Deconfinement Phase Transition Research Articles

Testing the dark SU(N) Yang-Mills theory confined landscape: From the lattice to gravitational waves

We pave the way for future gravitational-wave detection experiments, such as the big bang observer and DECIGO, to constraint dark sectors made of $SU(N)$ Yang-Mills confined theories. We go beyond the state-of-the-art by combining first principle lattice results and effective field theory approaches to infer essential information about the nonperturbative dark deconfinement phase transition driving the generation of gravitational-waves in the early Universe, such as the order, duration and energy budget of the phase transition which are essential in establishing the strength of the resulting gravitational-wave signal.

Multiplicity dependencies of midrapidity transverse momentum spectra of identified charged particles in p+p collisions at (s)1/2 = 13 TeV at LHC

Multiplicity dependencies of midrapidity [Formula: see text] spectra of identified charged particles in inelastic [Formula: see text] collisions at [Formula: see text] TeV at the Large Hadron Collider (LHC), measured by ALICE Collaboration, have been analyzed. The combined minimum [Formula: see text] fits with thermodynamically consistent Tsallis function as well as Hagedorn function with the embedded transverse flow describe quite satisfactorily the [Formula: see text] spectra of particles in the studied 10 different classes of charged-particle multiplicity in inelastic [Formula: see text] collisions at [Formula: see text] TeV. The obtained effective temperatures [Formula: see text] of thermodynamically consistent Tsallis function demonstrate a consistent growth with an increase in multiplicity of charged particles in inelastic [Formula: see text] collisions at [Formula: see text] TeV, and the corresponding [Formula: see text] versus the average charged-particle (pseudorapidity) multiplicity density [Formula: see text] dependence is described very well by the simple power function with exponent parameter [Formula: see text] (1/3) in the whole analyzed range [Formula: see text]. It is found that the transverse (radial) flow becomes significant at higher multiplicity events in [Formula: see text] collisions at [Formula: see text] TeV, reaching the maximum value [Formula: see text] at the largest studied multiplicity density [Formula: see text]. It is estimated from analysis of [Formula: see text] and [Formula: see text] versus [Formula: see text] dependencies, obtained using Hagedorn function with the embedded transverse flow, that the probable onset of deconfinement phase transition in inelastic [Formula: see text] collisions at [Formula: see text] TeV occurs at [Formula: see text].

Gluodynamics and deconfinement phase transition under rotation from holography

We investigate rotating effect on deconfinement phase transition in an Einstein-Maxwell-Dilaton (EMD) model in bottom-up holographic QCD approach. By constructing a rotating black hole, which is supposed to be dual to rotating strongly coupled nuclear matter, we investigate the thermodynamic quantities, including entropy density, pressure, energy density, trace anomaly, sound speed and specific heat for both pure gluon system and two-flavor system under rotation. It is shown that those thermodynamic quantities would be enhanced by large angular velocity. Also, we extract the information of phase transition from those thermodynamic quantities, as well as the order parameter of deconfinement phase transition, i.e. the loop operators. It is shown that, in the T − ω plane, for two-flavor case with small chemical potential, the phase transition is always crossover. The transition temperature decreases slowly with angular velocity and chemical potential. For pure gluon system with zero chemical potential, the phase transition is always first order, while at finite chemical potential a critical end point (CEP) will present in the T − ω plane.

Non-Wilson-Fisher kinks of $O(N)$ numerical bootstrap: from the deconfined phase transition to a putative new family of CFTs

It is well established that the O(N)O(N) Wilson-Fisher (WF) CFT sits at a kink of the numerical bounds from bootstrapping four point function of O(N)O(N) vector. Moving away from the WF kinks, there indeed exists another family of kinks (dubbed non-WF kinks) on the curve of O(N)O(N) numerical bounds. Different from the O(N)O(N) WF kinks that exist for arbitary NN in 2<d<42<d<4 dimensions, the non-WF kinks exist in arbitrary dimensions but only for a large enough N>N_c(d)N>Nc(d) in a given dimension dd. In this paper we have achieved a thorough understanding for few special cases of these non-WF kinks, which already hints interesting physics. The first case is the O(4)O(4) bootstrap in 2d, where the non-WF kink turns out to be the SU(2)_1SU(2)1 Wess-Zumino-Witten (WZW) model, and all the SU(2)_{k>2}SU(2)k>2 WZW models saturate the numerical bound on the left side of the kink. This is a mirror version of the Z_2Z2 bootstrap, where the 2d Ising CFT sits at a kink while all the other minimal models saturating the bound on the right. We further carry out dimensional continuation of the 2d SU(2)_1SU(2)1 kink towards the 3d SO(5)SO(5) deconfined phase transition. We find the kink disappears at around d=2.7d=2.7 dimensions indicating the SO(5)SO(5) deconfined phase transition is weakly first order. The second interesting observation is, the O(2)O(2) bootstrap bound does not show any kink in 2d (N_c=2Nc=2), but is surprisingly saturated by the 2d free boson CFT (also called Luttinger liquid) all the way on the numerical curve. The last case is the N=\inftyN=∞ limit, where the non-WF kink sits at (\Delta_\phi, \Delta_T)=(d-1, 2d)(Δϕ,ΔT)=(d−1,2d) in dd dimensions. We manage to write down its analytical four point function in arbitrary dimensions, which equals to the subtraction of correlation functions of a free fermion theory and generalized free theory. An important feature of this solution is the existence of a full tower of conserved higher spin current. We speculate that a new family of CFTs will emerge at non-WF kinks for finite NN, in a similar fashion as O(N)O(N) WF CFTs originating from free boson at N=\inftyN=∞.

Fluctuations of the order parameter in an SU(Nc) effective model

We investigate features of the deconfinement phase transition in an $SU({N}_{c})$ gauge theory as revealed by fluctuations of the order parameter. The tool of choice is an effective model built from one-loop expressions of the field determinants of gluon and ghost, in the presence of a Polyakov loop background field. We show that the curvature masses associated with the Cartan angles, which serve as a proxy to study the ${A}_{0}$-gluon screening mass, show a characteristic dip in the vicinity of the transition temperature. The strength of the observables, which reflects a competition between the confining and the deconfining forces, is sensitive to assumptions of dynamics, and thus provides an interesting link between the $Z({N}_{c})$ vacuum structure and the properties of gluon and ghost propagators.

Sound velocity in dense stellar matter with strangeness and compact stars * *Supported by National SKA Program of China (2020SKA0120300), the National Natural Science Foundation of China (11873040), the Youth Innovation Fund of Xiamen (3502Z20206061), Ningbo Natural Science Foundation (2019A610066), CAS “Light of West China” Program (2018-XBQNXZ-B-025) and Tianshan Youth Program (2018Q039)

The phase state of dense matter in the intermediate density range ( 1-10 times the nuclear saturation density) is both intriguing and unclear and can have important observable effects in the present gravitational wave era of neutron stars. As matter density increases in compact stars, the sound velocity is expected to approach the conformal limit ( ) at high densities and should also fulfill the causality limit ( ). However, its detailed behavior remains a prominent topic of debate. It was suggested that the sound velocity of dense matter could be an important indicator of a deconfinement phase transition, where a particular shape might be expected for its density dependence. In this work, we explore the general properties of the sound velocity and the adiabatic index of dense matter in hybrid stars as well as in neutron stars and quark stars. Various conditions are employed for the hadron-quark phase transition with varying interface tension. We find that the expected behavior of the sound velocity can also be achieved by the nonperturbative properties of the quark phase, in addition to a deconfinement phase transition. Moreover, it leads to a more compact star with a similar mass. We then propose a new class of quark star equation of states, which can be tested by future high-precision radius measurements of pulsar-like objects.

Topological or rotational non-Abelian gauge fields from Einstein-Skyrme holography

We report analytically known states at non-zero temperature which may serve as a powerful tool to reveal common topological and thermodynamic properties of systems ranging from the QCD phase diagram to topological phase transitions in condensed matter materials. In the holographically dual gravity theory, these are analytic solutions to a five-dimensional non-linear-sigma (Skyrme) model dynamically coupled to Einstein gravity. This theory is shown to be holographically dual to mathcal{N} = 4 Super-Yang-Mills theory coupled to an SU(2)-current. All solutions are fully backreacted asymptotically Anti-de Sitter (AdS) black branes or holes. One family of global AdS black hole solutions contains non-Abelian gauge field configurations with positive integer Chern numbers and finite energy density. Larger Chern numbers increase the Hawking-Page transition temperature. In the holographically dual field theory this indicates a significant effect on the deconfinement phase transition. Black holes with one Hawking temperature can have distinct Chern numbers, potentially enabling topological transitions. A second family of analytic solutions, rotating black branes, is also provided. These rotating solutions induce states with propagating charge density waves in the dual field theory. We compute the Hawking temperature, entropy density, angular velocity and free energy for these black holes/branes. These correspond to thermodynamic data in the dual field theory. For these states the energy-momentum tensor, (non-)conserved current, and topological charge are interpreted.

Hadron-quark mixed phase in the quark-meson coupling model

We explore the possibility of a structured hadron-quark mixed phase forming in the interior of neutron stars. The quark-meson coupling (QMC) model, which explicitly incorporates the internal quark structure of the nucleon, is employed to describe the hadronic phase, while the quark phase is described by the same bag model as the one used in the QMC framework, so as to keep consistency between the two coexisting phases. We analyze the effect of the appearance of hadron-quark pasta phases on the neutron-star properties. We also discuss the influence of nuclear symmetry energy and the bag constant $B$ in quark matter on the deconfinement phase transition. For the treatment of the hadron-quark mixed phase, we use the energy minimization method and compare it with the Gibbs construction. The finite-size effects like surface and Coulomb energies are taken into account in the energy minimization method; they play crucial roles in determining the pasta configuration during the hadron-quark phase transition. It is found that the finite-size effects can significantly reduce the region of the mixed phase relative to that of the Gibbs construction. Using a consistent value of $B$ in the QMC model and quark matter, we find that hadron-quark pasta phases are formed in the interior of massive stars, but no pure quark matter can exist.

Lattice QCD study of static quark and antiquark correlations at finite T via entanglement entropies

With the aim of clarification of color correlations among quarks, we investigate the color correlation between a static quark and an antiquark (static $q\bar q$) below and above the phase transition temperature $T_c$ through the entanglement entropy(EE). By a quenched lattice QCD calculation on an anisotropic lattice adopting the standard Wilson gauge action in the Coulomb gauge, we compute a reduced density matrix $\rho$ defined in the color space, and the entanglement entropy $S_{\rm EE}$ constructed from $\rho$. The spatial volume is $L^3 = 24^3$ and the temporal extents are $N_T = 12,13,14,15,16,18,20$ and $24$, with a gauge coupling $\beta = 5.75$ and a renormalized anisotropy $\xi = 4.0$, which corresponds to temperatures between 180 and 370 MeV. From an analysis of $\rho$ and $S_{\rm EE}$, the color correlation between $q\bar q$ pairs is obtained as a function of the interquark distance $R$ and the temperature $T$. Below $T_c$, the $R$-dependence of the color correlation resembles that at $T=0$: the quark's color correlation gradually decreases as $R$ increases due to the color screening by in-between gluons. Above $T_c$, due to the deconfinement phase transition, the color correlation among quarks is found to quickly dissappear. Further, we investigate the color screening effect via the screening mass defined by $\rho$, and discuss the differences in the screening properties between the small and large R regions.

Rapidly Spinning Compact Stars with Deconfinement Phase Transition

Abstract We study rapidly spinning compact stars with equations of state featuring a first-order phase transition between strongly coupled nuclear matter and deconfined quark matter by employing the gauge/gravity duality. We consider a family of models that allow purely hadronic uniformly rotating stars with masses up to approximately 2.9 M ⊙, and are therefore compatible with the interpretation that the secondary component ( ) in GW190814 is a neutron star. These stars have central densities that are several times the nuclear saturation density, so that strong coupling and non-perturbative effects become crucial. We construct models where the maximal mass of static (rotating) stars M TOV (M max) is either determined by the secular instability or a phase-transition induced collapse. We find the largest values for M max/M TOV in cases where the phase transition determines M max, which shifts our fit result to , a value slightly above the Breu–Rezzolla bound inferred from models without phase transition.

Strong-Interaction Matter under Extreme Conditions from Chiral Quark Models with Nonlocal Separable Interactions

We review the current status of the research on effective nonlocal NJL-like chiral quark models with separable interactions, focusing on the application of this approach to the description of the properties of hadronic and quark matter under extreme conditions. The analysis includes the predictions for various hadron properties in vacuum, as well as the study of the features of deconfinement and chiral restoration phase transitions for systems at finite temperature and/or density. We also address other related subjects, such as the study of phase transitions for imaginary chemical potentials, the possible existence of inhomogeneous phase regions, the presence of color superconductivity, the effects produced by strong external magnetic fields and the application to the description of compact stellar objects.

Investigating the similarity between the behavior of the order parameter derivatives and that of cumulants of the probability density for the thermal deconfining phase transition at zero chemical potential

In this work, we study the temperature driven deconfining phase transition, at zero chemical potential, in a statistical way, by means of the probability distribution of finding the mixed hadronic gas-QGP phase system in a finite volume, in a specific state defined by a parameter lying between 0 and 1, whose mean value represents the order parameter of the studied system. We calculate mean values of other characteristic quantities, called response functions, which are mainly the second, third and fourth cumulants of the probability distribution representing the variance, skewness and kurtosis respectively, as well as the three first thermal derivatives of the order parameter. Integral expressions are obtained for all these quantities, and their evaluation is done numerically. The such obtained results are adequately translated into graphs, illustrating the variations of the response functions with temperature, for various volumes. By examining their behavior, we notice a striking similarity between the behavior of the order parameter derivative and that of the cumulant, at the same order. We investigate this similarity and try to deeply analyze it, to obtain some important features characterizing the occurring deconfining phase transition.

Study of the effects of the curvature term in the density of states on some physical quantities characterizing the deconfining phase transition to a color-singlet QGP

In the present work, we study the effect of including the curvature term, in addition to the volume term, in the density of states used in the calculation of the projected color-singlet partition function of the Quark-Gluon Plasma (QGP), on some features characterizing the phase transition to this new phase of matter. By investigating the behavior of some physical quantities well describing the mixed system with temperature for varying volume, we especially examine the behavior with volume of the shift of the effective transition temperature in a finite volume from the true one, to determine the corresponding scaling exponent. We compare the present results to those obtained in our previous works, where we have used a color-singlet QGP partition function derived with a density of states containing the volume term only.

Sensitivity of the Polyakov Loop to Chiral Symmetry Restoration

In the heavy, static quark mass regime of QCD, the Polyakov loop is well known to be an order parameter of the deconfinement phase transition; however, the sensitivity of the Polyakov loop to the deconfinement of light, dynamical quarks is less clear. On the other hand, from the perspective of an effective Lagrangian written in the vicinity of the chiral transition, the Polyakov loop is an energy-like operator and should hence scale as any energy-like operator would. We show here that the Polyakov loop and heavy-quark free energy are sensitive to the chiral transition, i.e. their scaling is consistent with energy-like observables in 3-$d$ $O(N)$ universality classes.

Deconfinement phase transition under chemical equilibrium

AbstractIn this work, we investigate how the assumption of chemical equilibrium with leptons affects the deconfinement phase transition to quark matter. This is carried out within the framework of the Chiral Mean Field model allowing for nonzero net strangeness, corresponding to the conditions found in astrophysical scenarios. We build three‐dimensional quantum chromodynamics phase diagrams with temperature, baryon chemical potential, and either charge or isospin fraction or chemical potential to show how the deconfinement region collapses to a line in the special case of chemical equilibrium, such as the one established in the interior of cold catalyzed neutron stars.

Latent heat and pressure gap at the first-order deconfining phase transition of SU(3) Yang–Mills theory using the small flow-time expansion method

Abstract We study latent heat and the pressure gap between the hot and cold phases at the first-order deconfining phase transition temperature of the SU(3) Yang–Mills theory. Performing simulations on lattices with various spatial volumes and lattice spacings, we calculate the gaps of the energy density and pressure using the small flow-time expansion (SF$t$X) method. We find that the latent heat $\Delta \epsilon$ in the continuum limit is $\Delta \epsilon /T^4 = 1.117 \pm 0.040$ for the aspect ratio $N_s/N_t=8$ and $1.349 \pm 0.038$ for $N_s/N_t=6$ at the transition temperature $T=T_c$. We also confirm that the pressure gap is consistent with zero, as expected from the dynamical balance of two phases at $T_c$. From hysteresis curves of the energy density near $T_c$, we show that the energy density in the (metastable) deconfined phase is sensitive to the spatial volume, while that in the confined phase is insensitive. Furthermore, we examine the effect of alternative procedures in the SF$t$X method—the order of the continuum and the vanishing flow-time extrapolations, and also the renormalization scale and higher-order corrections in the matching coefficients. We confirm that the final results are all very consistent with each other for these alternatives.

Inverse catalysis effect of the quark anomalous magnetic moment to chiral restoration and deconfinement phase transitions

The effect of quark anomalous magnetic moment (AMM) to chiral restoration and deconfinement phase transitions under magnetic fields is investigated in a Pauli-Villars regularized Polyakov-extended Nambu--Jona-Lasinio model. A linear-in-$B$ term for quark anomalous magnetic moment is introduced to the Lagrangian density of our model, and it plays the role of inverse catalysis to the phase transitions. With fixed magnetic field, the critical temperature decreases with quark AMM. When fixing quark AMM, the critical temperature increases with magnetic field for a small quark AMM, but decreases with magnetic field for a large quark AMM. The critical temperature of chiral restoration and deconfinement phase transitions is determined by the two competing factors, the catalysis effect of magnetic field and inverse catalysis of quark anomalous magnetic moment.

A machine learning study on spinodal clumping in heavy ion collisions

Possible observables of baryon number clustering due to the instabilities occurring at a first order QCD phase transition are discussed. The dynamical formation of baryon clusters at a QCD phase transition can be described by numerical fluid dynamics, augmented with a gradient term and an equation of state with a mechanically unstable region. It is shown that the dynamical description of this phase transition, in nuclear collisions, will lead to the formation of dense baryon clusters at the phase boundary. State-of-the-art machine learning methods find that the coordinate space clumping leaves characteristic imprints on the spatial net density distribution in almost every event. On the other hand the momentum distributions do not show any clear event-by-event features. It is shown that the 'third order' cumulant, the skewness, shows a peak at the beam energy where the system, created in the heavy ion collision, reaches the deconfinement phase transition.

Note on Wess-Zumino-Witten models and quasiuniversality in 2+1 dimensions

We suggest the possibility that the two-dimensional SU(2)$_k$ Wess-Zumino-Witten (WZW) theory, which has global SO(4) symmetry, can be continued to $2+\epsilon$ dimensions by enlarging the symmetry to SO$(4+\epsilon)$. This is motivated by the three-dimensional sigma model with SO(5) symmetry and a WZW term, which is relevant to deconfined criticality. If such a continuation exists, the structure of the renormalization group flows at small $\epsilon$ may be fixed by assuming analyticity in $\epsilon$. This leads to the conjecture that the WZW fixed point annihilates with a new, unstable fixed point at a critical dimensionality $d_c>2$. We suggest that $d_c < 3$ for all $k$, and we compute $d_c$ in the limit of large $k$. The flows support the conjecture that the deconfined phase transition in SU(2) magnets is a ``pseudocritical'' point with approximate SO(5), controlled by a fixed point slightly outside the physical parameter space.

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.