Deconfinement Transition Temperature Research Articles

θ dependence of Tc in 4d SU(3) Yang-Mills theory with histogram method and the Lee-Yang zeros in the large N limit

The phase diagram on the θ-T plane in four dimensional SU(3) Yang-Mills theory is explored. We revisit the θ dependence of the deconfinement transition temperature, Tc(θ), on the lattice through the constraint effective potential for Polyakov loop. The θ term is introduced by the reweighting method, and the critical β is determined to θ ∼ 0.75, where the interpolation in β is carried out by the multipoint reweighting method. The θ dependence of Tc obtained here turns out to be consistent with the previous result by D’Elia and Negro [1, 2]. We also derive Tc(θ) by classifying configurations into the high and low temperature phases and applying the Clausius-Clapeyron equation. It is found that the potential barrier in the double well potential at Tc(θ) becomes higher with θ, which suggests that the first order transition continues robustly above θ ∼ 0.75. Using information obtained here, we try to depict the expected θ dependence of the free energy density at T ≲ Tc(0), which crosses the first order transition line at an intermediate value of θ. Finally, how the Lee-Yang zeros associated with the spontaneous CP violation appear is discussed formally in the large N limit, and the locations of them are found to be left({theta}_R,{theta}_Iright)=left(left(2m+1right)pi, frac{2n+1}{2chi {V}_4}right) with m and n arbitrary integers.

A quenched 2-flavour Einstein–Maxwell–Dilaton gauge-gravity model

We extend earlier work by introducing an Einstein–Maxwell–Dilaton (EMD) action with two quark flavours. We solve the corresponding equations of motion in the quenched approximation (probe quark flavours) via the potential reconstruction method in presence of a background magnetic field in search for a self-consistent dual magnetic AdS/QCD model. As an application we discuss the deconfinement transition temperature confirming inverse magnetic catalysis, whilst for moderate values of the magnetic field also the entropy density compares relatively well with corresponding lattice data in the vicinity of the transition.

Effects of quark anomalous magnetic moment on the thermodynamical properties and mesonic excitations of magnetized hot and dense matter in PNJL model

Various thermodynamic quantities and the phase diagram of strongly interacting hot and dense magnetized quark matter are obtained with the $ 2 $-flavour Nambu-Jona-Lasinio model with Polyakov loop considering finite values of the anomalous magnetic moment (AMM) of the quarks. Susceptibilities associated with constituent quark mass and traced Polyakov loop are used to evaluate chiral and deconfinement transition temperatures. It is found that, inclusion of the AMM of the quarks in presence of the background magnetic field results in a substantial decrease in the chiral as well as deconfinement transition temperatures in contrast to an enhancement in the chiral transition temperature in its absence. Using standard techniques of finite temperature field theory, the two point thermo-magnetic mesonic correlation functions in the scalar ($\sigma$) and neutral pseudoscalar ($\pi^0$) channels are evaluated to calculate the masses of $\sigma $ and $ \pi^0 $ considering the AMM of the quarks.

Induced QCD II: numerical results

We numerically explore an alternative discretization of continuum SU(Nc) Yang-Mills theory on a Euclidean spacetime lattice, originally introduced by Budzcies and Zirnbauer for gauge group U(Nc). This discretization can be reformulated such that the self-interactions of the gauge field are induced by a path integral over Nb auxiliary bosonic fields, which couple linearly to the gauge field. In the first paper of the series we have shown that the theory reproduces continuum SU(Nc) Yang-Mills theory in d = 2 dimensions if Nb is larger than Nc − frac{3}{4} and conjectured, following the argument of Budzcies and Zirnbauer, that this remains true for d > 2. In the present paper, we test this conjecture by performing lattice simulations of the simplest nontrivial case, i.e., gauge group SU(2) in three dimensions. We show that observables computed in the induced theory, such as the static q overline{q} potential and the deconfinement transition temperature, agree with the same observables computed from the ordinary plaquette action up to lattice artifacts. We also find evidence that the bound for Nb can be relaxed to Nc − frac{5}{4} as conjectured in our earlier paper. Studies of how the new discretization can be used to change the order of integration in the path integral to arrive at dual formulations of QCD are left for future work.

Stochastic reconstructions of spectral functions: Application to lattice QCD

We present a detailed study of the applications of two stochastic approaches, stochastic optimization method (SOM) and stochastic analytical inference (SAI), to extract spectral functions from Euclidean correlation functions. SOM has the advantage that it does not require prior information. On the other hand, SAI is a more generalized method based on Bayesian inference. Under mean field approximation SAI reduces to the often-used maximum entropy method (MEM), and for a specific choice of the prior SAI becomes equivalent to SOM. To test the applicability of these two stochastic methods to lattice QCD, firstly, we apply these methods to various reasonably chosen model correlation functions, and present detailed comparisons of the reconstructed spectral functions obtained from SOM, SAI and MEM. Next, we present similar studies for charmonia correlation functions obtained from lattice QCD computations using clover-improved Wilson fermions on large, fine, isotropic lattices at $0.75$ and $1.5T_c$, $T_c$ being the deconfinement transition temperature of a pure gluon plasma. We find that SAI and SOM give consistent results to MEM at these two temperatures.

Medium effects and parity doubling of hyperons across the deconfinement phase transition

We analyse the behaviour of hyperons with strangeness S = –1,–2,–3 in the hadronic and quark gluon plasma phases, with particular interest in parity doubling and its emergence as the temperature grows. This study uses our FASTSUM anisotropic Nf = 2+1 ensembles, with four temperatures below and four above the deconfinement transition temperature, Tc. The positive-parity groundstate masses are found to be largely temperature independent below Tc, whereas the negative-parity ones decrease considerably as the temperature increases. Close to the transition, the masses are almost degenerate, in line with the expectation from chiral symmetry restoration. This may be of interest for heavy-ion phenomenology. In particular we show an application of this effect to the Hadron Resonance Gas model. A clear signal of parity doubling is found above Tc in all hyperon channels, with the strength of the effect depending on the number of s-quarks in the baryons.

Strong magnetic fields in a nonlocal Polyakov chiral quark model

We study the behavior of strongly interacting matter under an external constant magnetic field in the context of nonlocal chiral quark models that incorporate a coupling to the Polyakov loop. We find that at zero temperature the behavior of the quark condensates shows the expected magnetic catalysis effect, our predictions being in good quantitative agreement with lattice QCD results. On the other hand when the analysis is extended to the case of finite temperature our results show that nonlocal models naturally lead to the Inverse Magnetic Catalysis effect for both the chiral restoration and deconfinement transition temperatures.

Chiral phase transition of three flavor QCD with nonzero magnetic field using standard staggered fermions

Lattice simulations for (2+1)-flavor QCD with external magnetic field demon-strated that the quark mass is one of the important parameters responsible for the (inverse) magnetic catalysis. We discuss the dependences of chiral condensates and susceptibilities, the Polyakov loop on the magnetic field and quark mass in three degenerate flavor QCD. The lattice simulations are performed using standard staggered fermions and the plaquette action with spatial sizes Nσ = 16 and 24 and a fixed temporal size Nτ = 4. The value of the quark masses are chosen such that the system undergoes a first order chiral phase transition and crossover with zero magnetic field. We find that in light mass regime, the quark chiral condensate undergoes magnetic catalysis in the whole temperature region and the phase transition tend to become stronger as the magnetic field increases. In crossover regime, deconfinement transition temperature is shifted by the magnetic field when quark mass ma is less than 0:4. The lattice cutoff effects are also discussed.

Light baryons below and above the deconfinement transition: medium effects and parity doubling

We study what happens to the N , Δ and Ω baryons in the hadronic gas and the quark-gluon plasma, with particular interest in parity doubling and its emergence as the plasma is heated. This is done using simulations of lattice QCD, employing the FASTSUM anisotropic Nf = 2 + 1 ensembles, with four temperatures below and four above the deconfinement transition temperature. Below Tc we find that the positive-parity groundstate masses are largely temperature independent, whereas the negative-parity ones are reduced considerably as the temperature increases. This may be of interest for heavy-ion phenomenology. Close to the transition, the masses are nearly degenerate, in line with the expectation from chiral symmetry restoration. Above Tc we find a clear signal of parity doubling in all three channels, with the effect of the heavier s quark visible.

Inverse magnetic catalysis and confinement within a contact interaction model for quarks

We evaluate the impact of an external magnetic field on the chiral symmetry and confinement–deconfinement transition temperatures by using a vector–vector contact interaction model for quarks regularized so as to include an explicit confining scale in the corresponding gap equation. Exploring the evolution of the chiral condensate and the confining scale with temperature T and magnetic field strength eB (e represents the fundamental electric charge), we determine the pseudo-critical temperatures for the chiral () and deconfinement (Tcc) transitions from their inflection points, respectively. By construction, in the chiral limit. Within a mean-field approximation, we observe the magnetic catalysis phenomenon, characterized by a rising behavior of and Tcc with growing eB. By considering a lattice-inspired running coupling which monotonically decreases with eB, inverse magnetic catalysis takes place in our model. We explore the role of the magnetic field in the traits of the confinement–deconfinement transition described by the model. Our findings are also in agreement with predictions derived from effective models of strong interactions.

Consistency of Perfect Fluidity and Jet Quenching in Semi-Quark-Gluon Monopole Plasmas**Supported by the USA DOE Nuclear Science under Grant No DE-FG02-93ER40764, the National Science Foundation under Grant No PHY-1352368, and the RIKEN BNL Research Center.

We utilize a new framework, CUJET3.0, to deduce the energy and temperature dependence of the jet transport parameter, q̂(E > 10 GeV, T), from a combined analysis of available data on nuclear modification factor and azimuthal asymmetries from high energy nuclear collisions at RHIC/BNL and LHC/CERN. Extending a previous perturbative-QCD based jet energy loss model (known as CUJET2.0) with (2+1)D viscous hydrodynamic bulk evolution, this new framework includes three novel features of nonperturbative physics origin: (i) the Polyakov loop suppression of color-electric scattering (aka ‘semi-QGP’ of Pisarski et al.), (ii) the enhancement of jet scattering due to emergent magnetic monopoles near Tc (aka ‘magnetic scenario’ of Liao and Shuryak), and (iii) thermodynamic properties constrained by lattice QCD data. CUJET3.0 reduces to v2.0 at high temperatures T >400 MeV, while greatly enhances q̂ near the QCD deconfinement transition temperature range. This enhancement accounts well for the observed elliptic harmonics of jets with pT > 10 GeV. Extrapolating our data-constrained q̂ down to thermal energy scales, E∼2 GeV, we find for the first time a remarkable consistency between high energy jet quenching and bulk perfect fluidity with η/s ∼ T3/q̂ ∼ 0.1 near Tc.

Deconfinement transition at high isospin chemical potential and low temperature

We consider QCD with two degenerate flavors of light quarks (up and down) at asymptotically high isospin (μI) with zero baryon chemical potential (μB) and calculate for the first time a quantitative expression for the critical temperature of the deconfinement transition in this regime. At high isospin chemical potential and sufficiently low temperatures this theory becomes equivalent to a pure Yang–Mills theory and accordingly has a first order deconfinement phase transition. Although this was conjectured in a seminal paper by Son and Stephanov in the year 2001, the critical temperature of this deconfinement phase transition was not computed. This paper computes the energy scale associated with this transition as a function of the chemical potential μI by relating the parameters of the equivalent Yang–Mills theory to those of the underlying theory. We also relate the equation of state in one strongly interacting regime of QCD namely at finite isospin density to that in pure Yang–Mills, with the latter being amenable to straightforward numerical calculation. Our results for the critical temperature of deconfinement transition can be compared with future lattice calculations.

Lattice NRQCD study of S- and P-wave bottomonium states in a thermal medium withNf=2+1light flavors

We investigate the properties of $S$- and $P$-wave bottomonium states in the vicinity of the deconfinement transition temperature. The light degrees of freedom are represented by dynamical lattice quantum chromodynamics (QCD) configurations of the HotQCD collaboration with ${N}_{f}=2+1$ flavors. Bottomonium correlators are obtained from bottom quark propagators, computed in nonrelativistic QCD under the background of these gauge field configurations. The spectral functions for the ${^{3}S}_{1}$ ($\mathrm{\ensuremath{\Upsilon}}$) and ${^{3}P}_{1}$ (${\ensuremath{\chi}}_{b1}$) channel are extracted from the Euclidean time correlators using a novel Bayesian approach in the temperature region $140\text{ }\text{ }\mathrm{MeV}\ensuremath{\le}T\ensuremath{\le}249\text{ }\text{ }\mathrm{MeV}$ and the results are contrasted to those from the standard maximum entropy method. We find that the new Bayesian approach is far superior to the maximum entropy method. It enables us to study reliably the presence or absence of the lowest state signal in the spectral function of a certain channel, even under the limitations present in the finite temperature setup. We find that ${\ensuremath{\chi}}_{b1}$ survives up to $T=249\text{ }\text{ }\mathrm{MeV}$, the highest temperature considered in our study, and put stringent constraints on the size of the medium modification of $\mathrm{\ensuremath{\Upsilon}}$ and ${\ensuremath{\chi}}_{b1}$ states.

Free energy versus internal energy potential for heavy quark systems at finite temperature

Abstract The strength of the J / ψ wave function at origin | ψ ( 0 ) | is calculated by using the finite temperature QCD sum rule with the gluon condensates determined from the lattice QCD. The result is compared with that from a potential model based on the static free or internal energy obtained from lattice calculations. We find that the | ψ ( 0 ) | decreases with temperature around the deconfinement transition temperature both in the QCD sum rule and in the potential model with the free energy potential. Our result thus suggests that the free energy potential from lattice calculations is appropriate for describing the properties of charmonia at finite temperature.

Hybrid neutron stars with the field correlator method

We study the quark deconfinement phase transition in cold (T = 0) neutron star matter and we calculate various structural properties of hybrid stars. For the quark phase, we use an equation of state (EOS) based on the Field Correlator Method (FCM) extended to the case of nonzero baryon density. For the confined hadronic phase we use a relativistic mean field model considering both pure nucleonic and hyperonic matter. We constrain the values of the gluon condensate G2, which is one of the EOS parameter within the FCM, making use of the measured mass, M = 1.97 ± 0.04 M⊙, of the neutron star in PSR J1614-2230. Our results show that the values of G2 extracted from the mass measurement of PSR J1614-2230 are consistent with the values of the same quantity derived, within the FCM, from recent lattice QCD calculations of the deconfinement transition temperature at zero baryon chemical potential.

Entanglement entropy of spherical domains in anti–de Sitter space

It was proposed by Ryu and Takayanagi that the entanglement entropy in conformal field theory (CFT) is related through the AdS/CFT correspondence to the area of a minimal surface in the bulk. We apply this holographic geometrical method of calculating the entanglement entropy to study the vacuum case of a CFT which is holographically dual to empty anti-de Sitter (AdS) spacetime. We present all possible minimal surfaces spanned on one or two spherical boundaries at AdS infinity. We give exact analytical expressions for the regularized areas of these surfaces and identify finite renormalized quantities. In the case of two disjoint boundaries the existence of two different phases of the entanglement entropy is confirmed. A trivial phase corresponds to two disconnected minimal surfaces, while the other one corresponds to a tube connecting the spherical boundaries. A transition between these phases is reminiscent of the finite temperature deconfinement transition in the CFT on the boundary. The exact analytical results are thus consistent with previous numerical and approximate computations. We also briefly discuss the character of a spacetime extension of the minimal surface spanned on two uniformly accelerated boundaries.

Deconfinement, chiral symmetry restoration and thermodynamics of (2+1)-flavor hot QCD matter in an external magnetic field

The entanglement extended Polyakov--Nambu--Jona-Lasinio model at zero chemical potential in the presence of an external magnetic field is studied. The effect of the entanglement parametrization is analyzed, in particular, on the pseudocritical transition temperatures and on the thermodynamical properties of the model. The model predicts that the coincidence or not of both chiral and deconfinement transition temperatures, in the presence of an external magnetic field, depends on the entanglement parametrization chosen.

Influence of hadronic bound states aboveTcon heavy-quark observables in Pb + Pb collisions at the CERN Large Hadron Collider

We investigate how the possible existence of hadronic bound states above the deconfinement transition temperature ${T}_{c}$ affects heavy-quark observables, such as the nuclear modification factor, the elliptic flow, and azimuthal correlations. Lattice QCD calculations suggest that above ${T}_{c}$ the effective degrees of freedom might not be exclusively partonic but that a certain fraction of hadronic degrees of freedom might already form at higher temperatures. This is an interesting question by itself but also has a strong influence on other probes of the strongly interacting matter produced in ultrarelativistic heavy-ion collisions. A substantial fraction of hadronic bound states above ${T}_{c}$ reduces on average the interaction of the heavy quarks with colored constituents of the medium. We find that all studied observables are highly sensitive to the active degrees of freedom in the quark-gluon plasma.

Chiral transition of fundamental and adjoint quarks

The chiral symmetry breaking transition of quarks in the fundamental and adjoint representation is studied in a model where the gap equation contains two contributions, one containing a confining propagator and another corresponding to the exchange of one-dressed dynamically massive gluons. When quarks are in the fundamental representation the confinement effect dominates the chiral symmetry breaking while the gluon exchange is suppressed due to the dynamical gluon mass effect in the propagator and in the coupling constant. In this case the chiral and deconfinement transition temperatures are approximately the same. For quarks in the adjoint representation, due to the larger Casimir eigenvalue, the gluon exchange is operative and the chiral transition happens at a larger temperature than the deconfinement one.

Quark deconfinement transition in neutron stars with the field correlator method

A phase of strong interacting matter with deconfined quarks is expected in the core of massive neutron stars. In this article, we perform a study of the hadron-quark phase transition in cold ($T=0$) neutron star matter and we calculate various structural properties of hybrid stars. For the quark phase, we make use of an equation of state (EOS) derived with the field correlator method (FCM) recently extended to the case of nonzero baryon density. For the hadronic phase, we consider both pure nucleonic and hyperonic matter, and we derive the corresponding EOS within a relativistic mean field approach. We make use of measured neutron star masses, and particularly the mass $M=1.97\ifmmode\pm\else\textpm\fi{}0.04{M}_{\ensuremath{\bigodot}}$ of PSR $\mathrm{J}1614\ensuremath{-}2230$ to constrain the values of the gluon condensate ${G}_{2}$, which is one of the EOS parameters within the FCM. We find that the values of ${G}_{2}$ extracted from the mass measurement of PSR $\mathrm{J}1614\ensuremath{-}2230$ are consistent with the values of the same quantity derived within the FCM from recent lattice QCD calculations of the deconfinement transition temperature at zero baryon chemical potential. The FCM thus provides a powerful tool to link numerical calculations of QCD on a space-time lattice with measured neutron star masses.