Dressed Polyakov Loop Research Articles

Chiral and deconfinement phase transition in the Hamiltonian approach to QCD in Coulomb gauge

The chiral and deconfinement phase transitions are investigated within the variational Hamiltonian approach to QCD in Coulomb gauge. The temperature $\beta^{- 1}$ is introduced by compactifying a spatial dimension. Thereby the whole temperature dependence is encoded in the vacuum state on the spatial manifold $\mathbb{R}^2 \times S^1 (\beta)$. The chiral quark condensate and the dual quark condensate (dressed Polyakov loop) are calculated as function of the temperature. From their inflection points the pseudo-critical temperatures for the chiral and deconfinement crossover transitions are determined. Using the zero-temperature quark and gluon propagators obtained within the variational approach as input, we find $168 \, \mathrm{MeV}$ and $196 \, \mathrm{MeV}$, respectively, for the chiral and deconfinement transition.

Effect of entanglement on dual condensates at finite isospin chemical potential from an entangled Polyakov-Nambu-Jona-Lasinio model

The dual observables as order parameters for deconfinement transition are investigated at finite isospin chemical potential μ I in an entangled Polyakov-Nambu-Jona-Lasinio model of QCD. Compared to PNJL, the four quark vertice with entanglement between the Polyakov loop and the chiral and pion condensates are considered in this model. We mainly concentrate on the role of this entanglement on the thermal behavior of the dressed polyakov loop and the dual pion condensate for μ I > m π /2. We find that the T-dependencesof these dual condensates are qualitatively consistent with the PNJL results. Due to the entanglement, the critical temperatures determined by the quark and pion condensates and their corresponding dual partners get close to that extracted from the Polyakov loop.

Physical interpretation of the dressed Polyakov loop in the Nambu–Jona-Lasinio model

We investigate the rapid rise of the dressed Polyakov loop in the Nambu--Jona-Lasinio (NJL) model as a function of temperature. In QCD such a behavior is interpreted as a confinement-deconfinement phase transition. However, we demonstrate that in the NJL model this is simply a remnant of the chiral transition.

Separation of Chiral and Deconfinement Phase Transitions in Curved Space-Time

We calculated the chiral condensate and the dressed Polyakov loop in the space-time $R\times S^{3}$ and $R\times H^{3}$. The chiral condensate is the order parameter for the chiral phase transition, and the dressed Polyakov loop is the order parameter for the deconfinement phase transition. When there is a current mass, critical points for the chiral and deconfinement phase transitions are different in the crossover region. We show that the difference is changed by the gravitational effect.

Dressed Polyakov loop and flavor dependent phase transitions

The chiral condensate and dressed Polyakov loop at finite temperature and density have been investigated in the framework of Nf = 2+1 Nambu-Jona-Lasinio (NJL) model with two degenerate u, d quarks and one strange quark. In the case of explicit chiral symmetry breaking with physical quark masses, it is found that the phase transitions for light u, d quarks and s quark are sequentially happened, and the separation between the transition lines for different flavors becomes wider and wider with the increase of baryon density. For each flavor, the pseudo-critical temperatures for chiral condensate and dressed Polyakov loop differ in a narrow transition range in the lower baryon density region, and the two transitions coincide in the higher baryon density region.

Chiral and deconfinement phase transitions of two-flavour QCD at finite temperature and chemical potential

We present results for the chiral and deconfinement transition of two flavor QCD at finite temperature and chemical potential. To this end we study the quark condensate and its dual, the dressed Polyakov loop, with functional methods using a set of Dyson–Schwinger equations. The quark propagator is determined self-consistently within a truncation scheme including temperature and in-medium effects of the gluon propagator. For the chiral transition we find a crossover turning into a first order transition at a critical endpoint at large quark chemical potential, μEP/TEP≈3. For the deconfinement transition we find a pseudo-critical temperature above the chiral transition in the crossover region but coinciding transition temperatures close to the critical endpoint.

Interplay between chiral and deconfinement phase transitions

By using the dressed Polyakov loop or dual chiral condensate as an equivalent order parameter of the deconfinement phase transition, we investigate the relation between the chiral and deconfinement phase transitions at finite temperature and density in the framework of three-flavor Nambu-Jona-Lasinio (NJL) model. It is found that in the chiral limit, the critical temperature for chiral phase transition coincides with that of the dressed Polyakov loop in the whole (T,µ) plane. In the case of explicit chiral symmetry breaking, it is found that the phase transitions are flavor dependent. For each flavor, the transition temperature for chiral restoration is smaller than that of the dressed Polyakov loop in the low baryon density region where the transition is a crossover, and, the two critical temperatures coincide in the high baryon density region where the phase transition is of first order. Therefore, there are two critical end points, i.e, and at finite density. We also explain the feature of = in the case of 1st and 2nd order phase transitions, and < in the case of crossover, and expect this feature is general and can be extended to full QCD theory.

Dressed Polyakov loop and phase diagram of hot quark matter in a magnetic field

We evaluate the dressed Polyakov loop for hot quark matter in strong magnetic field. To compute the finite temperature effective potential, we use the Polyakov extended Nambu-Jona Lasinio model with eight-quark interactions taken into account. The bare quark mass is adjusted in order to reproduce the physical value of the vacuum pion mass. Our results show that the dressed Polyakov loop is very sensitive to the strenght of the magnetic field, and it is capable to capture both the deconfinement crossover and the chiral crossover. Besides, we compute self-consistently the phase diagram of the model. We find a tiny split of the two aforementioned crossovers as the strength of the magnetic field is increased. Concretely, for the largest value of magnetic field investigated here, $eB=19 m_\pi^2$, the split is of the order of $10\%$. A qualitative comparison with other effective models and recent Lattice results is also performed.

Chiral condensate and dressed Polyakov loop in the Nambu–Jona-Lasinio model

We investigate the chiral condensate and the dressed Polyakov loop or dual chiral condensate at finite temperature and density in the two-flavor Nambu--Jona-Lasinio model. The dressed Polyakov loop is regarded as an equivalent order parameter of deconfinement phase transition in a confining theory. We find the behavior of a dressed Polyakov loop in the absence of any confinement mechanism quite interesting. With only quark degrees of freedom present, it still shows an order parameter like behavior. It is found that in the chiral limit, the critical temperature for chiral phase transition coincides with that of the dressed Polyakov loop in the whole $(T,\ensuremath{\mu})$ plane. In the case of explicit chiral symmetry breaking, it is found that the transition temperature for chiral restoration ${T}_{c}^{\ensuremath{\chi}}$ is smaller than that of the dressed Polyakov loop ${T}_{c}^{\mathcal{D}}$ in the low baryon density region where the transition is a crossover. With the increase of the current quark mass the difference between the two transition temperatures is found to be increasing. However, the two critical temperatures coincide in the high baryon density region where the phase transition is of first order. We give an explanation on the feature of ${T}_{c}^{\ensuremath{\chi}}={T}_{c}^{\mathcal{D}}$ in the case of 1st and 2nd order phase transitions, and ${T}_{c}^{\ensuremath{\chi}}&lt;{T}_{c}^{\mathcal{D}}$ in the case of crossover, and expect this feature is general and can be extended to full QCD theory. Our result might indicate that in the case of crossover, there exists a small region where chiral symmetry is restored, but the color degrees of freedom are still confined.

Chiral and deconfinement transition from Dyson-Schwinger equations

We determine the quark condensate and the dressed Polyakov loop from the finite temperature Landau gauge quark propagator evaluated with U(1)-valued boundary conditions in an approximation to quenched QCD. These gauge invariant quantities allow for an investigation of the chiral and deconfinement transitions. We compare results from Dyson-Schwinger equations on a lattice with infinite volume continuum results and study the temperature and quark mass dependence of both quantities. In particular we investigate the chiral condensate and the dressed Polyakov loop in the chiral limit. We also consider an alternative order parameter for the deconfinement transition, the dual scalar quark dressing, and compare it with the dressed Polyakov loop. As a result we find only slightly different transition temperatures for the chiral and the deconfinement transitions at finite quark masses; in the chiral limit both transitions coincide.