abstract

Bulk and shear viscosity coefficients for systems composed of quasiparticles with medium-modified dispersion relations are determined within an effective kinetic theory approach of Boltzmann–Vlasov type. Local conservation of energy and momentum, which is self-consistently embedded in the kinetic theory, implies in thermal equilibrium thermodynamic consistency in quasiparticle approaches.

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A mini-review of non-uniform phases in quark matter is presented, with particular attention to the pion condensation, also known as chiral density waves or chiral spirals. The phase diagram of strongly-interacting matter may involve such a phase, placed on the quarkyonic island between the baryonic phase and the chirally-restored quark-gluon plasma.

abstract

We present some recent developments in our study of inhomogeneous chiral symmetry breaking phases in the Nambu–Jona-Lasinio model. First, we investigate different kinds of one- and two-dimensional spatial modulations of the chiral condensate within the inhomogeneous “island” and compare their free energies. Next, we employ the Polyakov-loop extended version of the model to study the effects of varying the number of colors on the inhomogeneous region. Finally, we discuss the properties of an inhomogeneous “continent” which appears in our model at higher chemical potentials, and analyze its origin.

abstract

Transport coefficients can be obtained from 2-point correlators using the Kubo formulae. It has been shown that the full leading order result for electrical conductivity and (QCD) shear viscosity is contained in the re-summed 2-point function that is obtained from the 3-loop 3PI effective action. The theory produces all leading order contributions without the necessity for power counting, and in, this sense, provides a natural framework for the calculation and suggests that one can calculate the next-to-leading contribution to transport coefficients from the 4-loop 4PI effective action. The integral equations have been derived for shear viscosity for a scalar theory with cubic and quartic interactions, with a non-vanishing field expectation value. We review these results, and explain how the calculation could be done at higher orders.

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A short review is presented of some results related to the chemical equilibration of hadrons in the final state of \(p\)–\(p\) and heavy ion collisions. Expectations are discussed also for the production of more complex forms of antimatter like antinuclei and antihypernuclei.

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We discuss the formation of quarkyonic chiral spirals in the presence of a magnetic field. The explicit breaking of the rotational symmetry by the external magnetic field gives rise to an additional chiral spiral that varies along the field direction and rotates in the chiral space between pion and magnetic moment components.

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We summarize recent results obtained in the Dyson–Schwinger formalism to study the chiral and deconfinement phase transitions of QCD at finite temperature and chemical potential. We compare the quenched SU(2) and SU(3) gauge theories and find a clearer distinction between second and first order transitions as compared to previous studies. For the full theory with two degenerate quark flavors we find coinciding crossover transition lines for the chiral and deconfinement transition at finite chemical potential. These lines merge together at large chemical potential and end in a critical endpoint followed by a first order coexistence region. Our results suggest that there is no critical endpoint in the region \(\mu /T \lt 1\).

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We propose an extended schematic model for hadrons in which quarks as well as diquarks serve as building blocks. The outcome is a reclassification of the hadron spectrum in which there are no radially excited hadrons: all mesons and baryons previously believed to be radial excitations are orbitally excited states involving diquarks. Also, there are no exotic hadrons: all hadrons previously believed to be exotic are states involving diquarks and are an integral part of the model. We discuss the implications of this result for a new understanding of confinement and its relation to asymptotic freedom, as well as its implications for a novel relation between the size and energy of hadrons, whereby an excited hadron shrinks.

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I discuss the analytic structure of thermodynamic quantities for complex values of thermodynamic variables within Landau theory. In particular, the singularities connected with phase transitions of second order, first order, and cross over types are examined. A conformal mapping is introduced, which may be used to explore the thermodynamics of strongly interacting matter at finite values of the baryon chemical potential \(\mu \) starting from lattice QCD results at \(\mu ^{2}\leq 0\). This method allows us to improve the convergence of a Taylor expansion about \(\mu =0\) and to enhance the sensitivity to physical singularities in the complex \(\mu \) plane. The technique is illustrated by an application to a second-order transition in a chiral effective model.

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We overview a possible mechanism for confining but chirally symmetric matter at low temperatures and large densities. As a new development, we employ a diffused quark Fermi surface and show that such diffusion does not destroy possible existence of a confining but chirally symmetric matter at low temperatures and large density.

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Azimuthal correlations of particles produced in nucleus–nucleus collisions at CERN SPS are discussed. The correlations quantified by the integral measure \({\mit \Phi }\) are shown to be dominated by effects of collective flow.

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We study the effect of quantum and thermal fluctuations as well as the mass dependence of the phase structure of QCD at finite temperature and density within a dynamical Polyakov-loop-extended quark-meson model. The glue dynamics is simulated by the Polyakov-loop potential, also including the back-coupling of the matter sector to the glue dynamics. In the chiral limit, the chiral phase transition at large chemical potential and low temperature splits into two transition branches. For non-vanishing pion masses the chiral transition at small chemical potential changes from a phase transition to a crossover. We close with a discussion of a systematical improvement of the current model towards full QCD.

abstract

We discuss universal properties of higher order cumulants of net baryon number fluctuations and point out their relevance for the analysis of freeze-out and critical conditions in heavy ion collisions at LHC and RHIC. We focus on a discussion of universal properties of sixth order cumulants and compare with calculations performed in the Polyakov loop extended Quark Meson model.

abstract

Large neutron star masses as the recently measured \(1.97\pm 0.04\,M_\odot \) for PSR J1614-2230 provide a valuable lower limit on the stiffness of the equation of state of dense, nuclear and quark matter. Complementary, the analysis of the elliptic flow in heavy ion collisions suggests an upper limit on the EoS stiffness. We illustrate how this dichotomy permits to constrain parameters of effective EoS models which otherwise could not be derived unambiguously from first principles.

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In this contribution we will discuss current measurements of charge dependent particle correlations and their implication for possible local parity violation.

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The interweaving chiral spirals (ICS), that is defined as superposition of differently oriented chiral spirals, is important for qualitative understandings of the intermediate quark density region as well as quantitative estimates of the Quarkyonic region. We discuss how to construct the ICS, taking the (2+1) dimensional Fermi system as an example. We postulate that the presence of the ICS would delay the occurrence of the chiral restoration as well as deconfinement phase transition, by tempering the growth of quark fluctuations.

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Observable manifestations of the chiral/deconfinement phase transition in relativistic heavy-ion collisions may be strongly affected by the fast expansion of the produced quark-gluon plasma. We study this effect within the linear sigma model with constituent quarks, which predicts a chiral phase transition for a static system in thermal equilibrium. We derive coupled equations for the hydrodynamic variables and the order-parameter field, so-called chiral fluid dynamics. Stability of the chiral fluid in the static and expanding backgrounds is investigated by considering the evolution of fluctuations with respect to the mean-field solution. The effects of supercooling and reheating in the case of the first order phase transition are studied for the Bjorken-like background.

abstract

The phase structure of Polyakov-loop extended Nambu–Jona-Lasinio (PNJL) model is explored at imaginary chemical potential, with particular emphasis on the deconfinement transition. We point out that the statistical confinement nature of the model naturally leads to characteristic dependence of the chiral condensate \(\langle \bar {q}q \rangle \) on \(\theta =\mu _{\rm I}/T\). We introduce a dual parameter for the deconfinement transition by making use of this dependence. By changing a four-fermion coupling constant, we tune the location of the critical endpoint of the deconfinement transition.

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We discuss the QCD phase diagram from two different points of view. We first investigate the phase diagram structure in the strong coupling lattice QCD with Polyakov loop effects, and show that the chiral and \(Z_{N_c}\) deconfinement transition boundaries deviate at finite \(\mu \) as suggested from large \(N_c\) arguments. Next, we discuss the possibility to probe the QCD critical point during prompt black hole formation processes. The thermodynamical evolution during the black hole formation would result in quark matter formation, and the critical point in isospin asymmetric matter may be swept. \((T,\mu _B)\) region probed in heavy-ion collisions and the black hole formation processes cover most of the critical point locations predicted in recent lattice Monte Carlo simulations and chiral effective models.

abstract

The present knowledge of the QCD phase diagram based on simulations of lattice QCD is summarised. The main questions are whether there is a critical point in the QCD phase diagram and whether it is related to a chiral phase transition. It is shown that QCD at imaginary chemical potentials has a rich phase structure, which can be determined in a controlled way without the sign problem and which severely constrains the phase structure at real chemical potentials.

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We conclude our investigation on the QCD equation of state (EoS) with \(2+1\) staggered flavors and one-link stout improvement. We extend our previous study by choosing even finer lattices. These new results support our earlier findings. Lattices with \(N_t=6,8\) and \(10\) are used, and the continuum limit is approached by checking the results at \(N_t=12\). A Symanzik improved gauge and a stout-link improved staggered fermion action is taken; the light and strange quark masses are set to their physical values. Various observables are calculated in the temperature (\(T\)) interval of 100 to 1000 MeV. We also present our new results on flavor diagonal and non-diagonal quark number susceptibilities, in a temperature regime between 120 and 400 MeV. In this case, lattices with \(N_t=6,~8,~10,~12\) are used. We perform a continuum extrapolation of those observables for which the scaling regime is reached, and discretization errors are under control.

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We propose an effective chiral Lagrangian with a chiral scalar introduced as a dilaton associated with broken conformal symmetry and responsible for the trace anomaly in QCD, and discuss the properties of hadronic matter at high density and temperature. As the “dilaton limit” is taken, which drives a system from nuclear matter density to near chiral restoration density, a linear sigma model emerges from the highly non-linear structure. A striking prediction is that as the dilaton limit is approached, the omega-nucleon interaction gets strongly suppressed at high density. This is shown to be a firm statement at the quantum level protected by an infrared fixed point of the renormalization group equations derived in chiral perturbation theory.

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In order to describe hot and dense matter in heavy-ion collisions as well as potentially in hybrid stars theoretical models have to include hadronic as well as quark degrees of freedom. We discuss a theoretical approach that treats quarks and hadrons in a unified way. We compare model results with lattice QCD calculations and discuss the phase diagram depending on temperature and chemical potential. In an extended study we investigate the SU(3) parity doublet model and show the properties of highly excited strongly interacting matter in such an approach.

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I discuss the structure and composition of massive (two solar-mass) neutron stars containing hypernuclear and deconfined quark matter in color superconducting states. Stable configurations featuring such matter are obtained if the Equation of State of hadronic matter is stiff above the saturation density, the transition to quark matter takes place at a few times the nuclear saturation density, and the repulsive vector interactions in quark matter are substantial. I also discuss our recent progress in understanding the cooling of massive compact stars with color superconducting quark cores.

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In this paper, we review the properties of baryon number fluctuations close to the crossover transition at zero and finite baryon densities. We argue on a phenomenological importance of high order cumulants at zero baryon density. Main properties of the cumulants are illustrated beyond a mean-field approximations in an effective low energy model of QCD.

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The energy dependence of the observable two-particle correlator in search for local strong parity violation in Au+Au collisions is estimated within a simple phenomenological model. The model reproduces available RHIC data but predicts that at LHC the chiral magnetic effect (CME) will be about 20 times weaker than at RHIC, contrary to the first LHC measurements. In the lower energy range, this effect should vanish sharply at an energy somewhere above the top SPS one in agreement with the preliminary results of the Beam Energy Scan program. To elucidate CME background effects a transport HSD model including magnetic field evolution is put forward and electromagnetic dynamics at RHIC energies is investigated. It is observed that the electromagnetic field included into the hadronic model does not influence on observables due to mutual compensation of effects of electric and magnetic fields.

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We examine the phase diagram of hadronic matter when the number of colors, as well as temperature and density, are varied. We show that in this regime several phase transitions are possible, and we examine issues related to these transitions.

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The properties of strong-interaction matter are probed in ultra-relativistic heavy-ion collisions. In the context of measurements of the elliptic flow at RHIC and the LHC the shear viscosity is of particular interest. In this presentation, we discuss recent results for \(\eta /s\) in hadronic matter at vanishing baryo-chemical potential within kinetic theory. Using the Nambu–Jona-Lasinio model, special attention is paid to effects arising from the restoration of spontaneously broken chiral symmetry with increasing temperature.

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We systematically compare the \({\cal N} =1\) SUSY QED plasma to its non-supersymmetric counterpart which is QED plasma of electrons, positrons and photons. Collective excitations and collisional processes in the two systems are confronted to each other in a regime of small coupling. The collective and collisional characteristics of supersymmetric plasma are both very similar to those of QED plasma.

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We consider the pseudocritical temperatures for the chiral and deconfinement transitions within a Polyakov-loop Dyson–Schwinger equation approach which employs a nonlocal rank-2 separable model for the effective gluon propagator. These pseudocritical temperatures differ by a factor of two when the quark and gluon sectors are considered separately, but get synchronized and become coincident when their coupling is switched on. The coupling of the Polyakov-loop to the chiral quark dynamics narrows the temperature region of the QCD transition in which chiral symmetry and deconfinement is established. We investigate the effect of rescaling the parameter \(T_0\) in the Polyakov-loop (PL) potential on the QCD transition for both the logarithmic and polynomial forms of the potential. While the critical temperatures vary in a similar way, the width of the transition is stronger affected for the logarithmic potential. For this potential the character of the transition changes from crossover to a first order one when \(T_0 \lt 210\) MeV, but it remains crossover in the whole range of relevant \(T_0\) values for the polynomial form.

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In this work, we investigate the transport coefficients, i.e. shear and bulk viscosity \(\eta \) and \(\zeta \), and heat conductivity \(\kappa \) of the quark-gluon plasma within a virial expansion approach. We derive a realistic Equation of State using a virial expansion approach which allows us to include the interactions between the partons in the deconfined phase. From the interaction, we directly extract the effective coupling \(\alpha _{\rm V}\) for the determination of \(\eta \), \(\zeta \) and \(\kappa \). The shear viscosity and the heat conductivity show a pronounced temperature dependence. Furthermore, we find that the bulk viscosity \(\zeta \) is strongly suppressed. Our results for the ratio \(\eta \) to the entropy density \(s\) show a minimum near \(T_{\rm c}\), very close to the lowest bound \(\eta /s=1/(4\pi )\) and, furthermore, in line with the experimental value from RHIC as well as with the lattice calculations.

abstract

To accommodate recent RHIC data on \(\eta '\) multiplicity, we propose a minimal modification of the Witten–Veneziano relation at high temperature. This renders a significant drop of \(\eta '\) mass at high temperature signaling a restoration of the U\((1)_{A}\), and the Goldstone character of \(\eta '\).

abstract

The energy loss of a fast parton scattering elastically in a weakly coupled quark-gluon plasma is formulated as an initial value problem. The approach is designed to study an unstable plasma, but it reproduces the well known result in the case of an equilibrium plasma. Contributions to the energy loss due to unstable modes are shown to exponentially grow in time. An unstable two-stream system is considered as an example.

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We discuss how the ground state of the three-flavor color superconducting phase in the presence of a magnetic field is enriched with the presence of an extra condensate related with the alignment of the magnetic moments of Cooper pairs of charged quarks. The new condensate enhances the condensation energy of pairs formed by charged quarks. We point out possible consequences of the new order parameter on the issue of the chromomagnetic instability that appears in color superconductivity at moderate density and for the planned low-temperature/high-density heavy-ion collision experiments.

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The Bethe–Salpeter equation for the T-matrix of \(D^0\bar {D}^{*0}\) scattering is solved with a meson–meson potential that results from 2nd order Born approximation of quark exchange processes. This potential turns out to be complex and energy dependent due to the pole contribution from the coupling to the intermediate \(J/\psi \)–\(\rho \) meson pair propagator. As a consequence, a bound state with a mass close to \(3.872\) GeV occurs in the \(J/\psi \)–\(\rho \) continuum. This result suggests that quark exchange forces may provide the solution to the puzzling question for the origin of the interaction which leads to a binding of \(D\) and \(\bar {D}^{*}\) mesons in the \(X(3872)\) state.

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Motivated by lattice QCD studies, we investigate the RW transition endpoint at imaginary chemical potential in a two-flavor PNJL model. We focus on the quark-mass dependence of the endpoint using different forms of the Polyakov-loop potential.