# Sensitivity of the excitation functions of collective flow to relativistic scalar and vector meson interactions in the relativistic quantum molecular dynamics model RQMD.RMF

## TL;DR

This paper develops a relativistic quantum molecular dynamics model with scalar and vector meson interactions, analyzing its ability to reproduce flow data in heavy-ion collisions and suggesting a possible phase transition in high-density QCD matter.

## Contribution

It introduces the RQMD.RMF model with scalar and vector meson interactions into transport simulations and compares its predictions to experimental flow data across a wide energy range.

## Key findings

- The model describes the energy dependence of directed and elliptic flow from 2.5 to 20 GeV.
- Elliptic flow is sensitive to nuclear incompressibility at low energies.
- Directed flow shows a double sign change at high energies, indicating a possible phase transition.

## Abstract

Relativistic quantum molecular dynamics with scalar and vector interactions based on the relativistic mean meson field theory, RQMD.RMF, is developed.It is implemented into the microscopic transport code JAM.The sensitivity of the directed and of the elliptic proton flow in high energy heavy-ion collisions on the stiffness of the RMF equation of state (EoS) is examined. These new calculations are compared to experimental data at mid-central Au + Au collisions in the beam energy range $2.5 < \sqrt{s_{NN}} < 20$ GeV. This new RQMD model with the relativistic mean field scalar and vector meson interactions does describe consistently, with one RMF parameter set,the beam energy dependence of both the directed flow and the elliptic flow,from SIS18 to AGS and RHIC BES-II energies, $\sqrt{s_{NN}}< 10$ GeV.There are different sensitivities of these different kinds of flow to the EoS: elliptic flow is most sensitive to the nuclear incompressibility constant,at the moderate beam energies $\sqrt{s_{NN}}<3$ GeV,whereas the directed flow is most sensitive to the effective baryon mass at saturation density at $3< \sqrt{s_{NN}}<5 $ GeV. Matters abruptly change in the next higher energy range,$\sqrt{s_{NN}}\gtrsim 10-20$ GeV:the directed flow data show a double change of sign of the slope of $v_1$, inverting twice in this energy range,in sudden contradiction to the RQMD.RMF calculation for a monotonous, stiff EoS. This surprising oscillating behavior,a double change of sign of the $v_1$ slope, points to the appearance of a hitherto unknown first-order phase transition in excited QCD matter at high baryon densities in mid-central Au + Au collisions.