Chiral transition in a Non-Abelian Quasi-Particle Model with three quark flavours

Abstract

We combine the recently introduced Non-Abelian Quasi-Particle Model (NAQPM) for gluons with an ideal Fermi gas of three quark species with the aim to describe the equation of state (energy density vs. temperature) of $2+1$ - flavour Lattice-QCD at zero chemical potential. Allowing temperature dependent masses for the fermions, we show that above a critical temperature $T_c$ the quark mass has to drop rapidly in order to obtain energy density values compatible with the Lattice-QCD results. Within this framework, thus, the restoration of chiral symmetry in the system is observed. Furthermore, we demonstrate that the gluon variance -- which is a fundamental quantity of the NAQPM -- is strongly correlated to the fermion mass and decreases by orders of magnitude through the transition. The high temperature phenomenological characteristics of the gluon appear consistent to properties of the perturbative QCD gluon. The model indicates that color deconfinement and chiral symmetry restoration are interrelated and classical configurations of the QCD dynamics play an important role to the criticality of the system.

Figures (7)

• Figure 1: (a) The temperature dependence of the quark mass, $m_f(T)$, is shown for the three-flavor ENAQPM. In the $[155, 230]$ MeV interval the mass is the fitting parameter with the gluon variance fixed to a constant. In the $[230, 400]$ MeV interval, the quark mass is kept fixed to the 100 MeV value. The fitting procedure is described in Subsection 3.1. (b) The temperature-dependence of the gluon variance, $\sigma(T)$, is shown for the three-flavor ENAQPM. In the $[155, 230]$ MeV interval the variance is kept fixed, while in the $[230, 400]$ MeV interval is the fitting parameter.
• Figure 2: (a) The temperature dependence of the quark mass, $m_f(T)$, is shown for the family of monoparametric fits in the $[155, 400]$ MeV range for the three-flavor ENAQPM. The gluon variance, $\sigma(T)$, is analytically related to the quark mass by the formulas in the upper right part of the plot. (b) The temperature-dependence of the gluon variance, $\sigma(T)$, as determined by the analytic formulas from the fitted quark mass.
• Figure 3: (a) The energy density of 2+1 Lattice-QCD Karsch2014 as a function of temperature for $155 < T < 400$ MeV (red circles). The energy density of the ENAQPM is shown by the solid line. The Boltzmann limit for the massless anharmonic gauge bosons plus fermions is included in the plot by the dotted line. (b) The ENAQPM total energy density is shown by the black line along with the gluonic contribution (orange line) and the three quark flavors contribution (magenta line).
• Figure 4: (a) The pressure of 2+1 Lattice-QCD Karsch2014 as a function of temperature for $155 < T < 400$ MeV (red circles) versus the ENAQPM (solid line). (b) The trace anomaly, $\Delta= \epsilon-3 P$, for the ENAQPM (solid line) versus the Lattice-QCD data. The peak defining the (pseudo-) transition temperature is clear at the 200 MeV value.
• Figure 5: (a) The fermionic contribution (solid lines) and the gluonic contribution (dotted lines) to the energy density of the ENAQPM is displayed for a selection of variance - quark mass relations with specific exponents distinguished by color. (b) The fermionic and gluonic contributions to pressure with line and color selections as in (a). (c) The trace anomaly for the individual contributions as in (a)-(b).