Nuclear interaction models offer a baseline for heavy-ion fluctuation signals

Why particle-number fluctuations matter

Heavy-ion experiments study strongly interacting matter by colliding atomic nuclei at different energies. One quantity of interest is how the net number of baryons—baryons minus antibaryons—varies between collision events. Protons and neutrons are familiar baryons, although the experimentally measured net-proton number is not identical to the full net-baryon number.

Researchers examine more than the average and variance of these distributions. Higher-order measures describe their asymmetry and departures from a Gaussian shape. Such fluctuations may be sensitive to a possible critical point in the phase diagram of quantum chromodynamics, the theory of the strong interaction. Whether that critical point exists, and where it lies, remain unresolved.

The question here is more specific: how much of the observed collision-energy dependence can models of nuclear attraction and repulsion reproduce?

Calculating the response of nuclear matter

The study uses relativistic mean-field models, in which nucleons move through averaged fields representing meson-mediated interactions. A scalar field supplies attraction and reduces the effective nucleon mass; a vector field supplies repulsion. Nonlinear interactions among these fields distinguish the different model parameterizations.

The authors derive analytical expressions for baryon-number susceptibilities through fourth order. These quantities measure how pressure responds to changes in baryon chemical potential at fixed temperature. Chemical potential is a thermodynamic variable controlling the preference for adding baryon number to the system.

Crucially, the calculation includes how the mean fields themselves change with chemical potential. The fields must respond consistently with the matter they describe, rather than being held artificially fixed while pressure is differentiated. Analytical derivative expressions therefore work alongside the solution of the model’s field equations and momentum integrals; this is not a measurement of fluctuations in individual simulated collisions.

Seven parameter sets are compared: NL3, GM1, TM1, TM1e, FSU, FSU2 and FSU2R. They span different equations of state—the relationships among pressure, energy density and other thermodynamic properties. A stiffer equation of state generally produces more pressure at a given energy density.

For the heavy-ion calculations, the authors set the electric-charge and strangeness chemical potentials to zero. In this isospin-symmetric setup, the isovector mean field vanishes. Their separate neutron-star comparisons instead concern cold, charge-neutral matter in beta equilibrium. The two applications therefore do not describe identical physical conditions.

Similar trends, different low-energy predictions

To connect the equilibrium calculations with collision energies, the researchers adopt an existing chemical freeze-out parameterization. This assigns a temperature and baryon chemical potential to each beam energy using conditions inferred from hadron-yield analyses.

They then calculate three susceptibility ratios: χ3/χ1, χ3/χ2 and χ4/χ2. The latter two correspond to commonly studied combinations involving skewness and kurtosis, rather than to the unscaled shape measures alone.

All seven models produce broadly similar qualitative trends. The skewness-related ratio χ3/χ2 decreases as collision energy rises. The kurtosis-related ratio χ4/χ2 is non-monotonic: it falls toward a minimum and subsequently rises, approaching unity at high energies near 200 GeV. The χ3/χ1 ratio also develops a minimum near 5 GeV.

Model predictions separate most clearly at low collision energies, particularly around and below 5 GeV. At high energies, their predictions become much more alike. Within this framework, lower-energy measurements consequently offer greater leverage for distinguishing the nuclear interactions.

What the comparison establishes

The authors compare their predictions with published STAR fluctuation measurements using an average absolute fractional deviation for each observable. Adding the three reported deviations gives 0.371 for FSU, 0.401 for FSU2 and 0.404 for FSU2R, compared with 1.005 for NL3. Smaller values indicate closer agreement under this particular measure.

These scores are not an uncertainty-weighted statistical fit. They do not by themselves establish that one model is decisively preferred. Nor should agreement between calculated net-baryon fluctuations and measured net-proton observables be read as an exact identification of the two quantities.

FSU has the smallest combined fluctuation-deviation score. The authors nevertheless highlight FSU2R when considering nuclear-matter properties and neutron-star observations alongside the collision results. Those are distinct selection criteria, not contradictory rankings.

The analysis includes nucleons but not hyperons, which the authors identify as a possible extension. It provides an equilibrium, mean-field baseline showing that conventional hadronic interactions can generate non-monotonic fluctuation patterns; it does not locate or demonstrate a QCD critical point.

This article is based on the complete supplied paper text and original metadata for arXiv version 1, submitted on 6 November 2026. The source is a preprint, not an established peer-reviewed result.