A0--condensation in quark-gluon plasma with finite baryon density

TL;DR

This paper investigates the spontaneous generation of an $A_0$ background field in QCD at finite temperature and chemical potential, analyzing its dependence and gauge invariance, with implications for quark-gluon plasma properties.

Contribution

It extends previous work by including chemical potential effects on $A_0$ condensation in QCD and discusses gauge invariance via Nielsen's identity and Polyakov loop analysis.

Findings

Chemical potential weakly affects the condensate value.

Chemical potential significantly deepens the effective potential minima.

Polyakov loop behavior depends on chemical potential.

Abstract

In the present paper, we return to the problem on a spontaneous generation of the $A_0$-background field in QCD at finite temperature and include in addition a quark chemical potential, $\mu$. We reproduce the known expressions in terms of Bernoulli's polynomials for the gluons and quarks using the same formalism. Then we calculate the $\mu$-dependence, both for small $\mu$ as expansion, and numerically for finite $\mu$. One result is that the chemical potential only weakly changes the values of the condensed field, but quite strongly deepens the minima of the effective potential. The gauge dependence of the condensation is discussed in terms of Nielsen's identity. It also is expressed in terms of Polyakov's loop. Both these representations guarantee gauge invariance of the condensation phenomenon. Also, we discuss the dependence of the Polyakov loop in the minimum of the effective potential on the chemical potential.