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

TL;DR

This work presents TGlauberMC v3.3, an updated Monte Carlo Glauber implementation tailored for small-to-intermediate nuclear systems, with refined OO, NeNe, and pO initial-state modeling at LHC energies. It integrates diverse nuclear density parameterizations, including NNLO$_{sat}$ and Trajectum-derived NLEFT/PGCM densities, and a flexible transverse overlap function framework (Gamma, TRENTO, HIJING, PYTHIA) to generate event-by-event geometries and observables such as $N_{\rm part}$, $N_{\rm coll}$, and $\varepsilon_n$. The paper provides cross-section predictions at $\sqrt{s_{NN}}=5.36$ TeV for OO and NeNe and at $9.62$ TeV for pO, exploring the impact of overlap-profile choices on centrality and fluctuations, and presents MPI-based particle production predictions to connect initial geometry with mid-rapidity multiplicity. A key finding is that the ratio $\varepsilon_2^{\rm NeNe}/\varepsilon_2^{\rm OO}$ can reach $\sim 1.15$ depending on the density profile, offering a robust, testable proxy for the QGP geometry paradigm in small systems. The updated TGlauberMC, along with the new Trajectum-based nucleus generator (TrNucGen), provides a publicly available, flexible tool for interpreting small-system collision data and exploring the onset of collective phenomena across system sizes.

Abstract

The Glauber model is a widely used framework for describing the initial conditions in high-energy nuclear collisions. TGlauberMC is a Monte Carlo implementation of this model that enables detailed, event-by-event calculations across various collision systems. In this work, I present an updated version of TGlauberMC (3.3), which incorporates recent theoretical developments and improved parameterizations, especially relevant for small collision systems. I focus on the oxygen-oxygen (OO), neon-neon (NeNe), and proton-oxygen (pO) collisions at the Large Hadron Collider (LHC) in July 2025, where precise modelling of nuclear geometry and fluctuations is essential. The updated version includes revised nuclear density profiles and an enhanced treatment of nucleon substructure. Geometrical cross sections for all relevant collision systems are calculated and initial-state observables are explored to provide predictions for particle production trends at $\sqrt{s_{\rm nn}}$=5.36 TeV. In particular, a prediction for the centrality dependence of mid-rapidity multiplicity in OO and NeNe collisions is obtained. The updated code is publicly available to support the heavy-ion community with a robust and flexible tool for studying strongly interacting matter in small and intermediate-sized nuclear systems.

Figures (17)

• Figure 1: Nucleon--nucleon impact parameter distribution (left) and interaction probability (right) at 5.36 TeV shown for the different transverse overlap functions ($\Gamma$-parameterization with $0\le\omega\le1$, TRENTO with $0.4\le w\le0.7$, HIJING and PYTHIA tune Monash) as discussed in the text. The thin dashed line indicates the hard-sphere approximation.
• Figure 2: Nuclear charge density for $^{16}$O versus radius for various descriptions compared to data from electron scattering Sick:1970ma. As explained in the text, "Oho2" is a parameterization based on the HO model, whose parameters are fit to the data, while "Odat" was already provided in Sick:1970ma. "Osat" is the exact result of the NNLOsat calculation Soma:2019bso), and "Opar2" the respective 3pF fit. "Opar" and "Oho" profiles were previously included in TGlauberMC. The distributions are normalized as $\int \rho\,r^2\,{\rm d}r=Ze$. The respective $r_{\rm rms}$ values are given in the legend, denoted as $s$.
• Figure 3: Nuclear charge density for $^{16}$O (left) and $^{20}$Ne (right) versus radius obtained with TGlauberMC for the various parameterizations discussed in the text. The respective $r_{\rm rms}$ values are given in the legend, denoted as $s$. In case of oxygen, the calculated densities are compared to the fit of the data ("Oho2").
• Figure 4: Calculated cross sections for OO collisions (left) and NeNe collisions (right) at 5.36 TeV using TGlauberMC with $d_{\rm min}=0.4$ fm, and $\omega=0.0$ (hard-sphere approximation), using the nuclear profiles and nucleon configurations as described in Sec. \ref{['sec:nuclearprof']}. The average as well as the average $\pm$ the standard deviation are shown as vertical lines. (The same figures including available, but non-meaningful nuclear density profiles are shown in extra Fig. \ref{['fig:extraxsec']}).
• Figure 5: Dependence of the calculated cross sections on $\omega$ for OO collisions at 5.36 TeV using TGlauberMC with the $\Gamma$-parametrization of the nucleon--nucleon overlap profile Eq. (\ref{['eq:NN_coll_profile']}). Results using HIJING, PYTHIA (Monash) and TRENTO with $w=0.5$ overlap profiles are given by the thin lines.