Chiral Symmetry Restoring Phase Transition Research Articles

Role of the conserved charges in the chiral symmetry restoration phase transition

The effect of conserved baryon, isospin and strangeness charges on the behavior of phase transitions in dense matter is studied. Baryonic matter is described within the three-flavor Polyakov$-$Nambu$-$Jona-Lasinio model and several charge fractions $Y_Q$ are considered. The role of the vector interaction, which can be important to describe dense systems, is discussed. Special attention is given to the case with charge fraction $Y_Q=0.4$, due to its importance in heavy-ion collisions and core-collapse supernova matter. It is shown that the possible formation of chiral-symmetric quark matter in the laboratory will be favored in asymmetric matter. Besides, the inclusion of the vector interaction reinforces the formation of quark matter at lower densities.

Development of shashlik electromagnetic calorimeter for the NICA/MPD

The main goal of the NICA heavy-ion program at JINR is an experimental investigation into the properties of nuclear matter within the energy region of the maximum baryonic density. The Multi Purpose Detector (MPD) is one of the detectors at NICA collider, which is optimized for the study on properties of hot and dense matter in heavy-ion collisions and, in particular, the search for a manifestation of possible deconfinement and/or chiral symmetry restoration phase transitions, critical end-point and mixed quark-hadron phase. Electromagnetic calorimeter (ECal) is an important part of MPD . The particular goal of MPD-ECal is to measure position and energy of photons and electrons. Taking all factors (high energy resolution, high segmentation, large enough distance to the vertex, small Moliere radius, high magnetic field and high time resolution) into consideration, a shashlik-type electromagnetic calorimeter is selected. Therefore the tower consists of 220 layers of lead plates and scintillator plates whose thicknesses are namely 0.3mm/1.5mm. The tower cell is 4×4 cm2 in size. To reduce the dead zones effect, all towers should be cut from four sides at small angles, which will significantly improve the position resolution and the performance homogeneity of the ECal. Currently, energy deposition, energy resolution and position reconstruction are studied through Monte Carlo simulations. A prototype of shashlik Ecal has been built and the cosmic test results show that the number of photoelectrons (Npe) is around 522. By comparing with the previous ECal experimental results and simulation results, it is indirectly considered that the energy resolution of the prototype has reached 5%/√E (GeV) . Key technologies to increase light yield are being studied and will be used in the development of new prototypes.

Evidence of the QCD Tricritical Endpoint Existence at NICA-FAIR Energies

.

Chiral and deconfinement phase transitions in QED3 with finite gauge boson mass

Based on the experimental observation that there is a coexisting region between the antiferromagnetic (AF) and d-wave superconducting (dSC) phases, the influences of gauge boson mass m a on chiral symmetry restoration and deconfinement phase transitions in QED3 are investigated simultaneously within a unified framework, i.e., Dyson–Schwinger equations. The results show that the chiral symmetry restoration phase transition in the presence of the gauge boson mass m a is a typical second-order phase transition; the chiral symmetry restoration and deconfinement phase transitions are coincident; the critical number of fermion flavors N c f decreases as the gauge boson mass m a increases, which implies that there exists a boundary that separates the N c f –m a plane into chiral symmetry breaking/confinement region for (N c f , m a ) below the boundary and chiral symmetry restoration/deconfinement region for (N c f , m a ) above it.

Role of strangeness in hybrid stars and possible observables

We study the effects of strangeness on the quark sector of a hybrid star equation of state. Since the model we use to describe quarks is the same as the one we use to describe hadrons, we can also study the effects of strangeness on the chiral symmetry restoration and deconfinement phase transitions (first order or crossover). Finally, we analyze combined effects of hyperons and quarks on global properties of hybrid stars, like mass, radius and cooling profiles. It is found that a large amount of strangeness in the core is related to the generation of twin-star solutions, which can have the same mass as the lower or zero strangeness counterpart, but with smaller radii.

Zero mode in a strongly coupled quark gluon plasma

In connection with massless two-flavor QCD, we analyze the chiral symmetry restoring phase transition using three distinct gluon-quark vertices and two different assumptions about the long-range part of the quark-quark interaction. In each case, we solve the gap equation, locate the transition temperature ${T}_{c}$, and use the maximum entropy method to extract the dressed-quark spectral function at $T>{T}_{c}$. Our best estimate for the chiral transition temperature is ${T}_{c}=147\ifmmode\pm\else\textpm\fi{}8\text{ }\text{ }\mathrm{MeV}$, and the deconfinement transition is coincident. For temperatures markedly above ${T}_{c}$, we find a spectral density that is consistent with those produced using a hard thermal loop expansion, exhibiting both a normal and plasmino mode. On a domain $T\ensuremath{\in}[{T}_{c},{T}_{s}]$, with ${T}_{s}\ensuremath{\simeq}1.5{T}_{c}$, however, with each of the six kernels we considered, the spectral function contains a significant additional feature. Namely, it displays a third peak, associated with a zero mode, which is essentially nonperturbative in origin and dominates the spectral function at $T={T}_{c}$. We suggest that the existence of this mode is a signal for the formation of a strongly coupled quark-gluon plasma and that this strongly interacting state of matter is likely a distinctive feature of the QCD phase transition.

Temperature dependence of the effective bag constant and the radius of a nucleon in the global color symmetry model of QCD

We study the temperature dependence of the effective bag constant, the mass, and the radius of a nucleon in the formalism of the simple global color symmetry model in the Dyson-Schwinger equation approach of QCD with a Gaussian-type effective gluon propagator. We obtain that, as the temperature is lower than a critical value, the effective bag constant and the mass decrease and the radius increases with the temperature increasing. As the critical temperature is reached, the effective bag constant and the mass vanish and the radius tends to infinity. At the same time, the chiral quark condensate disappears. These phenomena indicate that the deconfinement and the chiral symmetry restoration phase transitions can take place at high temperature. The dependence of the critical temperature on the interaction strength parameter in the effective gluon propagator of the approach is given.

Influence of strong magnetic fields and instantons on the phase structure of the two-flavor Nambu–Jona-Lasinio model

Both in heavy-ion collisions as in magnetars very strong magnetic fields are produced, which has its influence on the phases of matter involved. In this paper we investigate the effect of strong magnetic fields (B = 5 m_pi^2 /e = 1.7 x 10^19 G) on the chiral symmetry restoring phase transition using the Nambu-Jona-Lasinio model. It is observed that the pattern of phase transitions depends on the relative magnitude of the magnetic field and the instanton interaction strength. We study two specific regimes in the phase diagram, high chemical potential and zero temperature and vice versa, which are of relevance for neutron stars and heavy-ion collisions respectively. In order to shed light on the behavior of the phase transitions we study the dependence of the minima of the effective potential on the occupation of Landau levels. We observe a near-degeneracy of multiple minima with differing occupation numbers, of which some become the global minimum upon changing the magnetic field or the chemical potential. These minima differ considerably in the amount of chiral symmetry breaking and in some cases also of isospin breaking.

Critical flavor number in the three dimensional Thirring model

We present results of a Monte Carlo simulation of the three dimensional Thirring model with the number of fermion flavors ${N}_{f}$ varied between 2 and 18. By identifying the lattice coupling at which the chiral condensate peaks, simulations are performed at couplings ${g}^{2}({N}_{f})$ corresponding to the strong coupling limit of the continuum theory. The chiral symmetry restoring phase transition is studied as ${N}_{f}$ is increased, and the critical number of flavors estimated as ${N}_{fc}=6.6(1)$. The critical exponents measured at the transition do not agree with self-consistent solutions of the Schwinger-Dyson equations; in particular, there is no evidence for the transition being of infinite order. Implications for the critical flavor number in ${\mathrm{QED}}_{3}$ are briefly discussed.

Hydrodynamics of Sakai–Sugimoto model in the quenched approximation

Abstract We study transport properties of the finite temperature Sakai–Sugimoto model. The model represents a holographic dual to ( 4 + 1 ) -dimensional supersymmetric SU ( N c ) gauge theory compactified on a circle with anti-periodic boundary conditions for fermions, coupled to N f left-handed quarks and N f right-handed quarks localized at different points on the compact circle. We analytically compute the speed of sound and the sound wave attenuation in the quenched approximation. Since confinement/deconfinement (and the chiral symmetry restoration) phase transitions are first order in this model, we do not see any signature of these phase transitions in the transport properties.

Self-consistent calculations of spectral densities in the [formula omitted] model: improving the Hartree–Fock approximation by including nonzero decay widths

We study the linear sigma model with O ( N ) symmetry at nonzero temperature in the framework of the Cornwall–Jackiw–Tomboulis formalism. Extending the set of two-particle irreducible diagrams by adding sunset diagrams to the usual Hartree–Fock contributions, we derive a new approximation scheme which extends the standard Hartree–Fock approximation by the inclusion of nonzero decay widths. In this approximation, in-medium modifications of the meson masses as well as decay and collisional broadening effects are self-consistently taken into account. As compared to the standard Hartree–Fock approximation, the temperature for the chiral symmetry restoring phase transition is lowered by ∼ 20 – 25 % . For large temperatures, the spectral densities of the σ-meson and the pion become degenerate, as required for the chirally symmetric phase.

Lattice study of anisotropic quantum electrodynamics in three dimensions

We present results from a Monte Carlo simulation of noncompact lattice QED in three dimensions on a ${16}^{3}$ lattice in which an explicit anisotropy between $x$ and $y$ hopping terms has been introduced into the action. This formulation is inspired by recent formulations of anisotropic ${\mathrm{QED}}_{3}$ as an effective theory of the non-superconducting portion of the cuprate phase diagram, with relativistic fermion degrees of freedom defined near the nodes of the gap function on the Fermi surface, the anisotropy encapsulating the different Fermi and Gap velocities at the node, and the massless photon degrees of freedom reproducing the dynamics of the phase disorder of the superconducting order parameter. Using a parameter set corresponding in the isotropic limit to broken chiral symmetry (in field theory language) or a spin density wave (in condensed matter physics language), our results show that the renormalized anisotropy, defined in terms of the ratio of correlation lengths of gauge invariant bound states in the $x$ and $y$ directions, exceeds the explicit anisotropy $\ensuremath{\kappa}$ introduced in the lattice action, implying in contrast to recent analytic results that anisotropy is a relevant deformation of ${\mathrm{QED}}_{3}$. There also appears to be a chiral symmetry restoring phase transition at ${\ensuremath{\kappa}}_{c}\ensuremath{\simeq}4.5$, implying that the pseudogap phase persists down to $T=0$ in the cuprate phase diagram.

Quantum vacuum in hot nuclearmatter: a non-perturbative treatment

We derive the equation of state for hot nuclear matterusing the Walecka model in a non-perturbative formalism.We include here the vacuum polarization effects arisingfrom the nucleon and scalar mesons through a realignmentof the vacuum. A ground state structure withbaryon-antibaryon condensates yields the resultsobtained through the relativistic Hartree approximationof summing baryonic tadpole diagrams. Generalization ofsuch a state to include the quantum effects for thescalar meson fields through the σ-mesoncondensates amounts to summing over a class of multiloopdiagrams. The techniques of the thermofield dynamicsmethod are used for the finite-temperature andfinite-density calculations. The in-medium nucleon andsigma meson masses are also calculated in aself-consistent manner. We examine the liquid-gas phasetransition at low temperatures (≈ 20 MeV), aswell as apply the formalism to high temperatures toexamine a possible chiral symmetry restoration phasetransition.

Influence of theU(1)Aanomaly on the QCD phase transition

The ${\mathrm{SU}(3)}_{r}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(3)}_{l}$ linear sigma model is used to study the chiral symmetry restoring phase transition of QCD at nonzero temperature. The line of second order phase transitions separating the first order and smooth crossover regions is located in the plane of the strange and nonstrange quark masses. It is found that if the ${U(1)}_{A}$ symmetry is explicitly broken by the ${U(1)}_{A}$ anomaly, then there is a smooth crossover to the chirally symmetric phase for physical values of the quark masses. However, if the ${U(1)}_{A}$ anomaly is absent, the region of first order phase transitions is significantly enlarged and it is found that there is a phase transition for physical values of the quark masses provided that the $\ensuremath{\sigma}$ meson mass is at least 600 MeV. In both cases, the region of first order phase transitions in the quark mass plane is enlarged as the mass of the $\ensuremath{\sigma}$ meson is increased.

Phase diagram of QCD

We analyze the phase diagram of QCD with two massless quark flavors in the space of temperature $T$ and chemical potential of the baryon charge \ensuremath{\mu} using available experimental knowledge of QCD, insights gained from various models, as well as general and model independent arguments including continuity, universality, and thermodynamic relations. A random matrix model is used to describe the chiral symmetry restoration phase transition at finite $T$ and \ensuremath{\mu}. In agreement with general arguments, this model predicts a tricritical point in the $T\ensuremath{\mu}$ plane. Certain critical properties at such a point are universal and can be relevant to heavy ion collision experiments.

Chiral symmetry and dileptons in heavy ion collisions

We study the consequences of chiral symmetry restoration for thermal production of dileptons in central nucleus-nucleus collisions. We discuss the temperature dependence of various hadronic parameters entering the dilepton cross-section, putting emphasis on universal properties in the vicinity of a 2nd order chiral symmetry restoring phase transition and the constraints on their temperature dependence known from lattice simulations. It is shown that the modifications of the hadron spectrum due to medium effects can lead to important changes of the thermal dilepton production rate in heavy ion collisions. In particular, it can imply the suppression of a thermalp peak.

QCD phase structure with 8 light quark flavors

The QCD phase structure with eight degenerate flavors is studied on 16 3 × N t lattices with N t = 4, 8, 16 and 32. A dynamical quark of mass ma = 0.015 was used in the simulation. In calculating 〈ḡcχ〉 and hadron propagator, we also used valence quark masses of ma = 0.004, 0.01 and 0.025 in order to study the chiral property of the phases. A strong, first order chiral symmetry restoring phase transition is seen at N t = 4 and 8 with different β c . However, β c becomes independent of N t when N t ≥ 8, indicating a bulk or zero temperature phase transition with β c = 4.59(2). A chirally symmetric phase at β = 5.0 is seen while in the region of weak coupling with β ≈ β c hadron propagators suggest a chirally asymmetric behavior.

A mean field theory study of lattice gauge theory with finite temperature and with finite fermion density

We have developed a mean field theory technique to study the confinement-deconfinement phase transition and chiral symmetry restoring phase transition with dynamical fermions and with finite chemical potential and finite temperature. The approximation scheme concerns the saddle point scenario and large space dimension. The static quark-antiquark potentials are identified from the Wilson loop correlation functions in both the fundamental and the adjoint representation of the gauge group with different temperatures. The difference between the responses of the chemical potential to the fermion number with singlet and non-singlet isospin configuration is found. We compare our results with recent Monte Carlo data.

The order of the QCD finite temperature transition and hybrid Monte Carlo

In this talk I describe results obtained in collaboration with Khalil Bitar, Roger Horsley, A.D. Kennedy and Pietro Rossi. Using Hybrid Monte Carlo we study the nature of the finite temperature transition for Lattice Quantum Chromodynamics with Kogut-Susskind staggered fermions at intermediate quark masses. We point out the importance of simulating the action without finite step size corrections. Applying finite size scaling we find indications for a first order chiral symmetry restoring phase transition for lattices with four time-slices and a range of spatial volumes.

Chiral-symmetry order parameter, the lattice, and nucleosynthesis.

I discuss an order parameter for the chiral-symmetry restoration phase transition which may be useful in computations of big-bang nucleosynthesis, a phenomenon which requires a finite baryon-number density. This parameter is strictly speaking an order parameter in the large-N limit, and distinguishes between a parity-doubled and a massless-fermion realization of chiral-symmetry restoration. This order parameter may be evaluated at a zero net baryon-number density at finite temperature, and is useful as long as the baryon chemical potential ..mu.. is much less than the temperature T.