The thermodynamics for a hadronic gas of fireballs with internal color structures and chiral fields

TL;DR

This paper analyzes the thermodynamics of a hadronic gas with internal color structures and chiral fields, revealing phase transitions from hadronic states to quark-gluon plasma, including a third order transition at the Hagedorn point.

Contribution

It provides a detailed review of the thermodynamical partition function for color-singlet bags with various particle statistics, exploring phase transitions and the role of chiral symmetry.

Findings

Identification of a third order phase transition at the Hagedorn threshold.

Hagedorn states appear just above the known hadronic spectrum.

A subsequent first order transition to quark-gluon plasma is observed.

Abstract

The thermodynamical partition function for a gas of color-singlet bags consisting of fundamental and adjoint particles in both $U(N_c)$ and $SU(N_c)$ group representations is reviewed in detail. The constituent particle species are assumed to satisfy various thermodynamical statistics. The gas of bags is probed to study the phase transition for a nuclear matter in the extreme conditions. These bags are interpreted as the Hagedorn states and they are the highly excited hadronic states which are produced below the phase transition point to the quark-gluon plasma. The hadronic density of states has the Gross-Witten critical point and exhibits a third order phase transition from a hadronic phase dominated by the discrete low-lying hadronic mass spectrum particles to another hadronic phase dominated by the continuous Hagedorn states. The Hagedorn threshold production is found just above the highest known experimental discrete low-lying hadronic mass spectrum. The subsequent Hagedorn phase undergoes a first order deconfinement phase transition to an explosive quark-gluon plasma. The role of the chiral phase transition in the phases of the discrete low-lying mass spectrum and the continuous Hagedorn mass spectrum is also considered. It is found crucial in the phase transition diagram. Alternate scenarios are briefly discussed for the Hagedorn gas undergoes a higher order phase transition through multi-processes of internal color-flavor structure modification.