Deconfinement Phase Transition In QCD Research Articles

Effective potential of the Polyakov loop in the Hamiltonian approach to QCD

We investigate the effective potential of the Polyakov loop, which is the order parameter for the deconfinement phase transition in finite temperature QCD. Our work is based on the Hamiltonian approach in Coulomb gauge where finite temperature $T$ is introduced by compactifying one space direction. We briefly review this approach and extend earlier work in the Yang-Mills sector by including dynamical quarks. In a first approximation, we follow the usual functional approach and include only 1-loop contributions to the energy, with the finite temperature propagators replaced by their $T=0$ counterparts. It is found that this gives a poor description of the phase transition, in particular for the case of full QCD with ${N}_{f}=3$ light flavors. The physical reasons for this unexpected result are discussed, and pinned down to a relative weakness of gluon confinement compared to the deconfining tendency of the quarks. We attempt to overcome this issue by including the relevant gluon contributions from the 2-loop terms to the energy. We find that the 2-loop corrections have indeed a tendency to strengthen the gluon confinement and weaken the unphysical effects in the confining phase, while slightly increasing the (pseudo)critical temperature ${T}^{*}$ at the same time. To fully suppress artifacts in the confining phase, we must tune the parameters to rather large values, increasing the critical temperature to ${T}^{*}\ensuremath{\approx}340\text{ }\text{ }\mathrm{MeV}$ for $G=SU(2)$.

Preliminary results on deconfinement phase transition in full QCD

We explore the profiles of the flux tube connecting a quark and an antiquark in hightemperature SU(3) lattice gauge theory in close vicinity to the critical temperature of thephase transition. In this work, we consider the more realistic case of the flux tube withdynamical quarks, extending the previous study to SU(3) gauge group and making use ofthe Gradient flow method in smoothing procedure for noise reduction. The profiles of thechromoelectric and chromomagnetic field strengths in the flux tube have been measuredfrom Polyakov loop-plaquette correlations using the highly improved staggered quark(HISQ) action on a lattice with temporal extent.

Parametric investigation of a thermally driven QCD Deconfining Phase Transition in a finite volume at zero chemical potential

This work deals with a statistical description of a thermally driven deconfining phase transition (DPT) from a hadronic gas consisting of massless pions to a color-singlet Quark- Gluon Plasma (QGP), in a finite volume. The thermodynamical approach, within a coexistence model is used to investigate the Quantum Chromo-Dynamics DPT occurring between the two phases, at vanishing chemical potential. Considering the color singletness condition for the QGP phase, with massless up and down quarks, the exact total partition function of the studied system is obtained and then employed to calculate mean values of physical quantities, well characterizing the system near the transition. The finite-size effects on the DPT have been investigated through the study of the thermal behavior of the order parameter, the susceptibility and the second cumulant of the probability density. The similarity between the susceptibility and the second cumulant representing the variance is probed for the studied DPT and a parameterization of the variance is proposed for the first time.

Charge transport and vector meson dissociation across the thermal phase transition in lattice QCD with two light quark flavors

We compute and analyze correlation functions in the isovector vector channel at vanishing spatial momentum across the deconfinement phase transition in lattice QCD. The simulations are carried out at temperatures $T/T_c=0.156, 0.8, 1.0, 1.25$ and $1.67$ with $T_c\simeq203$MeV for two flavors of Wilson-Clover fermions with a zero-temperature pion mass of $\simeq270$MeV. Exploiting exact sum rules and applying a phenomenologically motivated ansatz allows us to determine the spectral function $\rho(\omega,T)$ via a fit to the lattice correlation function data. From these results we estimate the electrical conductivity across the deconfinement phase transition via a Kubo formula and find evidence for the dissociation of the $\rho$ meson by resolving its spectral weight at the available temperatures. We also apply the Backus-Gilbert method as a model-independent approach to this problem. At any given frequency, it yields a local weighted average of the true spectral function. We use this method to compare kinetic theory predictions and previously published phenomenological spectral functions to our lattice study.

Finite-volume cumulant expansion in QCD-colorless plasma

Due to the finite size effects, the localisation of the phase transition in finite systems and the determination of its order, become an extremely difficult task, even in the simplest known cases. In order to identify and locate the finite volume transition point $T_{0}(V)$ of the QCD deconfinement phase transition to a Colorless QGP, we have developed a new approach using the finite size cumulant expansion of the order parameter and the $L_{mn}$-method. The first six cumulants $C_{1,2,3,4,5,6}$ with the corresponding under-normalized ratios(skewness $\Sigma$, kurtosis $\kappa$ ,pentosis $\Pi_{\pm}$ and hexosis $\mathcal{H}_{1,2,3}$) and three unnormalized combinations of them ($\mathcal{O}={\mathcal{\sigma }^{2} \mathcal{\kappa } }{\mathbf{\Sigma }^{-1} }$, $\mathcal{U} ={\mathcal{\sigma }^{-2} \mathbf{\Sigma }^{-1} }$, $\mathcal{N} = \mathcal{\sigma }^{2} \mathcal{\kappa }$) are calculated and studied as functions of $(T,V)$. A new approach, unifying in a clear and consistent way the definitions of cumulant ratios, is proposed. A numerical FSS analysis of the obtained results has allowed us to locate accurately the finite volume transition point. The extracted transition temperature value $T_{0}(V)$ agrees with that expected $T_{0}^{N}(V)$ from the order parameter and the thermal susceptibility $\chi _{T}\left( T,V\right)$, according to the standard procedure of localization to within about $2\%$. In addition to this, a very good correlation factor is obtained proving the validity of our cumulants method. The agreement of our results with those obtained by means of other models is remarkable.

Holographic calculation of the electric conductivity of the strongly coupled quark-gluon plasma near the deconfinement transition

The frequency dependent conductivity $\sigma(\omega)$ of the strongly coupled Quark-Gluon Plasma (QGP) is estimated using a bottom up holographic model that can adequately describe recent lattice data for QCD thermodynamics at zero chemical potential. Different choices for the coupling between the bulk gauge field and the other bulk fields that define the background (the metric and a scalar field) are used in order to fit the lattice data for the electric charge susceptibility $\chi_2^Q/T^2$. The ratio $\sigma_{DC}/T$ is found to vary near the deconfinement transition in a way that is similar to recent lattice results. This model is used to compute the charge diffusion coefficient $D$ of the strongly coupled plasma. We find that the dimensionless combination $DT$ has the same type of temperature dependence displayed by $\sigma_{DC}/T$ and, thus, charge diffusion is suppressed at low temperatures. The frequency dependent conductivity $\sigma(\omega)$ reveals some nontrivial structure for values of the temperature near the phase transition. None of these structures appear in the associated Euclidean correlator, which we also compute. Our results suggest that the conformal invariance violation near the QCD deconfinement phase transition may be seen in the Euclidean correlator through a downward shift of its value at the minimum, which gives a rough estimate of the temperature dependence of the DC conductivity in the plasma.

New critical point for QCD in a magnetic field

We provide a general argument for the possible existence of a new critical point associated with a deconfinement phase transition in QCD at finite temperature $T$ and in a magnetic field $B$ with zero chemical potential. This is the first example of a QCD critical point in a physical external parameter region that can be studied using lattice QCD simulations without suffering from a sign problem.

Polyakov Loop and the Hadron Resonance Gas Model

The Polyakov loop has been used repeatedly as an order parameter in the deconfinement phase transition in QCD. We argue that, in the confined phase, its expectation value can be represented in terms of hadronic states, similarly to the hadron resonance gas model for the pressure. Specifically, L(T)≈1/2[∑(α)g(α)e(-Δ(α)/T), where g(α) are the degeneracies and Δ(α) are the masses of hadrons with exactly one heavy quark (the mass of the heavy quark itself being subtracted). We show that this approximate sum rule gives a fair description of available lattice data with N(f)=2+1 for temperatures in the range 150 MeV<T<190 MeV with conventional meson and baryon states from two different models. For temperatures below 150 MeV different lattice results disagree. One set of data can be described if exotic hadrons are present in the QCD spectrum while other sets do not require such states.

Critical behavior of higher cumulants of order parameter in the 3D-Ising universality class

QCD deconfinement phase transition is supposed to be the same universality class as the 3D-Ising model. According to the universality of critical behavior, the Binder-like ratios and ratios of higher cumulants of order parameter near the critical temperature in the 3D-Ising model are studied. The Binder-like ratio is shown to be a step function of temperature. The critical point is the intersection of the ratios of different system sizes between two platforms. The normalized cumulant ratios, like the Skewness and Kurtosis, do not diverge with correlation length, contrary to the corresponding cumulants. Possible applications of these characters in locating critical point in relativistic heavy ion collisions are discussed.

Flux tube model signals for baryon correlations in heavy ion collisions

The flux tube model offers a pictorial description of what happens during the deconfinement phase transition in QCD. The 3-point vertices of a flux tube network lead to formation of baryons upon hadronisation. Therefore, correlations in the baryon number distribution at the last scattering surface are related to the preceding pattern of the flux tube vertices, and provide a signature of the nearby deconfinement phase transition. I discuss the nature of the expected signal, which should be observable in heavy ion collisions at RHIC and LHC.

Strange quark matter: Business as usual or phase transition?

We give an overview of some results presented at the Strange Quark Matter 2011 conference in Krakow, and interpret them in light of the search of the search for a QCD deconfinement phase transition in heavy ion collisions

Dynamical locking of the chiral and the deconfinement phase transition in QCD

We study the fixed-point structure of four-fermion interactions in two-flavor QCD with Nc colors close to the finite-temperature phase boundary. In particular, we analyze how the fixed-point structure of four-fermion interactions is related to the confining dynamics in the gauge sector. We show that there exists indeed a mechanism which dynamically locks the chiral phase transition to the deconfinement phase transition. This mechanism allows us to determine a window for the values of physical observables in which the two phase transitions lie close to each other.

CONFINEMENT–DECONFINEMENT PHASE TRANSITION IN HOT AND DENSE QCD AT LARGE N

We conjecture that the confinement–deconfinement phase transition in QCD at large number of colors N and Nf ≪ N at T ≠ 0 and µ ≠ 0 is triggered by the drastic change in θ behavior. The conjecture is motivated by the holographic model of QCD where confinement–deconfinement phase transition indeed happens precisely at T = Tc where θ dependence experiences a sudden change in behavior. The conjecture is also supported by quantum field theory arguments when the instanton calculations (which trigger the θ dependence) are under complete theoretical control for T &gt; Tc, suddenly break down immediately below T &lt; Tc with sharp changes in the θ dependence. Finally, the conjecture is supported by a number of numerical lattice results. We employ this conjecture to study confinement–deconfinement phase transition of hot and dense QCD in large N limit by analyzing the θ dependence. We estimate the critical values for Tc and µc where the phase transition happens by approaching the critical values from the hot and/or dense regions where the instanton calculations are under complete theoretical control. We also describe some defects of various codimensions within a holographic model of QCD by focusing on their role around the phase transition point.

A Quenched Study for QCD Phase-Transition on Anisotropic Lattices

The QCD deconfinement phase transition in pure SU(3) gauge theory is studied on an anisotropic lattice. The critical temperature is determined to be Tc ≈ 285 MeV. The relation between the deconfinement phase transition and the breakdown of Z(3) center symmetry is also discussed.

Confinement–deconfinement phase transition in hot and dense QCD at large N

We conjecture that the confinement–deconfinement phase transition in QCD at large number of colors N and N f ≪ N at T ≠ 0 and μ ≠ 0 is triggered by the drastic change in θ behavior. The conjecture is motivated by the holographic model of QCD where confinement–deconfinement phase transition indeed happens precisely at the value of temperature T = T c where θ dependence experiences a sudden change in behavior [A. Parnachev, A. Zhitnitsky, arXiv: 0806.1736 [hep-ph]]. The conjecture is also supported by quantum field theory arguments when the instanton calculations (which trigger the θ dependence) are under complete theoretical control for T > T c , suddenly break down immediately below T < T c with sharp changes in the θ dependence. Finally, the conjecture is supported by a number of numerical lattice results. We employ this conjecture to study confinement–deconfinement phase transition of dense QCD at large μ in large N limit by analyzing the θ dependence. We find that the confinement–deconfinement phase transition at N f ≪ N happens at very large quark chemical potential μ c ∼ N Λ QCD . This result agrees with recent findings by McLerran and Pisarski [L. McLerran, R.D. Pisarski, Nucl. Phys. A 796 (2007) 83]. We also speculate on case when N f ∼ N .

Deconfinement phase transition in holographic QCD with matter

In the framework of a holographic QCD approach we study the influence of matter on the deconfinement temperature ${T}_{c}$. We first consider the quark flavor number (${N}_{f}$) dependence of ${T}_{c}$. We observe that ${T}_{c}$ decreases with ${N}_{f}$, which is consistent with a lattice QCD result. We also delve into how the quark number density ${\ensuremath{\rho}}_{q}$ affects the value of ${T}_{c}$. We find that ${T}_{c}$ drops with increasing ${\ensuremath{\rho}}_{q}$. In both cases, we confirm that the contributions from quarks are suppressed by $1/{N}_{c}$, as it should be, compared to the ones from a gravitational action (pure Yang-Mills theory).

NATURE OF THE PHASE TRANSITION IN QCD AT FINITE TEMPERATURE

It is clear that the order of the deconfining phase transition in QCD at nonzero temperature and density (with realistic quark masses) is of great experimental interest. The importance of the transition at zero baryon density with only two (degenerate) quark flavors is perhaps less evident. As a matter of fact, the order of the transition in this case is still an open problem and corresponds to the last question mark in the zero-density phase diagram of QCD. We argue that establishing the nature of the transition in this case is also a crucial test for numerical simulations of lattice QCD, allowing precise estimates of the possible systematic errors related to the choice of fermion-simulation algorithm and of discretized formulation for fermions.

Short-time dynamics of percolation observables

We consider the critical short-time evolution of magnetic and droplet-percolation order parameters for the Ising model in two and three dimensions, through Monte Carlo simulations with the (local) heat-bath method. We find qualitatively different dynamic behaviors for the two types of order parameters. More precisely, we find that the percolation order parameter does not have a power-law behavior as encountered for the magnetization, but develops a scale (related to the relaxation time to equilibrium) in the Monte Carlo time. We argue that this difference is due to the difficulty in forming large clusters at the early stages of the evolution. Our results show that, although the descriptions in terms of magnetic and percolation order parameters may be equivalent in the equilibrium regime, greater care must be taken to interpret percolation observables at short times. In particular, this concerns the attempts to describe the dynamics of the deconfinement phase transition in QCD using cluster observables.

Glauber dynamics of phase transitions: SU(3) lattice gauge theory

Motivated by questions about the QCD deconfining phase transition, we studied in two previous papers Model A (Glauber) dynamics of 2D and 3D Potts models, focusing on structure factor evolution under heating (heating in the gauge theory notation, i.e., cooling of the spin systems). In the present paper we set for 3D Potts models (Ising and 3-state) the scale of the dynamical effects by comparing to equilibrium results at first and second order phase transition temperatures, obtained by re-weighting from a multicanonical ensemble. Our finding is that the dynamics entirely overwhelms the critical and non-critical equilibrium effects. In the second half of the paper we extend our results by investigating the Glauber dynamics of pure SU(3) lattice gauge on $N_{\tau} N_{\sigma}^3$ lattices directly under heating quenches from the confined into the deconfined regime. The exponential growth factors of the initial response are calculated, which give Debye screening mass estimates. The quench leads to competing vacuum domains of distinct $Z_3$ triality, which delay equilibration of pure gauge theory forever, while their role in full QCD remains a subtle question. As in spin systems we find for pure SU(3) gauge theory a dynamical growth of structure factors, reaching maxima which scale approximately with the volume of the system, before settling down to equilibrium. Their influence on various observables is studied and different lattice sizes are simulated to illustrate an approach to a finite volume continuum limit. Strong correlations are found during the dynamical process, but not in the deconfined phase at equilibrium.

Finite-size effects and scaling for the thermal QCD deconfinementphase transition within the exact color-singlet partition function

We study the finite-size effects for the thermal QCD Deconfinement Phase Transition (DPT), and use a numerical finite size scaling analysis to extract the scaling exponents characterizing its scaling behavior when approaching the thermodynamic limit. For this, we use a simple model of coexistence of hadronic gas and color-singlet Quark Gluon Plasma (QGP) phases in a finite volume. The Color-Singlet Partition Function (CSPF) of the QGP cannot be exactly calculated and is usually derived within the saddle point approximation. When we try to do calculations with such an approximate CSPF, a problem arises in the limit of small temperatures and/or volumes (VT3<<1), requiring then additional approximations if we want to carry out calculations. We propose in this work a new method for an accurate calculation of any quantity of the finite system, without explicitly calculating the CSPF itself and without any approximation. By probing the behavior of some useful thermodynamic response functions on the hole range of temperature, it turns out that in a finite size system, all singularities in the thermodynamic limit are smeared out and the transition point is shifted away. A numerical finite size scaling analysis of the obtained data allows us to determine the scaling exponents of the QCD DPT. Our results expressing the equality between their values and the space dimensionality is a consequence of the singularity characterizing a first order phase transition and agree very well with the predictions of other FSS theoretical approaches and with the results of both lattice QCD and Monte Carlo models calculations.