$$A_0$$-condensation in quark-gluon plasma with finite baryon density

Abstract

In the present paper, we return to the problem of spontaneous generation of the $$A_0$$ A 0 -background field in QCD at finite temperature and a quark chemical potential, $$\mu $$ μ . On the lattice, this problem was studied by different approaches where an analytic continuation to the imaginary potential $$i \mu $$ i μ has been used. Here we consider both, real and imaginary chemical potential, analytically within the two-loop gauge-fixing independent effective potential $$W_{eff.}$$ W e f f . . We realize the gauge independence in to ways: (1) on the base of Nielsen’s identity and (2) expressing the potential in terms of Polyakov’s loop. Firstly we reproduce the known expressions in terms of Bernoulli’s polynomials for the gluons and quarks. Then, we calculate the $$\mu $$ μ -dependence, either for small $$\mu $$ μ as expansion or numerically for finite $$\mu $$ μ , real and imaginary. One result is that the chemical potential only weakly changes the values of the condensate fields, but quite strongly deepens the minima of the effective potential. We investigate the dependence of Polyakov’s loop in the minimum of the effective potential, thermodynamic pressure and Debye’s mass on the chemical potential. Comparisons with other results are given.

Effective potential of gluodynamics in background of Polyakov loop and colormagnetic field

“…As mentioned in [20], (62) coincides with the gauge-invariant result for ξ = −1, what we assume in the following. The first term of the effective potential is the gluon black body radiation.…”

“…As can be seen, this first low-temperature correction to (15) has, as a function of a, a structure similar the high-temperature expansion (20) with the difference of a fast rotation (in the complex plane) of the arguments of the poly-logarithms.…”

“…In this section, we remind the known results for the case of a pure A 0 -background. We follow the recent paper [20], where this case was investigated in detail for SU (3). In our case of SU (2) the formulas are even easier.…”

Induced color charge and quark propagation at Polyakov’s loop background

“…This point was discussed for many years in the literature. The gauge fixing independent effective potential, expressed in terms of the PL, was derived recently in [1], [3] on the base of the Nielsen identity approach to the ξdependence of generating functionals and particle spectra.…”

“…The goal of the present paper is twofold. First we calculate the value for the A 0 condensate by using gauge invariant effective potential of order parameter derived recently [1]. Second, we compute the "tadpole" diagram (Fig.…”