Proceedings Series

Vol. 7 (2014), No. 1, pp. 1 - 230

XXXI Max Born Symposium and HIC for FAIR Workshop Three Days of Critical Behaviour in Hot and Dense QCD

Transverse Momentum Distributions at the LHC and Tsallis Thermodynamics

Acta Phys. Pol. B Proc. Suppl. 7, 9 (2014)

page 9 •


An overview is presented of transverse momentum distributions of particles at the LHC using the Tsallis distribution. The use of a thermodynamically consistent form of this distribution leads to an excellent description of charged and identified particles. The values of the Tsallis parameter \(q\) are truly remarkably consistent.

Some Intensive and Extensive Quantities in High-Energy Collisions

Acta Phys. Pol. B Proc. Suppl. 7, 17 (2014)

page 17 •


We review the evolution of some statistical and thermodynamical quantities measured in difference sizes of high-energy collisions at different energies. We differentiate between intensive and extensive quantities and discuss the importance of their distinguishability in characterizing possible critical phenomena of nuclear collisions at various energies with different initial conditions.

full authors' list

V. Dick, F. Karsch, E. Laermann, H. Sandmeyer, S. Sharma, S. Mukherjee

Hadronic Correlators and Symmetries

Acta Phys. Pol. B Proc. Suppl. 7, 27 (2014)

page 27 •


The nature of the QCD chiral transition depends crucially on the symmetries being restored at the transition temperature. These symmetries are reflected in the properties of correlations of meson operators as well as in the eigenmodes of the Dirac operator of the light quarks. The paper gives an account of our current results for these quantities which are based on lattice simulations with two light and a strange quark in improved discretization schemes.

Strangeness in QGP: Hadronization Pressure

Acta Phys. Pol. B Proc. Suppl. 7, 35 (2014)

page 35 •


We review strangeness as signature of quark–gluon plasma (QGP) and the hadronization process of a QGP fireball formed in relativistic heavy-ion collisions in the entire range of today accessible reaction energies. We discuss energy dependence of the statistical hadronization parameters within the context of fast QGP hadronization. We find that QGP breakup occurs for all energies at the universal hadronization pressure \(P = 80\pm 3\) MeV/fm\(^3\).

The Calibration of Quarkonium Production in Nuclear Collisions

Acta Phys. Pol. B Proc. Suppl. 7, 49 (2014)

page 49 •


Quarkonium production has been considered as a tool to study the medium formed in high energy nuclear collisions, assuming that the formation of a hot and dense environment modifies the production pattern observed in elementary collisions. The basic features measured there are the relative fractions of hidden to open heavy flavor and the relative fractions of the different hidden heavy flavor states. Hence the essential question is if and how these quantities are modified in nuclear collisions. We show how the relevant data must be calibrated, i.e., what reference has to be used, in order to determine this in a model-independent way.

Dynamics of the Chiral Phase Transition

Acta Phys. Pol. B Proc. Suppl. 7, 59 (2014)

page 59 •


The intention of this study is the search for signatures of the chiral phase transition in heavy-ion collisions. To investigate the impact of fluctuations, cf. , of the baryon number, at the transition or at a critical point, the linear \(\sigma \)-model is treated in a dynamical (3+1)-dimensional numerical simulation. Chiral fields are approximated as classical mean fields, and quarks are described as quasi-particles in a Vlasov equation. Additional dynamics is implemented by quark–quark and quark–sigma-field interactions. For a consistent description of field-particle interactions, a new Monte-Carlo-Langevin-like formalism has been developed and is discussed.

Probability Distribution of Conserved Charges in the Presence of the Chiral Phase Transition

Acta Phys. Pol. B Proc. Suppl. 7, 69 (2014)

page 69 •


We discuss the influence of the chiral phase transition on the structure of the probability distributions of conserved charges within the quark–meson model based on the functional renormalization group approach. By considering the ratio of the probability distribution of the net-baryon number to the Skellam function, we quantify characteristic features of the distribution that are related to the \(O(4)\) criticality at the chiral crossover. We explore the corresponding ratios for data obtained at RHIC by STAR Collaboration and discuss their possible interpretation.

Three-flavor Chiral Phase Transition and Axial Symmetry Breaking with the Functional Renormalization Group

Acta Phys. Pol. B Proc. Suppl. 7, 81 (2014)

page 81 •


The interplay of mesonic fluctuations with an axial U\((1)_{\rm A}\)-symmetry breaking and resulting effects on the location of a possibly existing critical endpoint in the QCD phase diagram are investigated in a framework of the functional renormalization group within a \(N_{\rm f} = 2+1\) flavor quark–meson model truncation. The axial U\((1)_{\rm A}\)-symmetry breaking is imposed by a mesonic Kobayashi–Maskawa–’t Hooft determinant. The quark mass sensitivity of the chiral phase transition with and without the U\((1)_{\rm A}\)-symmetry breaking is studied.

Renormalization Group Flow Equations from the 4PI Equations of Motion

Acta Phys. Pol. B Proc. Suppl. 7, 91 (2014)

page 91 •


The 4PI effective action provides a hierarchy of integral equations which have the form of Bethe–Salpeter equations. The vertex functions obtained from these equations can be used to truncate the exact renormalization group flow equations. This truncation has the property that the flow is a total derivative with respect to the flow parameter and is equivalent to solving the \(n\)PI equations of motion. This result establishes a direct connection between two non-perturbative methods.

Probing Deconfinement with Polyakov Loop Susceptibilities

Acta Phys. Pol. B Proc. Suppl. 7, 99 (2014)

page 99 •


We present new lattice results on Polyakov loop susceptibilities in the SU(3) pure gauge system. These observables reflect the spontaneous breaking of Z(3) center symmetry and can serve as excellent probes for deconfinement. An effective model is formulated for the Polyakov loop, with its parameters constrained by existing quenched lattice data, including fluctuations.

Yang–Mills Thermodynamics: an Effective Theory Approach

Acta Phys. Pol. B Proc. Suppl. 7, 107 (2014)

page 107 •


We derive the Polyakov-loop thermodynamic potential in the perturbative approach to pure SU(3) Yang–Mills theory. The potential expressed in terms of the Polyakov loop in the fundamental representation corresponds to that of the strong-coupling expansion, of which the relevant coefficients of the gluon energy distribution are specified by characters of the SU(3) group. At high temperatures, the derived gluon potential exhibits the correct asymptotic behavior, whereas at low temperatures, it disfavors gluons as appropriate dynamical degrees of freedom. In order to quantify the Yang–Mills thermodynamics in a confined phase, we propose a hybrid approach which matches the effective gluon potential to the one of glueballs constrained by the QCD trace anomaly in terms of a dilaton. We also discuss the interplay between the chromomagnetic and chromoelectric gluon dynamics.

Thermodynamics of Strong Interaction Matter from Lattice QCD and the Hadron Resonance Gas Model

Acta Phys. Pol. B Proc. Suppl. 7, 117 (2014)

page 117 •


We compare recent lattice QCD calculations of higher order cumulants of net-strangeness fluctuations with hadron resonance gas (HRG) model calculations. Up to the QCD transition temperature \(T_{\rm c}=( 154\pm 9)\) MeV we find good agreement between QCD and HRG model calculations of second and fourth order cumulants, even when subtle aspects of net-baryon number, strangeness and electric charge fluctuations are probed. In particular, the fourth order cumulants indicate that also in the strangeness sector of QCD the failure of HRG model calculations sets in quite abruptly in the vicinity of the QCD transition temperature and is apparent in most observables for \(T \gtrsim 160\) MeV.

The Phase Diagram of Lattice QCD in the Strong Coupling Limit and Away from It

Acta Phys. Pol. B Proc. Suppl. 7, 127 (2014)

page 127 •


The strong coupling limit of staggered lattice QCD has been studied for decades, both via Monte Carlo and mean field. In this model, the finite density sign problem is mild and the full phase diagram can be studied, even in the chiral limit. However, in the strong coupling limit the lattice is maximally coarse. Here, we propose a method to go beyond the strong coupling limit with first results and discuss the consequences on the QCD phase diagram in the \(\mu \)–\(T\) plane, in particular the existence of chiral critical end point which is sought in heavy ion collisions. We explain how to construct an effective theory for non-zero lattice coupling, valid to \(\mathcal {O}(\beta )\), and present Monte Carlo results incorporating these corrections.

Bulk Viscosity of the Gluon Plasma in a Holographic Approach

Acta Phys. Pol. B Proc. Suppl. 7, 137 (2014)

page 137 •


A gravity-scalar model in 5-dimensional Riemann space is adjusted to the thermodynamics of SU(3) gauge field theory in the temperature range of 1–10 \(T/T_{\rm c}\) to calculate holographically the bulk viscosity in 4-dimensional Minkowski space. Various settings are compared, and it is argued that, upon an adjustment of the scalar potential to reproduce exactly the lattice data within a restricted temperature interval above \(T_{\rm c}\), rather robust values of the bulk viscosity to entropy density ratio are obtained.

Super Yang–Mills Plasma

Acta Phys. Pol. B Proc. Suppl. 7, 145 (2014)

page 145 •


The \({\cal N} =4\) super Yang–Mills plasma is studied in the regime of weak coupling. Collective excitations and collisional processes are discussed and compared to those of QCD plasma. The two systems are concluded to be very similar to each other with the differences mostly reflecting different numbers of degrees of freedom.

Quark Matter in Core Collapse Supernova Simulations

Acta Phys. Pol. B Proc. Suppl. 7, 153 (2014)

page 153 •


Any reliable equation of state (EOS) for astrophysical applications faces recently sever constraints, in particular associated with high-precision observations of massive neutron stars. The associated stiffness of the EOS limits the freedom to include additional degrees of freedom at high density, cf. , hyperons and quarks. For supernova matter, featuring high temperatures and large isospin asymmetry, there are only few EOS constraints at high density. We use this freedom and construct a quark–hadron hybrid EOS based on the bag model for strange quark matter. Parameters are selected such that (a) cold compact stars are consistent with observations and (b) quark matter appears close to saturation density. The hadron–quark phase transition is constructed by applying the Gibbs condition. This novel EOS is implemented in core-collapse supernova simulations in spherical symmetry, where we observe only a mild softening of the EOS in the quark–hadron mixed phase. The central protoneutron star (PNS) remains stable at all considered times and pure quark matter is never reached. The resulting slow conversion of nuclear matter into strange quark matter due to compression leaves a mild feedback to the neutrino observables as a consequence of the structural reconfiguration of the PNS. Moreover, we give a brief outlook towards more sophisticated quark–matter descriptions, i.e. the Nambu–Jona-Lasinio model and the Dyson–Schwinger formalism.

Challenges in the Measurement of Neutron Star Radii

Acta Phys. Pol. B Proc. Suppl. 7, 163 (2014)

page 163 •


The recent discovery of neutron stars near two solar masses has placed strong constraints on the properties of cold matter at a few times nuclear saturation density. Even tighter constraints would come from precise and accurate measurements of the radii of neutron stars of known masses, but current inferences are dominated by systematic errors. We summarize the current methods used to estimate neutron star radii and assess the prospects for reliable radii from future electromagnetic and gravitational wave observations.

Hybrid Modeling of Heavy-ion Collisions in UrQMD

Acta Phys. Pol. B Proc. Suppl. 7, 173 (2014)

page 173 •


We show a broad range of results from the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) Boltzmann approach to relativistic heavy-ion collisions. The presented findings are calculated via Hybrid UrQMD with an intermediate hydrodynamic evolution. Results on photon emission, charmed mesons and dilepton production are shown.

full authors' list

C.M. Ko, L.-W. Chen, V. Greco, F. Li, Z.-W. Lin, S. Plumari, T. Song, J. Xu

Elliptic Flow Difference Between Particles and Antiparticles and the EOS of Baryon-rich Matter

Acta Phys. Pol. B Proc. Suppl. 7, 183 (2014)

page 183 •


We review our recent studies of mean-field effects on the elliptic flows of particles and antiparticles in heavy ion collisions at energies carried out in the Beam Energy Scan (BES) program at the Relativistic Heavy Ion Collider (RHIC). Including mean-field potentials in the hadronic phase of a multiphase transport (AMPT) model, we have found that the elliptic flows are larger for \(p\), \(K^+\), and \(\pi ^-\) than for \({\bar p}\), \(K^-\), and \(\pi ^+\), respectively, as observed by the STAR Collaboration. Using a partonic transport model based on the Nambu–Jona-Lasinio (NJL) model, we have also found that the vector mean-field potentials in the baryon-rich quark matter lead to a larger quark than antiquark elliptic flows in these collisions. Using the quark coalescence model to convert quarks and antiquarks to hadrons, we have further found a splitting of the \(p\) and \(\bar p\), \({\mit \Lambda }\) and \(\bar {\mit \Lambda }\), and \(K^+\) and \(K^-\) elliptic flows with their differences depending on the strength of the quark vector coupling. Our studies have thus demonstrated the possibility of extracting information on the properties of baryon-rich quark–gluon plasma from the BES program at RHIC.

Recent Developments of A Multi-phase Transport Model

Acta Phys. Pol. B Proc. Suppl. 7, 191 (2014)

page 191 •


After the public release of A Multi-Phase Transport (AMPT) model in 2004 and detailed descriptions of its physics in a 2005 paper, the model has been constantly updated and developed to make it more versatile and to include more physical processes. This is an overview of recent developments of the AMPT model. Ongoing work to fix the violation of charge conservation in the code as well as possible directions for future work are also discussed.

Relaxation and Coupling Coefficients in Third Order Relativistic Fluid Dynamics

Acta Phys. Pol. B Proc. Suppl. 7, 197 (2014)

page 197 •


From the third order entropy four-current expression for a non-equilibrium single component system, we calculate its third order relaxation and coupling coefficients at ultrarelativistic (high temperature) limit and also give the results for the non-relativistic case. The ultrarelativistic limit is more interesting as it is in this region where one could expect the formation of quark–gluon plasma (QGP) in heavy ion collisions. The coefficients arise as a result of the generalization of the second order theory of relativistic fluid dynamics to the third order theory.

Crossover Transition to Quark Matter in Heavy Hybrid Stars

Acta Phys. Pol. B Proc. Suppl. 7, 203 (2014)

page 203 •


We study the possibility that the transition from hadron matter to quark matter at vanishing temperatures proceeds via crossover, similar to the crossover behavior found with lattice QCD studies at high temperatures. The purpose is to examine astrophysical consequences of this postulate by constructing hybrid star sequences fulfilling current experimental data.

Energy Loss in Unstable QGP — the Upper Cut-off Dependence

Acta Phys. Pol. B Proc. Suppl. 7, 209 (2014)

page 209 •


The energy loss of a highly energetic parton in a weakly coupled quark–gluon plasma is studied as an initial value problem. An extremely prolate plasma, where the momentum distribution is infinitely elongated along one direction, is considered. The energy loss is strongly time and direction dependent and its magnitude can much exceed the equilibrium value. It is logarithmically ultraviolet divergent. We argue that a good approximation to the energy loss can be obtained if this divergence is cut off with the parton energy.

Pion and Sigma Meson Dissociation in a Modified NJL Model at Finite Temperature

Acta Phys. Pol. B Proc. Suppl. 7, 215 (2014)

page 215 •


We investigate pion and sigma meson correlations in hot quark matter within a modified NJL model. Special emphasis is on the transformation of mesonic bound states to resonances (Mott dissociation) when due to the partial chiral symmetry restoration with increasing temperature the threshold of quark–antiquark continuum states drops below the meson mass at the corresponding Mott temperature. The description is based on evaluating the polarization functions for quark–antiquark (meson) correlations as a function of the temperature, and the results can be represented by introducing modulus and phase of the complex propagator functions for the mesonic states. We study the effect of modelling confinement by introducing a low-momentum cutoff in loop integrals. We make the ansatz that this cutoff is identified with the dynamically generated quark mass gap and find an increase of the continuum threshold which makes the otherwise unbound sigma meson a bound state in the vacuum. We discuss the in-medium behaviour of the mesonic phase shifts including the Mott effect and find accordance with the Levinson theorem.

Chiral Condensate and the Structure of Hadrons

Acta Phys. Pol. B Proc. Suppl. 7, 225 (2014)

page 225 •


A model of hadron masses based on the quark structure of hadrons combined with effects of chiral dynamics is used to calculate \(2+1\) flavour chiral condensate in the hadron resonance gas framework. Results are discussed in the context of recent lattice QCD data. Improvements of the dynamical models of hadron structure will be suggested with the aim to estimate strange sigma term of the nucleon.


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