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

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, which includes both hadron resonances from the PDG book and string degrees of freedom. 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 high statistics experimental data at mid-central Au $+$ Au collisions in the beam energy range 2.5<√sNN<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, √sNN<10 GeV. This is interesting, as 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 √sNN<3 GeV, whereas the directed flow is most sensitive to the effective baryon mass at saturation density at 3<√sNN<5 GeV. This self-consistent relativistic N-body hadronic transport approach describes well the experimental flow data up to higher beam energies, √sNN<10 GeV, by a stiff, monotonous EoS. Matters abruptly change in the next higher energy range, √sNN10--20 GeV: the directed flow data show a double change of sign of the slope of v₁, 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 v₁ 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.