[Paper Review] Phase Diagram in Quantum Chromodynamics

M. Apostoł|arXiv (Cornell University)|Nov 23, 2013

High-Energy Particle Collisions Research21 references3 citations

TL;DR

This paper proposes that the hadronization of quark-gluon plasma in high-energy nucleus-nucleus collisions is a first-order phase transition governed by a critical curve derived from the van der Waals equation, with a critical point at quark density $ n_c \simeq 1\,\text{fm}^{-3} $ and temperature $ T_c \simeq 200\,\text{MeV} $. The transition arises from thermal expansion of a relativistic quark-gluon plasma, leading to hadronization when the system crosses the critical curve, closely matching nuclear saturation density and temperature.

ABSTRACT

It is suggested that the hadronization of the quark-gluon plasma is a first-order phase transition described by a critical curve in the temperature-(quark) density plane which terminates in a critical point. Such a critical curve is derived from the van der Waals equation and its parameters are estimated by using the theoretical approach given in M. Apostol, Roum. Reps. Phys. 59 249 (2007); Mod. Phys. Lett. B21 893 (2007). The main assumption is that quark-gluon plasma created by high-energy nucleus-nucleus collisions is a gas of ultrarelativistic quarks in equilibrium with gluons (vanishing chemical potential, indefinite number of quarks). This plasma expands, gets cool and dilute and hadronizes at a certain transition temperature and transition density. The transition density is very close to the saturation density of the nuclear matter and, it is suggested that both these points are very close to the critical point n~1fm^{-3} (quark density) and T~200MeV (temperature).

Motivation & Objective

• To model the hadronization of quark-gluon plasma as a first-order phase transition in the temperature-density plane.
• To identify a critical point in the QCD phase diagram using thermodynamic analogies with the van der Waals equation.
• To estimate the critical curve parameters by relating the quark-gluon plasma's expansion and cooling to known nuclear matter saturation properties.
• To link the transition temperature and density to the Compton wavelength and degenerate ultrarelativistic quark gas behavior.

Proposed method

• Derives a critical curve in the $ (n, T) $ plane using the van der Waals equation, assuming a first-order phase transition analogous to liquid-gas transitions.
• Applies the equation $ T = -Bn^2 + An $ to describe the hadronization transition, with $ A $ and $ B $ determined from physical constraints.
• Uses the relation $ T = \hbar c n^{1/3} $ to model the cooling of the expanding quark-gluon plasma along a thermal path.
• Estimates the transition density $ n_t $ from the condition $ \hbar c n_t^{1/3} \simeq f^{-1} m_0 c^2 $, where $ f \simeq 2 \times 10^{-2} $ and $ m_0 \simeq 4\,\text{MeV} $.
• Treats the quark-gluon plasma as a degenerate ultrarelativistic gas with vanishing chemical potential and assumes local thermal equilibrium during expansion.
• Matches the transition point to nuclear saturation density and temperature by setting $ n_t \simeq 1\,\text{fm}^{-3} $, $ T_t \simeq 200\,\text{MeV} $, and solving for $ A $ and $ B $.

Experimental results

Research questions

• RQ1 Can the hadronization of quark-gluon plasma in heavy-ion collisions be described as a first-order phase transition with a critical point?
• RQ2 What is the quantitative form of the phase boundary in the temperature-quark density plane for such a transition?
• RQ3 How do the critical parameters $ n_c $ and $ T_c $ relate to nuclear saturation density and temperature?
• RQ4 To what extent can the van der Waals equation model the QCD phase transition in quark-gluon plasma?
• RQ5 What is the physical origin of the transition density $ n_t \simeq 1\,\text{fm}^{-3} $, and how is it related to quark mass and degeneracy?

Key findings

• The critical point of the QCD phase transition is estimated at $ n_c = 1\,\text{fm}^{-3} $ and $ T_c = 200\,\text{MeV} $, matching nuclear saturation density and temperature.
• The transition curve is described by $ T = -200n^2 + 400n $, derived from the van der Waals equation with $ A = 400 $, $ B = 200 $.
• The transition density $ n_t \simeq 1\,\text{fm}^{-3} $ is obtained from $ n_t = f^{-3} (50\,\text{fm})^{-3} $ with $ f \simeq 2 \times 10^{-2} $, consistent with nuclear force saturation.
• The transition temperature $ T_t \simeq 200\,\text{MeV} $ is derived from $ T_t = f^{-1} T_m $, where $ T_m \simeq 4\,\text{MeV} $, and corresponds to the Compton wavelength of the average quark mass.
• The hadronization occurs at $ R_t \simeq 8R_0 $, after $ t \simeq 5 \times 10^{-23}\,\text{s} $, involving approximately $ 100N_n $ quarks.
• The critical curve intersects the $ n $-axis at $ n = 2\,\text{fm}^{-3} $, and the transition lies on the $ T = 200n^{1/3} $ curve, confirming consistency with the thermal path.