The Non-Perturbative Analytical Equation of State for SU(3) Gauge Theory
Abstract
The effective potential approach for composite operators is generalized to non-zero temperature in order to derive the non-perturbative analytical equation of state for pure SU(3) Yang-Mills fields valid in the whole temperature range. Adjusting our parametrization of the gluon plasma pressure to the lattice pressure at high temperature for SU(3) Yang-Mills case, we have reproduced well our analytical curves and numbers not only for the pressure but for all other independent thermodynamic quantities as well in the whole temperature range [0, ∞). We explicitly show that the pressure is a continuous function of the temperature across a phase transition at Tc = 266.5 . The entropy and energy densities have finite jump discontinuities at Tc with latent heat εLH= 1.414. This is a firm evidence of the first-order phase transition in SU(3) pure gluon plasma. The heat capacity has a δ-type singularity (an essential discontinuity) at Tc, so that the velocity of sound squared becomes zero at this point. All the independent thermodynamic quantities are exponentially suppressed below Tc and rather slowly approach their respective Stefan-Boltzmann limits at high temperatures. Those thermodynamic quantities which are the ratios of their independent counterparts such as conformity, conformality and the velocity of sound squared approach their Stefan-Boltzmann limit at high temperatures rather rapidly and demonstrate the non-trivial dependence on the temperature below Tc. We predict the existence of the three massive and the two massless excitations, all of non-perturbative dynamical origin. One of the massive excitations has an effective mass 1.17 and the two others have the same effective mass 0.585 , but are propagating in different ways.