The consequences of SU(3) colorsingletness, Polyakov Loop and Z(3) symmetry on a quark-gluon gas

TL;DR

This paper investigates the role of SU(3) color singlet states, Polyakov Loop, and Z(3) symmetry in a quark-gluon gas, revealing phase transitions, metastable states, and the emergence of color confinement phenomena.

Contribution

It establishes a connection between SU(3) color singlet ensembles and Polyakov Loop, and analyzes the effects of Z(3) symmetry breaking in quark-gluon systems.

Findings

Identification of a maximum in the normalized character indicating a phase transition.

Discovery of a metastable state in the 145-170 MeV temperature range due to Z(3) symmetry breaking.

Observation of color recombination and confinement mechanisms at low temperatures.

Abstract

Based on quantum statistical mechanics we show that the $SU(3)$ color singlet ensemble of a quark-gluon gas exhibits a $Z(3)$ symmetry through the normaized character in fundamental representation and also becomes equivalent, within a stationary point approximation, to the ensemble given by Polyakov Loop. Also Polyakov Loop gauge potential is obtained by considering spatial gluons along with the invariant Haar measure at each space point. The probability of the normalized character in $SU(3)$ vis-a-vis Polyakov Loop is found to be maximum at a particular value exhibiting a strong color correlation. This clearly indicates a transition from a color correlated to uncorrelated phase or vise-versa. When quarks are included to the gauge fields, a metastable state appears in the temperature range $145\le T({\rm{MeV}}) \le 170$ due to the explicit $Z(3)$ symmetry breaking in the quark-gluon system. Beyond $T\ge 170$ MeV the metastable state disappears and stable domains appear. At low temperature a dynamical recombination of ionized $Z(3)$ color charges to a color singlet $Z(3)$ confined phase is evident along with a confining background that originates due to circulation of two virtual spatial gluons but with conjugate $Z(3)$ phases in a closed loop. We also discuss other possible consequences of the center domains in the color deconfined phase at high temperature.