Calculating QCD Phase Diagram Trajectories of Nuclear Collisions using a Semi-analytical Model

At low to moderate collision energies where the parton formation time $\tau_F$ is not small compared to the nuclear crossing time, the finite nuclear thickness significantly affects the energy density $\epsilon(t)$ and net conserved-charge densities such as the net-baryon density $n_B(t)$ produced in heavy ion collisions. As a result, at low to moderate energies the trajectory in the QCD phase diagram is also affected by the finite nuclear thickness. Here, we first discuss our semi-analytical model and its results on $\epsilon(t)$, $n_B(t)$, $n_Q(t)$, and $n_S(t)$ in central Au+Au collisions. We then compare the $T(t)$, $\mu_B(t)$, $\mu_Q(t)$, and $\mu_S(t)$ extracted with the ideal gas equation of state (EoS) with quantum statistics to those extracted with a lattice QCD-based EoS. We also compare the $T-\mu_B$ trajectories with the RHIC chemical freezeout data. Finally, we discuss the effect of transverse flow on the trajectories.