The Hagedorn-type structure of the non-perturbative gluon pressure within the mass gap approach to QCD

TL;DR

This paper demonstrates that the non-perturbative gluon pressure in QCD exhibits a Hagedorn-type exponential spectrum related to the mass gap, with a characteristic temperature indicating a phase transition and specific high-temperature behavior.

Contribution

It reveals the Hagedorn-type structure of the gluon pressure and identifies the transition temperature with the Hagedorn temperature within the mass gap approach to QCD.

Findings

Gluon pressure has a maximum at T_c=266.5 MeV.

Exponential suppression of pressure as T approaches 0.

Exponential rise in degrees of freedom near T_c.

Abstract

We have shown in detail that the low-temperature expansion for the non-perturbative gluon pressure has the Hagedorn-type structure. Its exponential spectrum of all the effective gluonic excitations are expressed in terms of the mass gap. It is this which is responsible for the large-scale dynamical structure of the QCD ground state. The non-perturbative gluon pressure properly scaled has a maximum at some characteristic temperature $T=T_c = 266.5 \ \MeV$, separating the low- and high temperature regions. It is exponentially suppressed in the $T \rightarrow 0$ limit. In the $T \rightarrow T_c$ limit it demonstrates an exponential rise in the number of dynamical degrees of freedom. Its exponential increase behavior with temperature is valid only up to $T_c$. This makes it possible to identify $T_c$ with the Hagedorn-type transition temperature $T_h$, i.e., to put $T_h=T_c$ within the mass gap approach to QCD at finite temperature. The non-perturbative gluon pressure has a complicated dependence on the mass gap and temperature near $T_c$ and up to approximately $(4-5)T_c$. In the limit of very high temperatures $T \rightarrow \infty$ its polynomial character is confirmed, containing the terms proportional to $T^2$ and $T$, multiplied by the corresponding powers of the mass gap. \end{abstract}