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

Authors

  • Zi-Wei Lin East Carolina University
  • Todd Mendenhall East Carolina University

DOI:

https://doi.org/10.31349/SuplRevMexFis.3.040920

Keywords:

Quark-gluon plasma, QCD phase diagram, chemical potential, equation of state, high baryon density

Abstract

The finite nuclear thickness affects the energy density (t) and conserved-charge densities such as the net-baryon density nB(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 µ(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-µB 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 є(t), nB(t), nQ(t), and nS(t). Then, we will show the extracted T(t), µB(t), µQ(t), and µS(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-µB 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.

References

M. A. Stephanov, QCD phase diagram and the critical point, Prog. Theor. Phys. Suppl. 153 (2004) 139, 10.1142/S0217751X05027965

M. M. Aggarwal et al., Higher Moments of Net-proton Multiplicity Distributions at RHIC, Phys. Rev. Lett. 105 (2010) 022302, 10.1103/PhysRevLett.105.022302

J. Adam et al., Nonmonotonic Energy Dependence of NetProton Number Fluctuations, Phys. Rev. Lett. 126 (2021) 092301, 10.1103/PhysRevLett.126.092301

I. C. Arsene, et al., Dynamical phase trajectories for relativistic nuclear collisions, Phys. Rev. C 75 (2007) 034902, 10.1103/PhysRevC.75.034902

H.-S. Wang, et al., Thermodynamics of partonic matter in relativistic heavy-ion collisions from a multiphase transport model, Phys. Rev. C 105 (2022) 034912, 10.1103/PhysRevC.105.034912

J. Noronha-Hostler, et al., Lattice-based equation of state at finite baryon number, electric charge and strangeness chemical potentials, Phys. Rev. C 100 (2019) 064910, 10.1103/PhysRevC.100.064910

T. Mendenhall and Z.-W. Lin, Semi-analytical calculation of the trajectory of relativistic nuclear collisions in the QCD phase diagram, arXiv:2111.13932 [nucl-th] (2021)

A web interface that performs our semi-analytical calculation is available at http://myweb.ecu.edu/linz/densities/ (2022)

J. D. Bjorken, Highly Relativistic Nucleus-Nucleus Collisions: The Central Rapidity Region, Phys. Rev. D 27 (1983) 140, 10.1103/PhysRevD.27.140

Z.-W. Lin, Extension of the Bjorken energy density formula of the initial state for relativistic heavy ion collisions, Phys. Rev. C 98 (2018) 034908, 10.1103/PhysRevC.98.034908

T. Mendenhall and Z.-W. Lin, Calculating the initial energy density in heavy ion collisions by including the finite nuclear thickness, Phys. Rev. C 103 (2021) 024907, 10.1103/PhysRevC.103.024907

J. Grefa, et al., Hot and dense quark-gluon plasma thermodynamics from holographic black holes, Phys. Rev. D 104 (2021) 034002, 10.1103/PhysRevD.104.034002

W.-j. Fu, J. M. Pawlowski, and F. Rennecke, QCD phase structure at finite temperature and density, Phys. Rev. D 101 (2020) 054032, 10.1103/PhysRevD.101.054032

Downloads

Published

2022-12-10

How to Cite

1.
Lin Z-W, Mendenhall T. A Semi-analytical Method of Calculating Nuclear Collision Trajectory in the QCD Phase Diagram. Supl. Rev. Mex. Fis. [Internet]. 2022 Dec. 10 [cited 2023 Feb. 6];3(4):040920 1-5. Available from: https://rmf.smf.mx/ojs/index.php/rmf-s/article/view/6842