# RMF models with $\sigma$-scaled hadron masses and couplings for description of heavy-ion collisions below 2A GeV

## TL;DR

This paper extends relativistic mean-field models with density-dependent hadron masses and couplings to finite temperatures, analyzing nuclear matter properties relevant for heavy-ion collisions below 2A GeV, including phase transitions and particle ratios.

## Contribution

It introduces finite-temperature extensions of existing models with hadron mass and coupling dependencies, and studies their implications for heavy-ion collision observables and phase transitions.

## Key findings

- Models reproduce thermodynamic characteristics of the liquid-gas phase transition.
- Effects of $elta$ resonances and pion interactions on particle ratios are quantified.
- Thermodynamic properties align with experimental data.

## Abstract

Within the relativistic mean-field framework with hadron masses and coupling constants dependent on the mean scalar field we study properties of nuclear matter at finite temperatures, baryon densities and isospin asymmetries relevant for heavy-ion collisions at laboratory energies below 2$A$ GeV. Previously constructed (KVORcut-based and MKVOR-based) models for the description of the cold hadron matter, which differ mainly by the density dependence of the nucleon effective mass and symmetry energy, are extended for finite temperatures. The baryon equation of state, which includes nucleons and $\Delta$ resonances is supplemented by the contribution of the pion gas described either by the vacuum dispersion relation or with taking into account the $s$-wave pion-baryon interaction. Distribution of the charge between components is found. Thermodynamical characteristics on $T-n$ plane are considered. The energy-density and entropy-density isotherms are constructed and a dynamical trajectory of the hadron system formed in heavy-ion collisions is described. The effects of taking into account the $\Delta$ isobars and the $s$-wave pion-nucleon interaction on pion differential cross sections, pion to proton and $\pi^-/\pi^+$ ratios are studied. The liquid-gas first-order phase transition is studied within the same models in isospin-symmetric and asymmetric systems. We demonstrate that our models yield thermodynamic characteristics of the phase transition compatible with available experimental results. In addition, we discuss the scaled variance of baryon and electric charge in the phase transition region. Effect of the non-zero surface tension on spatial redistribution of the electric charge is considered for a possible application to heavy-ion collisions at low energies.