Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Liberation of dynamical quarks at high temperature

Vladimir Voronin

TL;DR

The paper addresses how to formulate thermodynamics for confining QCD-like matter by focusing on hadronic collective excitations in a background that enforces analytic confinement. It develops a mean-field model with a homogeneous Abelian self-dual background, derives a gap equation for an effective quark mass, and uses bosonization to obtain an effective meson action whose masses follow from a pole condition. Finite-temperature behavior is described by a free energy $F(T,\Lambda)$ that combines a zero-temperature part with a thermal meson gas, with the background field strength $\Lambda$ acting as an order parameter for both confinement and chiral symmetry breaking; deconfinement occurs when the free-energy minima become degenerate, yielding a rough critical temperature around $T_c \approx 134$ MeV. The framework reproduces a qualitative hadron-resonance-gas picture below $T_c$ and illustrates how nonperturbative vacuum structure governs thermodynamics, while acknowledging limitations from the simplified vacuum field and the need to incorporate more hadronic states and interactions.

Abstract

Confinement of dynamical fields can be attributed to the absence of corresponding asymptotic states. Thermodynamical properties of such system are more appropriately formulated in terms of collective excitations of these fields, if they appear as particles. This mechanism is investigated in the mean-field quark model of confinement and hadronization. In this model, deconfinement and restoration of chiral symmetry happen simultaneously at certain critical temperature.

Liberation of dynamical quarks at high temperature

TL;DR

The paper addresses how to formulate thermodynamics for confining QCD-like matter by focusing on hadronic collective excitations in a background that enforces analytic confinement. It develops a mean-field model with a homogeneous Abelian self-dual background, derives a gap equation for an effective quark mass, and uses bosonization to obtain an effective meson action whose masses follow from a pole condition. Finite-temperature behavior is described by a free energy that combines a zero-temperature part with a thermal meson gas, with the background field strength acting as an order parameter for both confinement and chiral symmetry breaking; deconfinement occurs when the free-energy minima become degenerate, yielding a rough critical temperature around MeV. The framework reproduces a qualitative hadron-resonance-gas picture below and illustrates how nonperturbative vacuum structure governs thermodynamics, while acknowledging limitations from the simplified vacuum field and the need to incorporate more hadronic states and interactions.

Abstract

Confinement of dynamical fields can be attributed to the absence of corresponding asymptotic states. Thermodynamical properties of such system are more appropriately formulated in terms of collective excitations of these fields, if they appear as particles. This mechanism is investigated in the mean-field quark model of confinement and hadronization. In this model, deconfinement and restoration of chiral symmetry happen simultaneously at certain critical temperature.
Paper Structure (7 sections, 55 equations, 3 figures)

This paper contains 7 sections, 55 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Effective quark mass
  3. Bosonization
  4. Free energy
  5. Discussion
  6. Evaluation of quark one-loop zero-temperature free energy
  7. Contribution of mesons to zero-temperature free-energy

Figures (3)

  • Figure 1: Total free energy $F(T,\Lambda)$ given by Eq. \ref{['free_energy_nonzero']} at different values of temperature. The zero-temperature part is given by formula \ref{['free_energy_zero_one-loop']}. The minima become degenerate at certain critical temperature.
  • Figure 2: Dependence of the background field strength found by minimizing free energy \ref{['free_energy_nonzero']}. The value of $\Lambda(0)=\Lambda_\text{min}$ is given by Eq. \ref{['parameters']}. Solid line corresponds to the stable phase, dotted line corresponds to the metastable one.
  • Figure 3: A series of diagrams contributing to zero-temperature free-energy. The LHS is derived from Eq. \ref{['functional_gluons_integrated_truncated']}, and the RHS is given by formula \ref{['free_energy_zero_mesons_series']}.