Critical Temperature For Deconfinement Research Articles

Critical Temperature of Deconfinement in a Constrained Space Using a Bag Model at Vanishing Baryon DensitySupported by the National Natural Science Foundation of China (Grant Nos. 11547043 and 11705125), and the “Qinggu” Project of Tianjin University (Grant No. 1701).

The geometry of fireballs in relativistic heavy ion collisions is approximated by a static box, which is infinite in two directions while finite in the other direction. The critical temperature of deconfinement phase transition is calculated explicitly in the MIT bag model at vanishing baryon density. It is found that the critical temperature shifts to a value higher than that in an unconstrained space.

Fully Quantum String Representation of a Wilson Loop in the Finite-Temperature 3D Yang–Mills Theory

We demonstrate the emergence of the Polchinski–Strominger term in the string representation of a Wilson loop in the confinement phase of the finite-temperature 3D Yang–Mills theory. At a temperature which is roughly twice smaller than the deconfinement critical temperature, the value of the coupling of that term becomes such that the string conformal anomaly cancels out, thereby admitting a fully quantum description of the quark–antiquark string in 3D rather than 26D.

Phase structure of lattice Yang-Mills theory on T2×R2

We study properties of SU(2) Yang-Mills theory on a four-dimensional Euclidean spacetime in which two directions are compactified into a finite two-dimensional torus ${\mathbb T}^2$ while two others constitute a large ${\mathbb R}^2$ subspace. This Euclidean ${\mathbb T}^2 \times {\mathbb R}^2$ manifold corresponds simultaneously to two systems in a (3+1) dimensional Minkowski spacetime: a zero-temperature theory with two compactified spatial dimensions and a finite-temperature theory with one compactified spatial dimension. Using numerical lattice simulations we show that the model exhibits two phase transitions related to the breaking of center symmetries along the compactified directions. We find that at zero temperature the transition lines cross each other and form the Greek letter $\gamma$ in the phase space parametrized by the lengths of two compactified spatial dimensions. There are four different phases. We also demonstrate that the compactification of only one spatial dimension enhances the confinement property and, consequently, increases the critical deconfinement temperature.

Interplay between the holographic QCD phase diagram and mutual & n-partite information

In an earlier work, we studied holographic entanglement entropy in QCD phases using a dynamical Einstein-Maxwell-dilaton gravity model whose dual boundary theory mimics essential features of QCD above and below deconfinement. The model although displays subtle differences compared to the standard QCD phases, however, it introduces a notion of temperature in the phase below the deconfinement critical temperature and captures quite well the entanglement and thermodynamic properties of QCD phases. Here we extend our analysis to study the mutual and n-partite information by considering n strips with equal lengths and equal separations, and investigate how these quantities leave their imprints in holographic QCD phases. We discover a rich phase diagram with n ≥ 2 strips and the corresponding mutual and n-partite information shows rich structure, consistent with the thermodynamical transitions, while again revealing some subtleties. Below the deconfinement critical temperature, we find no dependence of the mutual and n-partite information on temperature and chemical potential.

Deconfinement phase transition in a magnetic field in 2 + 1 dimensions from holographic models

Using two different models from holographic quantum chromodynamics (QCD) we study the deconfinement phase transition in 2+1 dimensions in the presence of a magnetic field. Working in 2+1 dimensions lead us to exact solutions on the magnetic field, in contrast with the case of 3+1 dimensions where the solutions on the magnetic field are perturbative. As our main result we predict a critical magnetic field Bc where the deconfinement critical temperature vanishes. For weak fields meaning B<Bc we find that the critical temperature decreases with increasing magnetic field indicating an inverse magnetic catalysis (IMC). On the other hand, for strong magnetic fields B>Bc we find that the critical temperature raises with growing field showing a magnetic catalysis (MC). These results for IMC and MC are in agreement with the literature.

Finite Temperature QCD Sum Rules: A Review

The method of QCD sum rules at finite temperature is reviewed, with emphasis on recent results. These include predictions for the survival of charmonium and bottonium states, at and beyond the critical temperature for deconfinement, as later confirmed by lattice QCD simulations. Also included are determinations in the light-quark vector and axial-vector channels, allowing analysing the Weinberg sum rules and predicting the dimuon spectrum in heavy-ion collisions in the region of the rho-meson. Also, in this sector, the determination of the temperature behaviour of the up-down quark mass, together with the pion decay constant, will be described. Finally, an extension of the QCD sum rule method to incorporate finite baryon chemical potential is reviewed.

Deconfinement and chiral transition in AdS/QCD wall models supplemented with a magnetic field

We discuss the phenomenon of (inverse) magnetic catalysis for both the deconfinement and chiral transition. We discriminate between the hard and soft wall model, which we suitably generalize to include a magnetic field. Our findings show a critical deconfinement temperature going down, in contrast with the chiral restoration temperature growing with increasing magnetic field. This is at odds with contemporary lattice data, so the quest for a holographic QCD model capable of capturing inverse magnetic catalysis in the chiral sector remains open.

Holographic picture of heavy vector meson melting

The fraction of heavy vector mesons produced in a heavy ion collision, as compared to a proton proton collision, serves as an important indication of the formation of a thermal medium, the quark gluon plasma. This sort of analysis strongly depends on understanding the thermal effects of a medium like the plasma on the states of heavy mesons. In particular, it is crucial to know the temperature ranges where they undergo a thermal dissociation, or melting. AdS/QCD models are know to provide an important tool for the calculation of hadronic masses, but in general are not consistent with the observation that decay constants of heavy vector mesons decrease with excitation level. It has recently been shown that this problem can be overcome using a soft wall background and introducing an extra energy parameter, through the calculation of correlation functions at a finite position of anti-de Sitter space. This approach leads to the evaluation of masses and decay constants of S wave quarkonium states with just one flavor dependent and one flavor independent parameters. Here we extend this more realistic model to finite temperatures and analyse the thermal behavior of the states $1S, 2S$ and $ 3S$ of bottomonium and charmonium. The corresponding spectral function exhibits a consistent picture for the melting of the states where, for each flavor, the higher excitations melt at lower temperatures. We estimate for these six states, the energy ranges in which the heavy vector mesons undergo a transition from a well defined peak in the spectral function to complete melting in the thermal medium. A very clear distinction between the heavy flavors emerges, with bottomonium state $\Upsilon (1S)$ surviving deconfinemet transition at temperatures much larger than the critical deconfinement temperature of the medium.

No inverse magnetic catalysis in the QCD hard and soft wall models

In this paper, we study the influence of an external magnetic field in holographic QCD models where the backreaction is modeled in via an appropriate choice of the background metric. We add a phenomenological soft wall dilaton to incorporate better IR behavior (confinement). Elaborating on previous studies conducted by [JHEP 1505 (2015) 121], we first discuss the Hawking-Page transition, the dual of the deconfinement transition, as a function of the magnetic field. We confirm that the critical deconfinement temperature can drop with the magnetic field. Secondly, we study the quark condensate holographically as a function of the applied magnetic field and demonstrate that this model does not exhibit inverse magnetic catalysis at the level of the chiral transition. The quest for a holographic QCD model that qualitatively describes the inverse magnetic catalysis at finite temperature is thus still open. Throughout this work, we pay special attention to the different holographic parameters and we attempt to fix them by making the link to genuine QCD as close as possible. This leads to several unanticipated and so far overlooked complications (such as the relevance of an additional length scale in the confined geometry) that we discuss in detail.

Theta Dependence in Yang-Mills from Holography

In this contribution we review how holographic tools can be used to study the dependence on the CP-breaking θ parameter of various observables in a large Nc Yang-Mills model. Relevant examples are the ground-state energy density, the string tension, the glueball mass spectrum and the critical temperature for deconfinement. These observables have been also studied, in the small θ regime and up to very few powers of θ 2 , in pure Yang-Mills on the Lattice. The holographic results qualitatively agree with available Lattice data and, being exact in θ , provide benchmarks for higher order corrections.

Dilepton and photon production in the presence of a nontrivial Polyakov loop

We calculate the production of dileptons and photons in the presence of a nontrivial Polyakov loop in QCD. This is applicable to the semi-Quark Gluon Plasma (QGP), at temperatures above but near the critical temperature for deconfinement. The Polyakov loop is small in the semi-QGP, and near unity in the perturbative QGP. Working to leading order in the coupling constant of QCD, we find that there is a mild enhancement, ~ 20%, for dilepton production in the semi-QGP over that in the perturbative QGP. In contrast, we find that photon production is strongly suppressed in the semi-QGP, by about an order of magnitude, relative to the perturbative QGP. In the perturbative QGP photon production contains contributions from 2->2 scattering and collinear emission with the Landau- Pomeranchuk-Migdal (LPM) effect. In the semi-QGP we show that the two contributions are modified differently. The rate for 2->2 scattering is suppressed by a factor which depends upon the Polyakov loop. In contrast, in an SU(N) gauge theory the collinear rate is suppressed by 1/N, so that the LPM effect vanishes at infinite N. To leading order in the semi-QGP at large N, we compute the rate from 2->2 scattering to the leading logarithmic order and the collinear rate to leading order.

Notes on theta dependence in holographic Yang-Mills

Effects of the theta parameter are studied in Witten's model of holographic 4d Yang-Mills, where theta is the coefficient of the CP-breaking topological term. First, the gravity background, including the full backreaction of the RR form dual to the theta parameter, is revisited. Then, a number of observables are computed holographically: the ground-state energy density, the string tension, the 't Hooft loop, the light scalar glueball mass, the baryon mass scale, the critical temperature for deconfinement - and thus the whole (T, theta) phase diagram - and the entanglement entropy. A simple rule is provided to derive the theta corrections to (at least) all the CP-neutral observables of the model. Some of the observables we consider can and have been in fact studied in pure 4d Yang-Mills on the lattice. In that framework the results, obtained in the small theta regime, are given up to very few powers of theta^2. The corresponding holographic results agree qualitatively with available lattice data and signal an overall mass scale reduction by theta. Moreover, being exact in theta, they provide a benchmark for higher order corrections in Yang-Mills.

Quark spectral function and deconfinement at nonzero temperature

The maximum entropy method is used to compute the quark spectral function at nonzero temperature. We solve the gap equation of quantum chromodynamics (QCD) self-consistently, employing a rainbow kernel which phenomenologically models results from Dyson-Schwinger equations and lattice QCD. We use the criterion of positivity restoration of the spectral function as a signal for deconfinement. Our calculation indicates that the critical temperature of deconfinement ${T}_{d}$ is slightly smaller than the one of chiral symmetry restoration ${T}_{c}$: ${T}_{d}\ensuremath{\sim}94%{T}_{c}$ in the chiral limit and ${T}_{d}\ensuremath{\sim}96%{T}_{c}$ with physical light quark masses. Since these deviations are within the systematic error of our approach, it is reasonable to conclude that chiral symmetry restoration and deconfinement coincide at zero chemical potential.

LargeNcdeconfinement transition in the presence of a magnetic field

We investigate the effect of a homogeneous magnetic field on the thermal deconfinement transition of QCD in the large ${N}_{c}$ limit. First we discuss how the critical temperature decreases due to the inclusion of ${N}_{f}\ensuremath{\ll}{N}_{c}$ flavors of massless quarks in comparison to the pure glue case. Then we study the equivalent correction in the presence of an external Abelian magnetic field. To leading order in ${N}_{f}/{N}_{c}$, the deconfinement critical temperature decreases with the magnetic field if the flavor contribution to the pressure behaves paramagnetically, with a sufficiently large magnetization as to overcome any possible magnetic effects in the string tension. Finally, we discuss the effects from a finite quark mass and its competition with magnetic effects.

Thermodynamics of SU(N) Yang-Mills theories in 2 + 1 dimensions II — The deconfined phase

Abstract We present a non-perturbative study of the equation of state in the deconfined phase of Yang-Mills theories in D = 2 + 1 dimensions. We introduce a holographic model, based on the improved holographic QCD model, from which we derive a non-trivial relation between the order of the deconfinement phase transition and the behavior of the trace of the energy-momentum tensor as a function of the temperature T. We compare the theoretical predictions of this holographic model with a new set of high-precision numerical results from lattice simulations of SU(N) theories with N = 2, 3, 4, 5 and 6 colors. The latter reveal that, similarly to the D = 3 + 1 case, the bulk equilibrium thermodynamic quantities (pressure, trace of the energy-momentum tensor, energy density and entropy density) exhibit nearly perfect proportionality to the number of gluons, and can be successfully compared with the holographic predictions in a broad range of temperatures. Finally, we also show that, again similarly to the D = 3 + 1 case, the trace of the energy-momentum tensor appears to be proportional to T 2 in a wide temperature range, starting from approximately 1.2 T c , where T c denotes the critical deconfinement temperature.

QCD sum rules and thermal properties of Charmonium in the vector channel

The thermal evolution of the hadronic parameters of charmonium in the vector channel, i.e. the J / ψ resonance mass, coupling (leptonic decay constant), total width, and continuum threshold is analyzed in the framework of thermal Hilbert moment QCD sum rules. The continuum threshold s 0 , as in other hadronic channels, decreases with increasing temperature until the PQCD threshold s 0 = 4 m Q 2 is reached at T ≃ 1.22 T c ( m Q is the charm quark mass) and the J / ψ mass is essentially constant in a wide range of temperatures. The other hadronic parameters behave in a very different way from those of light-light and heavy-light quark systems. The total width grows with temperature up to T ≃ 1.04 T c beyond which it decreases sharply with increasing T. The resonance coupling is also initially constant beginning to increase monotonically around T ≃ T c . This behavior strongly suggests that the J / ψ resonance might survive beyond the critical temperature for deconfinement, in agreement with lattice QCD results.

Charmonium in the vector channel at finite temperature from QCD sum rules

Thermal Hilbert moment QCD sum rules are used to obtain the temperature dependence of the hadronic parameters of charmonium in the vector channel, i.e. the $J/\ensuremath{\psi}$ resonance mass, coupling (leptonic decay constant), total width, and continuum threshold. The continuum threshold ${s}_{0}$, which signals the end of the resonance region and the onset of perturbative QCD, behaves as in all other hadronic channels, i.e. it decreases with increasing temperature until it reaches the perturbative QCD threshold ${s}_{0}=4{m}_{Q}^{2}$, with ${m}_{Q}$ the charm quark mass, at $T\ensuremath{\simeq}1.22{T}_{c}$. The rest of the hadronic parameters behave very differently from those of light-light and heavy-light quark systems. The $J/\ensuremath{\psi}$ mass is essentially constant in a wide range of temperatures, while the total width grows with temperature up to $T\ensuremath{\simeq}1.04{T}_{c}$ beyond which it decreases sharply with increasing $T$. The resonance coupling is also initially constant and then begins to increase monotonically around $T\ensuremath{\simeq}{T}_{c}$. This behavior of the total width and of the leptonic decay constant provides a strong indication that the $J/\ensuremath{\psi}$ resonance might survive beyond the critical temperature for deconfinement.

Thermodynamics of the QCD Plasma and the Large-NLimit

The equilibrium thermodynamic properties of the SU(N) plasma are studied nonperturbatively in the large-N limit, via high-precision lattice simulations at temperatures from 0.8T(c) to 3.4T(c) (T(c) being the critical deconfinement temperature). Our results for SU(N) Yang-Mills theories with N=3, 4, 5, 6, and 8 colors show a very mild dependence on N, supporting the idea that the QCD plasma could be described by models based on the large-N limit. We compare our data with various theoretical descriptions, including, in particular, the improved holographic QCD model proposed by Kiritsis and collaborators. We also comment on the relevance of an AdS/CFT description in a phenomenologically interesting temperature range where the system, while still strongly coupled, becomes approximately scale invariant. Finally, we extrapolate our results to the N --> infinity limit.

Pressure and interaction measure of the gluon plasma

We explore the thermodynamics of the gluon plasma in SU ( 3 ) Yang–Mills theory emerging from the nontrivial spatial dynamics of valence gluons. The lattice data suggest that these gluons interact with each other linearly at large spatial separations. At high temperatures, valence gluons should reproduce the pressure of the noninteracting Stefan–Boltzmann plasma along with the leading perturbative correction. These properties of valence gluons can be modeled in terms of the integral over their trajectories. We calculate such a world-line integral analytically and obtain the pressure and the interaction measure ( ε − 3 p ) / T 4 of the gluon plasma. Additionally, we account for the contributions of stochastic background fields to these thermodynamic quantities. The results turn out to be in a good agreement with the corresponding lattice data. In particular, the lattice-simulated peak of the interaction measure near the deconfinement critical temperature is reproduced.

Spectral Properties of Quarks at Finite Temperature in Lattice QCD

We analyze the quark spectral function above and below the critical temperature for deconfinement and at finite momentum in quenched lattice QCD. It is found that the temporal quark correlation function in the deconfined phase near the critical temperature is well reproduced by a two-pole ansatz for the spectral function. The bare quark mass and momentum dependences of the spectral function are analyzed with this ansatz. In the chiral limit we find that even near the critical temperature the quark spectral function has two collective modes corresponding to the normal and plasmino excitations in the high temperature ( T) limit. The pole mass of these modes at zero momentum, which should be identified to be the thermal mass of the quark, is approximately proportional to T in a rather wide range of T in the deconfined phase.