The non-perturbative analytical equation of state for the gluon matter. I

TL;DR

This paper derives a non-perturbative, analytical equation of state for gluon matter in SU(3) Yang-Mills theory, capturing thermodynamic behavior and phase transition at a critical temperature, based on the effective potential approach.

Contribution

It introduces a temperature-dependent Bag constant into the effective potential framework, providing a novel analytical description of gluon thermodynamics without relying on coupling constants.

Findings

Identifies a critical temperature T_c=266.5 MeV for phase transition.

Calculates thermodynamic quantities like pressure, energy, and entropy densities.

Reproduces properties of fuzzy bag models through the mass gap dependence.

Abstract

The effective potential approach for composite operators has been generalized to non-zero temperatures in order to derive equation of state for the pure SU(3) Yang-Mills fields from first principles. In the absence of external sources it is nothing but the vacuum energy density. The key element of this derivation was an introduction of the temperature dependence into the expression for the Bag constant. Such obtained non-perturbative analytical equation of state for the gluon matter does not depend on the coupling constant, only the dependence on the mass gap, which is responsible for the large-scale structure of the QCD ground state, is present. The important thermodynamic quantities such as the pressure, energy and entropy densities, etc. have been calculated. We have shown explicitly that the pressure may continuously change its regime at $T_c=266.5 Mev$. All other thermodynamic quantities are to be understood to have drastic changes in their regimes at this point. The proposed analytical approach makes it possible to controll thermodynamics of the gluon matter at low temperatures below $T_c$ for the first time. We automatically reproduce the so-called "fuzy"-type bag models properties because of the mass gap explicit presence in our equation of state. We have also analytically calculated the NP gluon condensate as a function of temperature.