Neutron Stars consistent Equations of State with Phase Transitions and their Impact in Heavy Ion Collision Observables

Abstract

We explore the impact of different equations of state (EoS) on heavy ion collision observables using a Chiral Mean Field (CMF) framework constrained by astrophysical and lattice QCD inputs. The investigated family of EoS simultaneously reproduce neutron stars with masses above two solar masses and exhibit a first order phase transition around two times the nuclear saturation density. This is achieved by varying the relative vector and scalar couplings of $Δ$ resonances with the scalar $σ$ and vector $ω$ fields with respect to nucleons. These EoS are compared to the QCD trace anomaly at finite temperature. We implement both, the default CMF EoS and the modified EoS featuring a phase transition into the UrQMD transport model to study the effects of the phase transition on a qualitative and quantitative level. In particular Au+Au collisions at beam energies of 0.5-3 GeV, the GSI/FAIR energy range of the HADES and CBM experiments, shows visible sensitivity on the EoS. Transverse momentum distributions for protons, the directed flow ($v_1$) and its slope near mid-rapidity for $π^+$ as well as the $K^+/π^+$ ratio is analyzed. Clear differences emerge between the results obtained with the default CMF EoS, the modified EoS, and the cascade mode, particularly the slope of $v_1$ of the pions and in strangeness production. These findings demonstrate the sensitivity of heavy ion observables to the nuclear EoS and highlight potential experimental signatures of a phase transition.