A Semi-analytical Method of Calculating Nuclear Collision Trajectory in the QCD Phase Diagram

TL;DR

This paper introduces a semi-analytical method to accurately calculate the trajectories of nuclear collisions in the QCD phase diagram by incorporating nuclear thickness effects, especially relevant at low to moderate energies.

Contribution

The paper presents a novel semi-analytical approach that includes nuclear thickness effects to determine temperature and chemical potential trajectories in the QCD phase diagram.

Findings

The method effectively computes densities and thermodynamic variables including temperature and chemical potentials.

Results show the impact of nuclear thickness on the T-μB trajectories at low energies.

The approach aids in exploring the possible location of the QCD critical end point.

Abstract

The finite nuclear thickness affects the energy density $\epsilon(t)$ and conserved-charge densities such as the net-baryon density $n_B(t)$ produced in heavy ion collisions. While the effect is small at high collision energies where the Bjorken energy density formula for the initial state is valid, the effect is large at low collision energies, where the nuclear crossing time is not small compared to the parton formation time. The temperature $T(t)$ and chemical potentials $\mu(t)$ of the dense matter can be extracted from the densities for a given equation of state (EOS). Therefore, including the nuclear thickness is essential for the determination of the $T$-$\mu_B$ trajectory in the QCD phase diagram for relativistic nuclear collisions at low to moderate energies such as the RHIC-BES energies. In this proceeding, we will first discuss our semi-analytical method that includes the nuclear thickness effect and its results on the densities $\epsilon(t), n_B(t), n_Q(t)$, and $n_S(t)$. Then, we will show the extracted $T(t), \mu_B(t), \mu_Q(t)$, and $\mu_S(t)$ for a quark-gluon plasma using the ideal gas EOS with quantum or Boltzmann statistics. Finally, we will show the results on the $T$-$\mu_B$ trajectories in relation to the possible location of the QCD critical end point. This semi-analytical model provides a convenient tool for exploring the trajectories of nuclear collisions in the QCD phase diagram.