### Proceedings Series

#### Transverse Momentum and Multiplicity Fluctuations in Ar+Sc Collisions at the CERN SPS from NA61/SHINE

abstract

The NA61/SHINE experiment aims to discover the critical point of strongly interacting matter and study the properties of the onset of deconfinement. For these goals, a scan of the two dimensional phase diagram ($T$–$\mu _{\rm B}$) is being performed at the SPS by measurements of hadron production in proton–proton, proton–nucleus and nucleus–nucleus interactions as a function of collision energy and system size. In this contribution, preliminary results on transverse momentum and multiplicity fluctuations expressed in terms of strongly intensive quantities from the Ar+Sc energy scan will be presented. These fluctuations are expected to be sensitive to the existence of a critical point. The results are compared with results from the $p$+$p$ and Be+Be energy scan as well as with NA49 measurements.

#### Systematic Extraction of QGP Properties

abstract

We investigate the collision energy dependence of shear viscosity over the entropy density ratio $\eta /s$ in Au+Au collisions at $\sqrt {s_{NN}}=19.6, 39$, and $62.4$ GeV, using Bayesian statistical analysis and Gaussian process emulators to explore the full input parameter space of a transport+hydrodynamics hybrid model. The ratio is found to decrease as a function of collision energy, supporting the results from previous studies performed with the same hybrid model.

#### Probing the Nature of Phases Across the Phase Transition at Finite Isospin Chemical Potential

abstract

We compare the low-eigenvalue spectra of the Overlap Dirac operator on two sets of configurations at $\mu _I/\mu _I^{\rm c}=0.5$ and 1.5 generated with dynamical staggered fermions at these isospin chemical potential on $24^3 \times 6$ lattices. We find very small changes in the number of zero modes and low-lying modes which is in stark contrast with those across the corresponding finite temperature phases where one sees a drop across the phase transition. Possible consequences are discussed.

#### Surprises for the Chemical Freeze-out Lines from the New Data in $p$+$p$ and $A$+$A$ Collisions

abstract

We summarize the surprising results obtained in the fit of the new $p$+$p$ and updated $A$+$A$ data on mean multiplicities. The available range of thermal parameters for the NA61/SHINE energy and system-size scan program is squeezed and shifted compared to expectations. The $p$+$p$ freeze-out line touches the $A$+$A$ line in the vicinity of the $K^+/\pi ^+$ horn, although the touching point corresponds to different energies in $A$+$A$ and $p$+$p$. It is found that stable fit results for $p$+$p$ reactions are obtained if particles and antiparticles containing all three conserved charges are measured. It requires at least 6 particles, if strange baryons are not measured, to get the temperature and chemical potential of the freeze-out.

#### Generalized Beth–Uhlenbeck Approach to the Equation of State for Quark–Hadron Matter

abstract

A unified equation of state for quark–hadron matter is presented in the generalized Beth–Uhlenbeck form. It follows from a ${\mit \Phi }$-derivable approach to the thermodynamic potential where the Ansatz for the ${\mit \Phi }$ functional contains all 2PI diagrams at two-loop order formed with quark cluster Green’s functions for quark, diquark, meson and baryon propagators. We present numerical results using an effective model for the generic behaviour of hadron masses and phase shifts at finite temperature which shares basic features with recent developments within the PNJL model for correlations in quark matter. We obtain the transition between a hadron resonance gas phase and the quark–gluon plasma where the Mott dissociation of hadrons is encoded in the hadronic phase shifts. The resulting thermodynamics is in a very good agreement with recent lattice QCD simulations.

#### From Cold Fermi Fluids to the Hot QGP

abstract

Strongly coupled quantum fluids are found in different forms, including ultracold Fermi gases or tiny droplets of extremely hot Quark–Gluon Plasma. Although the systems differ in temperature by many orders of magnitude, they exhibit a similar almost inviscid fluid dynamical behavior. In this work, we summarize some of the recent theoretical developments toward better understanding of this property in cold Fermi gases at and near unitarity.

all authors

C. Bonati, M. D'Elia, M. Mariti, M. Mesiti, F. Negro, F. Sanfilippo

#### Across the Deconfinement

abstract

The deconfinement transition at vanishing chemical potential can be reliably studied by lattice simulations and its general features are by now well-known. On the contrary, what happens at finite density is still largely unknown and we will review the results obtained in the last year regarding the dependence, for small density, of the (pseudo)critical temperature on the baryonic chemical potential.

all authors

V. Bornyakov, D. Boyda, V. Goy, A. Molochkov, A. Nakamura, A. Nikolaev, V. Zakharov

#### How to Use Lattice and Experimental Data for QCD Critical Point Search

abstract

We show that the canonical approach is a promising tool to find the critical point of the QCD phase both in the experimental study and the lattice QCD simulations.

#### Collective Dynamics in Small Systems

abstract

Signatures of collective expansion in relativistic collisions involving small projectiles are presented. The observed phenomena can be described in the framework of relativistic hydrodynamic models. Limits of applicability of hydrodynamics in small systems are discussed.

#### Chiral Symmetry Restoration in Heavy-ion Collisions at High Baryon Density

abstract

We study the effect of the chiral symmetry restoration (CSR) in heavy-ion collisions from $\sqrt {s_{NN}}=3$–20 GeV within the Parton–Hadron String Dynamics (PHSD) transport approach. The PHSD includes the deconfinement phase transition as well as essential aspects of CSR in the dense and hot hadronic medium, which are incorporated in the Schwinger mechanism for the hadronic particle production. Our systematic studies show that chiral symmetry restoration plays a crucial role in the description of heavy-ion collisions giving an increase of the hadronic particle production in the strangeness sector with respect to the non-strange one. We identify particle abundances and rapidity spectra to be suitable probes in order to extract information about CSR, while transverse mass spectra are less sensitive. Furthermore, the appearance/disappearance of the ‘horn’ structure in the $K^+/\pi ^+$ ratio is investigated as a function of the system size in central $A+A$ collisions.

#### Wounded Quarks at the LHC

abstract

We review the results of the wounded-quark model with a stress on eccentricity observables in small systems. A new element is a presentation of symmetric cumulants for the elliptic and triangular flow correlations, obtained in the wounded-quark approach.

#### Frequency Dependence in Dynamical Gap Generation in Graphene

abstract

We study frequency dependencies in the renormalization of the fermion Green function for the $\pi$-band electrons in graphene and their influence on dynamical gap generation at sufficiently strong interaction. We use the effective QED-like description for the low-energy excitations within the Dirac-cone region and self consistently solve the fermion Dyson–Schwinger equation using different approximations for the photon propagator and the vertex function. We specifically study frequency-dependent Lindhard screening and retardation effects.

#### Elastic $qq$ Cross Sections at Finite Chemical Potential in the Nambu–Jona-Lasinio Lagrangian

abstract

We discuss the elastic $qq$ cross sections at finite chemical potential in the Nambu–Jona-Lasinio model. We comment the generic features of the cross sections as functions of the chemical potential, temperature and collision energy. Finally, we discuss their relevance in the construction of a relativistic transport model for heavy-ion collisions based on this effective Lagrangian.

#### Collisions of Small Nuclei in the Thermal Model

abstract

An analysis is presented of the expectations of the thermal model for particle production in collisions of small nuclei. The maxima observed in particle ratios of strange particles to pions as a function of beam energy in heavy-ion collisions are reduced when considering smaller nuclei. Of particular interest is that the ${\mit \Lambda }/\pi ^+$ ratio shows the strongest maximum which survives even in collisions of small nuclei.

#### Searching for the QCD Critical Point Through Power-law Fluctuations of the Proton Density in Heavy-ion Collisions

abstract

One of the goals of the NA61/SHINE experiment is to discover the critical point (CP) of QCD, which is an object of much experimental and theoretical interest. To this end, a scan of the 2-dimensional phase diagram $(T,\mu _{\rm B})$ through proton–nucleus and nucleus–nucleus collisions is being performed at the SPS, with varying collision energy and system size. One of the most promising observables that signal the approach to the CP are local power-law fluctuations of the order parameter of the QCD chiral phase transition, subject to universal scaling laws. In particular, fluctuations of the proton density probed through the method of intermittency analysis of scaled factorial moments for a number of NA49 collision data sets provide evidence of power-law fluctuations in the “Si”+Si dataset, consistent with an approach to the critical point, within errors. In this contribution, we expand on previous work by studying the prospects for an intermittency analysis in NA61 Be+Be and Ar+Sc collisions at 150 $A$ GeV, through Monte Carlo simulations of critical protons mixed with a non-critical background.

#### Polyakov Loop Fluctuations in Terms of Dirac Eigenmodes

abstract

We investigate, both numerically and analytically, the Polyakov loop and its fluctuations in terms of Dirac eigenmodes in the lattice QCD. Based on the analytical relation between the Polyakov loop and the Dirac eigenmodes, it is found that the Polyakov loop and its fluctuations, contrary to the chiral condensate, are insensitive to the density of the low-lying Dirac modes. This result suggests that there is no direct one-to-one correspondence between quark confinement and chiral symmetry breaking in QCD. Our argument is also generalized for the Wilson-type Dirac operator on the lattice.

#### Probing the QCD Phase Diagram with Dileptons — a Study Using Coarse-grained Transport Dynamics

abstract

Dilepton production in heavy-ion collisions at various energies is studied using coarse-grained transport simulations. Microscopic output from the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model is hereby put on a grid of space-time cells which allows to extract the local temperature and chemical potential in each cell via an equation of state. The dilepton emission is then calculated applying in-medium spectral functions from hadronic many-body theory and partonic production rates based on lattice calculations. The comparison of the resulting spectra with experimental data shows that the dilepton excess beyond the decay contributions from a hadronic cocktail reflects the trajectory of the fireball in the $T$–$\mu _{\rm B}$ plane of the QCD phase diagram.

#### Various Approaches to Anisotropic Hydrodynamics

abstract

Various approaches to anisotropic hydrodynamics are shortly reviewed.

#### Perspectives for Heavy-ion Collisions at Future Facilities

abstract

Starting from the next decade, new accelerator facilities will become available for the investigation of the QCD phase diagram at high net-baryon densities. We discuss and compare the current status of these projects, the opportunities they will offer for the research with nuclear collision experiments, and the mid-term prospects for experimental access to observables characterising dense QCD matter and the features of the QCD phase diagram.

#### Modeling Chiral Criticality

abstract

We discuss the critical properties of net-baryon-number fluctuations at the chiral restoration transition in matter at non-zero temperature and net-baryon density. The chiral dynamics of quantum chromodynamics (QCD) is modeled by the Polykov-loop extended Quark–Meson Lagrangian, that includes the coupling of quarks to temporal gauge fields. The Functional Renormalization Group is employed to account for the criticality at the phase boundary. We focus on the ratios of the net-baryon-number cumulants, $\chi _B^n$, for $1\leq n\leq 4$. The results are confronted with recent experimental data on fluctuations of the net proton number in nucleus–nucleus collisions.

#### Magnetic Shift of the Chemical Freezeout and Electric Charge Fluctuations

abstract

The phenomenological implication of the inverse magnetic catalysis, i.e. a modification in the QCD phase transition temperature under a strong magnetic field, is discussed.

#### SU$(2N_{\mathrm {F}})$ Symmetry of QCD at High Temperature and Its Implications

abstract

If above a critical temperature not only the SU$(N_{\rm F})_{\rm L} \times \mathrm {SU}(N_{\rm F})_{\rm R}$ chiral symmetry of QCD but also the U(1)$_{\rm A}$ symmetry is restored, then the actual symmetry of the QCD correlation functions and observables is SU$(2N_{\rm F})$. Such a symmetry prohibits existence of deconfined quarks and gluons. Hence, QCD at high temperature is also in the confining regime and elementary objects are SU$(2N_{\rm F})$ symmetric “hadrons” with not yet known properties.

#### News from Strong Interactions Program of the NA61/SHINE Experiment

abstract

The NA61/SHINE experiment aims to discover the critical point of strongly interacting matter and study the properties of the onset of deconfinement. This is performed by a two-dimensional phase diagram ($T$–$\mu _{\rm B}$) scan of measurements of particle spectra and fluctuations in proton–proton, proton–nucleus and nucleus–nucleus interactions as a function of collision energy and system size. In this contribution, new NA61/SHINE results on negative pion production, as well as transverse momentum and multiplicity fluctuations in Ar+Sc collisions are presented. Moreover, the latest results on higher order moments of net-charge multiplicity distribution in $p+p$ collisions are also discussed. The Ar+Sc results are compared to NA61 $p+p$ and Be+Be data as well as to NA49 $A+A$ results.

#### Relaxation Rates and Phase Transitions at Strong Coupling

abstract

In the present work, we compute relaxation rates of strongly coupled field theories exhibiting non-trivial phase structures. Our method of choice is a bottom-up gauge/gravity construction. Two different scenarios for a holographic first order phase transition are examined, and in both cases we establish the existence of a spinodal region. In addition, for a model with linear confinement in the meson spectrum, we find a region of temperatures with unstable non-hydrodynamic modes within a branch of black hole solutions.

#### Static Critical Fluctuations on the Freeze-out Surface

abstract

In this proceeding, we summarize the main results of our recent paper, which introduces a freeze-out scheme to the dynamical models near the QCD critical point. Within such a framework of static critical fluctuations, the Beam Energy Scan (BES) data of $C_4$ and $\kappa \sigma ^2$ for net protons within different $p_{\rm T}$ ranges can be roughly described. Besides, the momentum acceptance dependence of higher cumulants at lower collision energies can also be qualitatively described. However, $C_2$ and $C_3$ are always over-predicted due to the positive static critical fluctuations.

#### Chiral Thermodynamics in a Finite Box

abstract

Finite-volume modifications of the two-flavor chiral phase diagram are investigated within an effective quark–meson model in various mean-field approximations. The role of vacuum fluctuations and boundary conditions, their influence on higher cumulants and signatures of a possible pseudo-critical endpoint are amplified with smaller volumes.

#### QCD Thermodynamics in the Crossover/Freeze-out Region

abstract

We use results from a $6^{\rm th}$ order Taylor expansion of the QCD equation of state to construct expansions for cumulants of conserved charge fluctuations and their correlations. We show that these cumulants strongly constrain the range of applicability of hadron resonance gas model calculations. We point out that the latter is inappropriate to describe equilibrium properties of QCD at zero and non-zero values of the baryon chemical potential already at $T\sim 155$ MeV.

#### Non-perturbative Production Rate of Photons with a Lattice Quark Propagator: Effect of Vertex Correction

abstract

We analyze the production rate of photons from the thermal medium above the deconfinement temperature with a quark propagator obtained from a lattice QCD numerical simulation. The photon–quark vertex is determined gauge-invariantly, so as to satisfy the Ward–Takahashi identity. The obtained photon-production rate shows a suppression compared to perturbative results.

#### PHENIX Results on Lévy Analysis of Bose–Einstein Correlation Functions

abstract

The nature of the quark–hadron phase transition can be investigated through analysing the space-time structure of the hadron emission source. For this, the Bose–Einstein or HBT correlations of identified charged particles are among the best observables. In this paper, we present the latest results from the RHIC PHENIX experiment on such measurements.

#### Understanding Experimentally-observed Fluctuations

abstract

We discuss two topics on the experimental measurements of fluctuation observables in relativistic heavy-ion collisions. First, we discuss the effects of the thermal blurring, i.e. the blurring effect arising from the experimental measurement of fluctuations in the momentum space as a proxy of the thermal fluctuations defined in coordinate space, on higher order cumulants. Second, we discuss the effect of imperfect efficiency of detectors on the measurement of higher order cumulants. We derive effective formulas which can carry out the correction of this effect for higher order cumulants based on the binomial model.

#### Fluctuations and the QCD Phase Diagram

abstract

In this contribution, we will discuss various issues related with the interpretation of fluctuation observables. In particular, we will focus on the effect of fluctuations induced by the initial stopping of baryons at low beam energies.

#### Pion Spectra in Ar+Sc Interactions at SPS Energies

abstract

This contribution discusses recent results from analysis of Ar+Sc interactions recorded with the NA61/SHINE detector at six beam momenta: $13\,A$, $19\,A$, $30\,A$, $40\,A$, $75\,A$, $150\,A$ GeV/$c$ at the CERN SPS. Rapidity and transverse mass spectra of pions obtained with the “h$^-$” analysis method are presented and compared to results from $p+p$, Be+Be and Pb+Pb collisions.

#### S-matrix Approach to Pion Gas

abstract

S-matrix formalism is applied to analyze a gas of interacting pions.

#### Higher Order Moments of Net-charge and Multiplicity Distributions in $p+p$ Interactions at SPS Energies from NA61/SHINE

abstract

NA61/SHINE at the CERN SPS is a fixed-target experiment pursuing a rich physics program including measurements for heavy-ion, neutrino and cosmic ray physics. The main goal of the ion program is to study the properties of the onset of deconfinement and to search for the signatures of the critical point. A specific property of the critical point, the increase in the correlation length, makes fluctuations its basic signal. Higher order moments of suitable observables are of special interest as they are more sensitive to the correlation length than typically studied second order moments. In this contribution, preliminary results on higher order fluctuations of negatively-charged hadron multiplicity and net charge in $p+p$ interactions will be shown. The new data will be compared with model predictions.

#### From the Glasma to the QCD Phase Boundary

abstract

In this paper, I qualitatively discuss the matter formed in the fragmentation region of nuclear collisions at the highest energies. I argue that although the initial temperature and baryon number density can become very large, the ratio of initial baryon chemical potential to initial temperature, $\mu _{\rm B}/T$, is approximately independent of energy, when measured at a fixed rapidity measured from the end of the fragmentation region. This quantity is argued to be roughly invariant under expansion, and, therefore, the value measured at decoupling should be approximately the same as the initial value and largely independent of energy. The values of the initial temperature and initial baryon number are energy-dependent and become large as the center-of-mass collision energy increases.

#### Motion of Confined Particles

abstract

We carry out numerical evaluations of the motion of classical particles in Minkowski space $\mathbb {M}^{4}$ which are confined to the inside of a bag. In particular, we analyze the structure of the paths evolving from the breaking of the dilatation symmetry, the conformal symmetry and the combination of both together. The confining forces arise directly from the corresponding nonconserved currents. We demonstrate in our evaluations that these particles under certain initial conditions move toward the interior of the bag.

#### Fluctuations of Charges at the Phase Boundary

abstract

Properties of fluctuations of conserved charges in thermal equilibrium are discussed. Particular emphasis is put on possible origin of deviations from the Skellam distribution in higher order cumulants of net-baryon-number fluctuations around the chiral critical line and those of net-electric charge fluctuations at the chemical freeze-out. Importance of understanding the reference distribution is stressed.

#### Cumulative Pion Production via Successive Collisions in Nuclear Medium

abstract

Production of pions in proton–nucleus ($p+A$) reactions outside of a kinematical boundary of proton–nucleon collisions, the so-called cumulative effect, is studied. The kinematical restrictions on pions emitted in the backward direction in the target rest frame are analyzed. It is shown that cumulative pion production requires a presence of massive baryonic resonances that are produced during successive collisions of the projectile with nuclear nucleons. After each successive collision, the mass of created resonance may increase and, simultaneously, its longitudinal velocity decreases. Simulations within Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model reveals that successive collisions of baryonic resonances with nuclear nucleons play the dominant role in the cumulative pion production in $p+A$ reactions.

#### Toward the Description of Fluid Dynamical Fluctuations in Heavy-ion Collisions

abstract

In this article, we present results obtained when fluid dynamical fluctuations are included in relativistic 3+1 dimensional viscous fluid dynamics. We discuss effects of the interactions of fluctuations due to nonlinearities and the cutoff dependence.

#### Mean Pion Multiplicities in Ar+Sc Collisions

abstract

Preliminary results for the mean negatively-charged pion multiplicities $\langle \pi ^- \rangle$ using the h$^-$ method are presented for central Ar+Sc collisions at 13, 19, 30, 40, 75 and 150 A GeV/$c$ beam momentum. The data were recorded by the NA61/SHINE detector at the CERN SPS. Starting with rapidity distributions ${{\rm d}n}/{{\rm d}y}$, the procedure of obtaining total multiplicities is presented. The mean number of wounded nucleons $\langle W\rangle$ extracted from the Glissando MC model is used to calculate the ratio $\langle \pi ^- \rangle /\langle W\rangle$. The results are compared to those from other experiments and their dependence on colliding systems and collision energy is discussed.

#### Directed Flow in Heavy-ion Collisions and Softening of Equation of State

abstract

We analyze the directed flow of protons and pions in high-energy heavy-ion collisions in the incident energy range from $\sqrt {s_{_{NN}}}=7.7$ to 27 GeV within a microscopic transport model. While standard hadronic transport approaches do not describe the collapse of directed flow below $\sqrt {s_{_{NN}}}\simeq 20$ GeV, a model that simulates effects of a softening of the equation of state by introducing the attractive orbits describes well the behavior of directed flow data. The equation of state with the attractive orbits is as soft as the one with the first-order phase transition.

#### Critical Phenomena in the Non-extensive Nambu–Jona-Lasinio Model

abstract

It is nowadays widely accepted that in many branches of physics, experimental data indicate the necessity of a departure from the standard extensive Boltzmann–Gibbs (BG) statistics, which is then replaced by a non-extensive statistics. Here, non-extensive calculation in a dense nuclear matter (NM) is proposed.

#### Horizons, Causality and Strangeness Production

abstract

Boost-invariant hadron production in high-energy collisions implies that the produced hadrons arise from causally disconnected fireballs. Discrete quantum numbers have thus to be conserved locally. For strangeness production, this defines a local conservation volume, which in an ideal resonance gas formulation leads to a suppression of strange particle rates. As a result, the strangeness suppression factor $\gamma _{\rm s}$ becomes a universal function of the initial energy density of the collision, for all collision configurations and energies. This prediction is found to be very well-satisfied for all $pp,~pA$ and $AA$ data.

abstract

Electromagnetic probes are radiated during all stages of a heavy-ion collision and leave the fireball without further rescattering. Thus, they transmit important information about the matter created in the interior of the collision zone. Utilizing a coarse-graining method, we extract local thermodynamic properties from hadronic transport simulations at SIS energies. These serve as an input for the calculation of the pertinent radiation of thermal dileptons based on an in-medium $\rho$ spectral function that describes available spectra at ultrarelativistic collision energies. The results provide a baseline for future measurements by the HADES and CBM experiments at GSI/FAIR.

#### Multiplicity Fluctuations in Ar+Sc Collisions at the CERN SPS from NA61/SHINE

abstract

Multiplicity fluctuations were investigated in Ar+Sc collisions at 13$A$, 19$A$, 30$A$, 40$A$, 75$A$, 150$A$ GeV/$c$ using the NA61/SHINE detector at the SPS. Centrality selection is based on the nucleon-spectator energy in the forward hemisphere as measured by the projectile spectator detector. Preliminary results on the scaled variance $\omega$ and the strongly intensive measure ${\mit \Omega }$ were obtained for the multiplicity distribution of all, negatively and positively charged hadrons. Results are discussed and compared with $p+p$ results and Pb+Pb data of NA49 and EPOS 1.99 simulations.

#### Recent Progress in Understanding Deconfinement and Chiral Restoration Phase Transitions

abstract

Paradigm shift in gauge topology, from instantons to their constituents — instanton–dyons — has recently lead to very significant advances. Like instantons, they have fermionic zero modes, and their collectivization at sufficiently high density explains the chiral symmetry breaking. Unlike instantons, these objects have electric and magnetic charges. Their back-reaction on the mean value of the Polyakov line (holonomy) allows to explain the deconfinement transition. The paper summarizes recent works on the dyon ensemble, done in the mean field approximation (MFA), and also by direct numerical statistical simulation. Introduction of non-trivial quark periodicity conditions leads to drastic changes in both deconfinement and chiral transitions. In particularly, in the so-called $Z(N_{\rm c})$-QCD model the former gets much stronger, while the latter does not seem to occur at all.

#### Interplay Between Deconfinement and Chiral Properties

abstract

We study interplay between confinement/deconfinement and chiral properties. We derive some analytical relations of the Dirac modes with the confinement quantities, such as the Polyakov loop, its susceptibility and the string tension. For the confinement quantities, the low-lying Dirac eigenmodes are found to give negligible contribution, while they are essential for chiral symmetry breaking. This indicates no direct, one-to-one correspondence between confinement/deconfinement and chiral properties in QCD. We also investigate the Polyakov loop in terms of the eigenmodes of the Wilson, the clover and the domain-wall fermion kernels, respectively.

#### Kinetics of the Chiral Phase Transition

abstract

We study the dynamics of the chiral phase transition in a linear quark–meson $\sigma$ model using a novel approach based on semiclassical wave-particle duality. The quarks are treated as test particles in a Monte Carlo simulation of elastic collisions and the coupling to the $\sigma$ meson, which is treated as a classical field. The exchange of energy and momentum between particles and fields is described in terms of appropriate Gaussian wave packets. It has been checked that energy-momentum conservation and the principle of detailed balance are fulfilled, and that the dynamics leads to the correct equilibrium limit. First schematic studies of the dynamics of matter produced in heavy-ion collisions are presented.

#### Critical Fluctuations in Models with van der Waals Interactions

abstract

Particle number fluctuations are considered within the van der Waals (VDW) equation, which contains both attractive (mean-field) and repulsive (eigenvolume) interactions. The VDW equation is used to calculate the scaled variance of particle number fluctuations in the generic Boltzmann VDW system and in nuclear matter. The strongly intensive measures ${\mit \Delta }[E^*,N]$ and ${\mit \Sigma }[E^*,N]$ of the particle number and excitation energy fluctuations are also considered, and, similarly, show singular behavior near the critical point. The ${\mit \Delta }[E^*,N]$ measure is shown to attain both positive and negative values in the vicinity of critical point. Based on universality argument, similar behavior is expected to occur in the vicinity of the QCD critical point.

#### The Phase Diagram in the Vector Meson Extended Linear Sigma Model

abstract

We investigate the chiral phase transition of the strongly interacting matter at nonzero temperature and baryon chemical potential $\mu _{\rm B}$ within an extended (2+1) flavor Polyakov constituent quark–meson model which incorporates the effect of the vector and axial vector mesons. The parameters of the model are determined by comparing masses and tree-level decay widths with experimental values. We examine the restoration of the chiral symmetry by monitoring the temperature evolution of condensates. We study the $T$–$\rho _{\rm B}$ phase diagram of the model and find that a critical end point exists, although at very low density.

#### Importance of Volume Corrections on the Net-charge Distributions at the RHIC BES Energies

abstract

The paper presents my recent investigations of volume corrections on the cumulant products of net-charge distributions in statistical model, corresponding to the data reported by the STAR Collaboration. The corrected statistical expectations, under simple Poisson approximations, can reasonably explain the data measured in experiment. The results indicate that volume corrections play crucial role in event-by-event multiplicity fluctuation studies.

#### Thermal Vorticity Production in Relativistic Dissipative Fluids

abstract

We have computed the circulation integrations of thermal vorticity with and without charged currents in dissipative fluids. We find that the relativistic Kelvin circulation theorem will be modified by the dissipative effects, therefore, the circulation integrations of thermal vorticity may not be conserved during the fluid evolution.

#### Novel Picture of the Soft Modes at the QCD Critical Point Based on the FRG Method

abstract

We investigate the soft mode at the QCD critical point (CP) on the basis of the functional renormalization group. We calculate the spectral functions in the meson channels in the two-flavor quark–meson model. Our result shows that the energy of the peak position of the particle–hole mode in the sigma channel becomes vanishingly small as the system approaches the QCD CP, which is a manifestation of the softening of the phonon mode. We also extract the dispersion curves of the mesonic and the phonon mode, a hydrodynamic mode which leads to a finding that the dispersion curve of the sigma-mesonic mode crosses the light-cone into the space-like momentum region, and then eventually merges into the phonon mode as the system approaches further close to the CP. This may suggest that the sigma-mesonic mode forms the soft mode together with the hydrodynamic mode at the CP.

#### Symmetry Breaking Effect on the Inhomogeneous Chiral Phase in the External Magnetic Field

abstract

We investigate the effect of the current quark mass on the inhomogeneous chiral phase in the QCD phase diagram, to discuss the properties of the phase transition using the generalized Ginzburg–Landau (GL) expansion. The external magnetic field spreads this phase over the low chemical potential region even if the current quark mass is finite, which implies that the existence of this phase can be explored by the lattice QCD simulation.

#### Extended Soft-wall Model for the QCD Phase Diagram

abstract

The soft-wall model, emerging as bottom-up holographic scenario anchored in the AdS/CFT correspondence, displays the disappearance of normalisable modes referring to vector mesons at a temperature $T_{\rm dis}$ depending on the chemical potential $\mu$, $T_{\rm dis}(\mu )$. We explore options for making $T_{\rm dis}(\mu )$ consistent with the freeze-out curve $T_{\rm fo}(\mu )$ from relativistic heavy-ion collisions and the cross-over curve $T_{\rm c}(\mu )$ from QCD at small values of $\mu$.

all authors

A. Ayriyan, D.E. Alvarez-Castillo, S. Benic, D. Blaschke, H. Grigorian, S. Typel

#### Bayesian Analysis for a New Class of Hybrid EoS Models Using Mass and Radius Data of Compact Stars

abstract

We present a Bayesian analysis for a new class of realistic models of two-phase equations of state (EoS) for hybrid stars and demonstrate that the observation of a pair of high-mass twin stars would have a sufficient discriminating power to favour hybrid EoS with a strong first-order phase transition over alternative EoS. Such a measurement would provide evidence for the existence of a critical endpoint in the QCD phase diagram.

#### Inhomogeneous Chiral Condensates in the QCD Phase Diagram: Critical or Lifshitz Point?

abstract

We discuss how the phase diagram of strong interaction matter is modified if inhomogeneous chiral condensates are allowed to form. In particular, we investigate the appearance of a Lifshitz point and the fate of the critical point in presence of an inhomogeneous phase.

#### Exploring the In-medium Momentum Dependence of the Dynamical Quark Mass

abstract

We review the two standard equations of states based on the Nambu–Jona-Lasinio (NJL) model and the thermodynamic bag (tdBag) model for dense, cold quark matter from a perspective based on the Dyson–Schwinger (DS) formalism. A different, but technically not more complicated approximation reproduces the model of Munczek and Nemirovsky (MN) which accounts in a simplified way for chiral symmetry breaking and confinement as a dynamic process rooted in the momentum dependence of QCD model gap solutions. We review the mass gap solutions for the MN model in the chiral limit and sketch the behavior of mass gap solutions for finite bare quark masses at the finite chemical potential.

#### Cooling of Neutron Stars with Stiff Stellar Matter

abstract

Recent evidence for high masses ($\sim 2 M_\odot$) pulsars PSR J1614-2230 and PSR J0348-0432 requires neutron star matter to have a stiff equation of state (EoS). The thermal evolution of compact stars (CS) with stiff hadronic EoS necessitates the application of the “nuclear medium cooling” scenario with a selection of appropriate proton gap profiles together with in-medium effects (like pion softening) on cooling mechanisms in order to achieve a satisfactory explanation of all existing observational data for the temperature–age relation of CS. Here, we focus on two examples from [H. Grigorian, D.N. Voskresensky, D. Blaschke, Eur. Phys. J. A 52, 67 (2016)] for a stiff hadronic EoS without (DD2 EoS) and with (DD2vex) excluded volume correction.

#### Correspondence of Many-flavor Limit and Kaluza–Klein Degrees of Freedom in the Description of Compact Stars

abstract

We present the correspondence between non-interacting multi-hadron fermion star equation of state in the many-flavor limit and the degrees of freedom of a Kaluza–Klein compact star. Many flavors can be interpreted in this framework as one extra compactified spatial dimension with various, more-and-more massive hadron state excitations. The effect of increasing the degrees of freedom was investigated on the equation of state and in connection with the mass-radius relation, $M(R)$. The maximum mass of the star, $M_{\max }$, was also calculated as a function of the maximum number of excited states, $n$, and the size of the compactified extra dimension, $R_{{\rm c}}$.

#### QCD in Stars

abstract

We discuss cold dense QCD by examining constraints from neutron stars, nuclear experiments, and QCD calculations at low and high baryon density. The two solar mass constraint and suggestive small radii ($\sim 10$–13 km) of neutron stars constrain the strength of hadron–quark matter phase transitions. Assuming the adiabatic continuity from hadronic to quark matter, we use a schematic quark model for hadron physics and examine the size of medium coupling constants. We find that to baryon density, $n_{\rm B} \sim 10n_0$ ($n_0$: nuclear saturation density), the model coupling constants should be as large as in the vacuum, indicating that gluons remain non-perturbative even after the quark matter formation.

#### Energetic Scans of Marek Gaździcki

abstract

As an introduction to this special session on the occasion of Marek Gaździcki’s imminent $60^{\rm th}$ birthday his main research activities are briefly reviewed.

#### Critical Point

abstract

My friend and collaborator Marek Gaździcki celebrates his $60^{\rm th}$ in 2016. It is my great pleasure to present this report. It shows a small part of Marek’s scientific achievements connected to his theoretical results. My presentation will be even more restricted, I will only consider several selected topics — those which we studied together.

#### My Adventures with Marek Event-by-event

abstract

On the occasion of the $60^{\rm th}$ birthday of Marek Gaździcki, I present some personal recollections and briefly discuss a few research projects we worked together.

#### The Mar(e)k of QGP: Strangeness

abstract

Strangeness signature of quark–gluon plasma (QGP) is central to the exploration of baryon-dense matter: the search for the critical point and onset of deconfinement. I report on the discovery of QGP by means of strangeness: the key historical figures and their roles in this quest are introduced and the experimental results obtained are discussed. The important role of antihyperons is emphasized. The statistical hadronization model and sudden hadronization are described. Results of present day data analysis — strangeness and entropy content of a large fireball, and the universal hadronization condition describing key features of all explored collision systems — are presented.

#### Phase Diagram of the Three-flavor Color Superconducting PNJL Model

abstract

The phase diagram of the color superconducting three-flavor Polyakov-loop extended Nambu–Jona-Lasinio model is analyzed for symmetric matter with a parametrization consistent with the $2M_{\odot }$ mass constraint from the pulsars PSR J1614-2230 and PSR J0348+0432. The relevance of the result for heavy-ion collisions in the NICA/FAIR energy range is discussed.

#### Light Cluster Production at NICA

abstract

Measuring abundances and flow of light clusters as “rare probes” in future heavy-ion collision experiments at NICA and FAIR energies would provide unique insights into the QCD phase diagram.

#### Charge Conservation Effects for High-order Fluctuations

abstract

The exact charge conservation significantly impacts multiplicity fluctuations. The result depends strongly on the part of the system charge carried by the particles of interest. Along with the expected suppression of fluctuations for large systems, charge conservation may lead to negative skewness or kurtosis for small systems.

#### Pauli Blocking Effect Within the Relativistic Pion Gas

abstract

We show that the ${\mit \Phi }$-derivable formulation of the cluster virial expansion for quark–meson matter contains the quark Pauli blocking effect in a pion gas in the lowest order expansion with respect to the backreaction of pions on the quark dynamics.

#### Phase Diagram in Entanglement PNJL Model

abstract

Effects of vector interaction on the structure of the phase diagram are studied in the Nambu–Jona-Lasinio model with Polyakov loop in combination with entanglement interaction between quark and pure gauge sector. We showed that the first order chiral phase transition and its critical point disappear for sufficiently large values of the vector interaction constant $G_{\rm v}$.

#### Dynamical Fluctuations Near the QCD Critical Point and Their Impact on the Net-proton Kurtosis

abstract

We investigate the kurtosis of the net proton number and the chiral order parameter within the model of nonequilibrium chiral fluid dynamics for a crossover scenario near the critical point. Our model describes the interplay between a dynamical order parameter and a quark–gluon fluid during the expansion of the hot fireball created in a heavy-ion collision. A subsequent particlization process allows us to study experimental observables via an event-by-event analysis. We aim at understanding the interplay of two types of fluctuations: First, fluctuations in the chiral order parameter, and second, fluctuations in the net proton number. Our results show that both follow the same trend in a dynamical setup of a crossover transition. Although effects of finite size and inhomogeneity are present, the signal in the net-proton kurtosis develops clearly.

#### Freeze-out at Constant Knudsen Number in Event-by-event Hydrodynamics

abstract

We employ a dynamical freeze-out criterion where freeze-out is assumed to happen when the ratio of the expansion rate to the pion scattering rate, i.e. the local Knudsen number, reaches a certain value in an ideal fluid hydrodynamical calculation of spectra at RHIC. We find that once the freeze-out Knudsen number is chosen to reproduce the $p_{\rm T}$-spectra evaluated using freeze-out at constant temperature, the $p_{\rm T}$ differential momentum anisotropies, $v_2(p_{\rm T})$ and $v_3(p_{\rm T})$, are similar as well.

#### Nonlocal Quark Model for the Composite Higgs Particle

abstract

We propose an interpretation of the Higgs boson as a scalar $\bar {t}t$ bound state within a nonlocal Nambu model. The momentum-dependent top-quark mass is generated dynamically by the nonlocal four-quark interaction which results in a top-quark condensate that breaks chiral symmetry. We present a formula for the Higgs mass that elucidates how the nonlocality leads to true binding in the scalar channel with a Higgs mass below the sum of the constituent top-quark masses, in accordance with phenomenology.

#### Quark–Nuclear Hybrid EoS with Excluded-volume Effects

abstract

We employ a new quark–nuclear matter hybrid equation of state that takes into account both quark Pauli blocking in hadronic matter and screening of interactions in quark matter as excluded-volume effects. We obtain mass-radius relations for hybrid stars that fulfill the $2M_\odot$ constraint while exhibiting the high-mass twin phenomenon.

#### Centrality Determination in Heavy-ion Collisions with CBM

abstract

The size and evolution of the medium created in a heavy-ion collision depends on collision geometry. Experimentally, collisions are characterized by the measured particles multiplicities around midrapidity or energy measured in the forward rapidity region, which is sensitive to the spectator fragments. The performance for collision centrality determination in CBM using the multiplicity of produced particles measured with the silicon tracking system (STS) and the projectile spectator detector (PSD), which is sensitive to spectator fragments, is presented.

#### Composite Particles in Medium — Effects of Substructure

abstract

The role of phase-space occupation effects for the formation of two- and three-particle bound states in a dense medium is investigated for systems with short-range interactions. While for two-fermion bound states due to the Pauli blocking in a dense medium the binding energy is reduced and vanishes at a critical density (Mott effect), for three-fermion bound states, it is shown to be nonzero and positive. Therefore, beyond the Mott density of the two-fermion bound state, three-fermion bound states can exist in a medium and, therefore, be denoted as the in-medium Borromean states.

#### Temperature Effects on Superfluid Phase Transition in Bose–Hubbard Model with Three-body Interaction

abstract

We study the combined effects of two- and three-body local interactions as well as the finite temperature on the phase diagram of the Bose–Hubbard model. To handle the system with strong local interactions, we use the resolvent expansion technique, based on the contour integral representation of a partition function, and to find the phase diagram, we derive Landau-type expansion for free energy in terms of the superfluid order parameter.

top

ver. 2023.01.26 • we use cookies and MathJax