens the instant these atoms collide.

This paper is essentially a new, upgraded instruction manual for a computer program called TGlauberMC. Think of this program as a sophisticated "crash simulator" that predicts how two atomic nuclei will look and behave the moment they hit each other.

Here is a breakdown of what the author, Constantin Loizides, has done in simple terms:

1. The Problem: The Old Map Wasn't Detailed Enough

For years, scientists have used a standard model (the Glauber model) to guess the shape of these collisions. It's like trying to predict the splash of a water balloon by assuming the balloon is a perfect, smooth sphere. But real atoms aren't perfect spheres; they are fuzzy, lumpy, and their insides (nucleons) are jiggling around.

When you smash tiny atoms like Oxygen (16 particles) or Neon (20 particles), those little lumps and jiggles matter a lot. The old "smooth sphere" map wasn't accurate enough for these small systems.

2. The Solution: A High-Definition Upgrade (v3.3)

The author has released version 3.3 of the simulator. He didn't just tweak the numbers; he completely overhauled how the program sees the atoms.

• New Blueprints: He updated the "blueprints" (density profiles) for Oxygen and Neon. Instead of assuming they are smooth balls, the new version uses complex math to account for how the particles inside might cluster together (like how water molecules might clump in a specific way).
• Smearing the Edges: In the old days, the program assumed particles hit like hard billiard balls. The new version admits that particles are more like fuzzy clouds. It uses a "smearing" technique to account for the fact that the edge of a nucleus isn't a sharp line but a soft gradient.

3. The Predictions: What Happens at 5.36 TeV?

The paper focuses on collisions scheduled for July 2025 at the LHC, where Oxygen-Oxygen (OO) and Neon-Neon (NeNe) atoms will smash together at incredible speeds.

• The Size of the Crash: The author calculated exactly how big the "cross-section" (the effective target area) is for these crashes. He found that if you treat the atoms as fuzzy clouds rather than hard balls, the collision area gets slightly bigger (about 1.5% to 2% larger).
• The Shape of the Debris: When two round atoms collide, they don't always hit dead-center. If they graze each other, the overlap looks like a football (oval). The program predicts how "oval" (eccentric) this shape is.
  • Why does this matter? In the world of heavy-ion physics, the more oval the collision, the more the resulting plasma swirls. The author predicts that Neon collisions will create a slightly more oval shape than Oxygen collisions, which helps scientists understand if the "swirl" (flow) is caused by the initial shape or something else.
• Counting the Particles: The paper predicts how many new particles will be created in the crash. By comparing the new Oxygen/Neon predictions to existing data from larger Lead-Lead crashes, the author estimates that Oxygen and Neon will produce a specific, predictable number of particles depending on how "central" (head-on) the crash is.

4. The "Alpha Cluster" Mystery

A key theme in the paper is the idea of Alpha Clusters.

• The Analogy: Imagine an Oxygen atom isn't just a bag of 16 random marbles. Instead, it might be made of 4 distinct "clumps" (Alpha particles), like a tetrahedron (a pyramid shape).
• The Simulation: The new software allows scientists to test two scenarios: one where the Oxygen atom is a smooth bag of marbles, and one where it's made of these 4 distinct clumps. The paper shows that if the "clump" theory is true, it changes the shape of the collision significantly. This gives experimentalists a way to test if nature really builds Oxygen this way.

5. The Takeaway

This paper doesn't claim to have discovered a new particle or solved the mystery of the universe. Instead, it provides the heavy-duty toolkit the physics community needs to interpret the upcoming data.

It's like a cartographer drawing a new, highly detailed map of a coastline before a fleet of ships arrives. The author says, "Here is the most accurate map we have of how Oxygen and Neon atoms look when they crash. When the LHC data comes in next year, use this map to figure out what's really happening inside the crash."

The code is now public, allowing other scientists to run their own simulations and check these predictions against the real-world crashes happening in July 2025.

Technical Summary

Technical Summary: Glauber Predictions for Oxygen and Neon Collisions at LHC Energies

Problem Statement
The study of high-energy nuclear collisions aims to characterize the Quark-Gluon Plasma (QGP). While QGP signatures such as collective flow and jet quenching are well-established in large systems (AuAu, PbPb), their presence in small systems (pp, pPb) remains a subject of intense debate, particularly regarding the absence of observed jet quenching in small systems. To bridge the gap between small and large systems, the Large Hadron Collider (LHC) scheduled Oxygen-Oxygen (OO) and Neon-Neon (NeNe) collisions at a center-of-mass energy per nucleon pair of $\sqrt{s_{NN}} = 5.36$ TeV in July 2025. Additionally, Proton-Oxygen (pO) collisions at $\sqrt{s_{NN}} = 9.62$ TeV were proposed to refine hadronic interaction models for cosmic-ray physics. A critical prerequisite for interpreting these future measurements is a precise theoretical description of the initial state, specifically the nuclear geometry, fluctuations, and cross sections. Standard Glauber Monte Carlo (MCG) models require updated parameterizations for light nuclei like $^{16}$O and $^{20}$Ne, which may exhibit $\alpha$-cluster structures and significant density fluctuations not captured by traditional smooth density profiles.

Methodology
The paper presents an updated version (v3.3) of the TGlauberMC Monte Carlo code, a widely used framework for calculating initial conditions in heavy-ion collisions. The methodology involves:

1. Nuclear Density Profiles: The author incorporates a comprehensive set of nuclear density parameterizations for $^{16}$O and $^{20}$Ne. These include:

   • Standard 3-parameter Fermi (3pF) and Harmonic Oscillator (HO) fits to electron scattering data.
   • Profiles derived from ab-initio calculations, specifically the NNLOsat chiral Hamiltonian calculation and explicit nucleon configurations from Nuclear Lattice Effective Field Theory (NLEFT) and the Projected Generator Coordinate Method (PGCM).
   • Explicit treatment of $\alpha$-clustering (both enforced and non-enforced) to investigate its impact on initial geometry.
   • A "reweighting" procedure is applied to counteract biases introduced by enforcing a minimum inter-nucleon separation ($d_{min} = 0.4$ fm) and recentering the nucleus.

2. Nucleon-Nucleon Overlap: The model moves beyond the "hard-sphere" approximation ($\omega = 0$) for the nucleon-nucleon interaction probability. It utilizes the $\Gamma$-parametrization (Eq. 5), which interpolates between hard-sphere and Gaussian profiles via a parameter $\omega$. The paper analyzes the sensitivity of cross sections to $\omega$ and compares results with TRENTO, HIJING, and PYTHIA tunes. A value of $\omega = 0.3$ is selected based on consistency with existing LHC cross-section data (PbPb, pPb).

3. Particle Production Modeling: To predict charged-particle multiplicity ($dN/d\eta$), the paper employs a two-component model combining contributions from participant nucleons ($N_{part}$) and binary collisions ($N_{coll}$). Alternatively, it utilizes the number of multiple parton interactions ($N_{mpi}$) as implemented in HIJING, which correlates strongly with event multiplicity and allows for centrality classification without relying solely on geometric $N_{coll}$.

4. Simulation: The code calculates geometric cross sections, distributions of $N_{part}$, $N_{coll}$, and eccentricity moments ($\varepsilon_2, \varepsilon_3, \varepsilon_4$) for OO, NeNe, pO, pPb, and PbPb collisions.

Key Contributions

• TGlauberMC v3.3 Release: The author provides a publicly available, updated version of the TGlauberMC code (v3.3.2) that includes revised nuclear density profiles, enhanced nucleon substructure treatment, and smearing capabilities compatible with TRENTO initial conditions.
• Comprehensive Density Library: The paper catalogs and evaluates numerous density profiles for Oxygen and Neon, including explicit ab-initio configurations (NLEFT, PGCM) and exact NNLOsat results, quantifying the spread in predicted observables arising from nuclear structure uncertainties.
• Cross Section Predictions: Geometric cross sections for OO, NeNe, and pO collisions are calculated and corrected for the nucleon-nucleon overlap profile (using $\omega=0.3$), providing values with associated uncertainties that align with existing LHC measurements for larger systems.
• Initial State Observables: Detailed predictions are provided for the centrality dependence of $N_{part}$, $N_{coll}$, and eccentricity moments. Crucially, the paper calculates the ratio of eccentricities $\varepsilon_2^{NeNe}/\varepsilon_2^{OO}$, which serves as a proxy for the ratio of elliptic flow coefficients ($v_2$) in these systems, a key test for the QGP paradigm.

Results

• Cross Sections: The predicted geometric cross sections at $\sqrt{s_{NN}} = 5.36$ TeV are $\sigma_{OO} \approx 1.36$ b and $\sigma_{NeNe} \approx 1.73$ b (with $\omega=0.3$). For pO at 9.62 TeV, $\sigma_{pO} \approx 481$ mb. These values include a relative uncertainty of roughly 3–7% depending on the system and profile choice.
• Fluctuations: The spread in $N_{coll}$ and $N_{part}$ distributions due to different nuclear density profiles is significant, reaching 5–10% for $N_{coll}$ and up to 15% for eccentricity in central collisions.
• Eccentricity Ratios: The ratio of participant eccentricity $\varepsilon_2^{NeNe}/\varepsilon_2^{OO}$ is predicted to be approximately 1.05 in central collisions, rising to 1.10–1.15 in peripheral collisions. This ratio is found to be robust against Gaussian smearing and the choice of overlap function (TRENTO vs. arithmetic mean).
• Multiplicity Predictions: Using existing data from XeXe and PbPb collisions at similar energies, the paper predicts the mid-rapidity charged-particle multiplicity per participant pair ($2/N_{part} \cdot dN/d\eta$) for OO and NeNe collisions. The predictions follow a two-component fit, with values around 7.3–7.8 for central collisions, decreasing to $\sim 5.4$ for peripheral collisions.
• Substructure Impact: Configurations including explicit $\alpha$-clustering (e.g., TR_OXYGEN_V15) exhibit a dip in nuclear charge density at small radii, leading to distinct differences in initial-state observables compared to smooth density profiles.

Significance
The paper positions TGlauberMC v3.3 as a robust and flexible tool for the heavy-ion community to interpret upcoming data from OO and NeNe collisions at the LHC. By providing precise predictions for initial-state geometry and cross sections, the work enables experimentalists to disentangle system-size effects from nuclear structure effects (such as $\alpha$-clustering) in the final-state flow measurements. The author notes that the availability of OO data from both RHIC (200 GeV) and LHC (5.36 TeV) offers a unique opportunity to explore particle production and collective flow across a wide energy range, for which this updated model is intended to serve as a foundational reference. The paper does not claim to prove the existence of QGP in small systems but rather provides the necessary geometric baseline to test the "minimal conditions" for QGP formation and the onset of jet quenching.