Search

The mechanism for generating directed and elliptic flow in heavy-ion collisions is investigated and quantified for the SIS18 and SIS100 energy regimes. The observed negative elliptic flow $v_2$, at midrapidity has been explained either via (in-plane) shadowing or via (out-of-plane) squeeze-out. To settle this question, we employ the Ultra-relativistic Quantum Molecular Dynamics model (UrQMD) to calculate Au+Au collisions at E$_\mathrm{lab}=0.6A$ GeV, E$_\mathrm{lab}=1.23A$ GeV and $\sqrt{s_\mathrm{NN}}=3.0$ GeV using a hard Skyrme type Equation-of-State to calculate the time evolution and generation of directed flow and elliptic flow. We quantitatively distinguish the impact of collisions and of the potential on $v_1$ and $v_2$ during the evolution of the system. These calculations reveal that in this energy regime the generation of $v_1$ and $v_2$ follows from a highly intricate interplay of different processes and is created late, after the system has reached its highest density and has created a matter bridge between projectile and target remnant, which later breaks. Initially, we find a strong out-of-plane pressure. Then follows a strong stopping and the built up of an in-plane pressure. The $v_2$, created by both processes, compensate to a large extend. The finally observed $v_2$ is caused by the potential, reflects the freeze-out geometry and can neither be associated to squeeze-out nor to shadowing. The results are highly relevant for experiments at GSI, RHIC-FXT and the upcoming FAIR facility, but also for experiments at FRIB, and strengthens understanding on the Equation-of-State at large baryon densities., Comment: 19 pages, 18 figures

We investigate the influence of the equation-of-state (EoS) of nuclear matter on collective observables, the directed ($v_1$) and the elliptic flow ($v_2$) of nucleons and light clusters in heavy-ion collisions at GeV beam energies employing the Parton-Hadron-Quantum-Molecular Dynamics (PHQMD) microscopic transport approach. Here the clusters are formed dynamically during the entire heavy-ion collision by potential interaction between nucleons, including additionally deuteron production by hadronic kinetic reactions. We employ three different EoS - realized via potential interactions: two static EoS, dubbed 'soft' and 'hard', which differ in the compressibility modulus, as well as a soft momentum dependent EoS, adjusted to pA elastic scattering data. We find that the momentum dependent potential has different consequences for rapidity and transverse momentum spectra than for flow coefficients. We obtain the best description of the HADES and FOPI data on the directed and elliptic flow coefficients of protons and light clusters applying a momentum dependent EoS. Moreover, we observe a scaling behavior of $v_2$ versus $p_T$ with atomic number $A$. Finally we demonstrate that flow observables can help to identify the cluster production mechanisms.

We investigate light cluster and anti-cluster production in heavy-ion collisions from SIS to RHIC energies within the Parton-Hadron-Quantum-Molecular Dynamics (PHQMD) microscopic transport approach which propagates (anti-)baryons using n-body QMD dynamics. In PHQMD the clusters are formed dynamically by potential interactions between baryons - and recognized by the Minimum Spanning Tree (MST) algorithm - as well as by kinetic reactions in case of deuterons. We present the novel PHQMD results for different observables such as excitation functions of the multiplicity of deuterons, anti-deuterons and tritons, as well as their transverse momentum spectra. Moreover, we investigate the system size dependence of proton and deuteron production in p+A collisions and show the PHQMD results for p+A collisions (A = Be, Al, Cu, Au) at 14 AGeV/c, as well as for asymmetric Au+A collisions (A = Al, Cu, Pb) at a bombarding energy of about 10 AGeV., Comment: Contribution to: QNP2024

We describe bottomonium production not only in pp collisions but also in heavy-ion collisions by using the Remler's formalism where quarkonium density operator is applied to all possible combination of heavy quark and heavy antiquark pairs. In pp collisions heavy (anti)quark momentum is provided by the PYTHIA event generator after rescaling $p_T$ and rapidity to imitate the FONLL calculations. Then spatial separation between heavy quark and heavy antiquark is introduced based on the uncertainty principle. In heavy-ion collisions quarkonium wavefunction changes with temperature assuming heavy quark potential equals the free energy of heavy quark and heavy antiquark system in heat bath. The density operator is updated whenever heavy quark or heavy antiquark scatters in QGP produced in heavy-ion collisions. Our results are consistent with the experimental data from ALICE and CMS Collaborations assuming that the interaction rate of heavy (anti)quark in quarkonium is suppressed to 10 \% that of unbound heavy (anti)quark. We also find that off-diagonal recombination of bottomonium barely happens even in Pb+Pb collisions at $\sqrt{s}=5.02$ TeV., Comment: 4 pages, 2 figures

We study the system size dependence of heavy quark (HQ) observables at a center of mass energy of $\sqrt{s_{\rm NN}}=5.02$ TeV to explore whether it can provide further constraints on the physical processes which are involved: energy loss of HQs in the quark gluon plasma (QGP), hadronization and hadronic rescattering. We use the EPOS4HQ approach to study p-p and 0-10\% central O-O, Ar-Ar, Kr-Kr and Pb-Pb reactions and investigate in detail the momentum change of heavy quarks from creation until their detection as part of a hadron as well as the enhancement of heavy baryon production at low $p_T$. We investigate furthermore the origin and the system size dependence of the azimuthal correlations between the heavy quark $Q$ and the heavy antiquark $\bar Q$ and how one can bypass the problem that correlations are washed out due to the combinatorial background. We conclude that a systematic study of the system size dependence of the momentum loss allows to separate the momentum loss due to the passage through the QGP from the momentum change due to hadronization and the $Q\bar Q$ correlations allow to gain inside into the different pQCD processes in which the heavy quarks are created.

We present a new model for jet quenching in a quark gluon plasma (QGP). The jet energy loss has two steps. The initial jet parton with a high virtuality loses energy by a perturbative vacuum parton shower modified by medium interactions until it becomes on shell. Subsequent energy loss originates from elastic and radiative collisions with the medium constituents. Coherency of the radiative collisions is achieved by starting with virtual gluons that act as field dressing of the initial jet parton. These are formed according to a Gunion-Bertsch seed. The QCD version of the LPM effect is obtained by increasing the phase of the virtual gluons through elastic scatterings with the medium. Above a phase threshold, the virtual gluons will be formed and can produce coherent radiation themselves. The model has been implemented in a Monte Carlo code and is validated by successfully reproducing the BDMPS-Z prediction for the energy spectrum of radiated gluons in a static medium. Results for the more realistic case, in which the assumptions of the BDMPS-Z approach are released, are also shown. We investigate the influence of various parameters on the energy spectrum and the transverse momentum distribution, such as the in-medium quark masses, the energy transfer in the recoil process, and the phase accumulation criteria, especially for low and intermediate energy gluons.

Employing the recently developed EPOS4HQ event generator, we study the production of different heavy-flavor mesons in relativistic heavy-ion collisions at RHIC and LHC energies. The transverse momentum spectra, yield ratio, nuclear modification factor, and elliptic flow can be well described in the EPOS4HQ framework. We furthermore analyze the processes which modify these observables as compared to $pp$ collisions and are at the origin of the experimentally determined nuclear modification factor $R_{AA}$., Comment: 17 pages, 25 figures

We investigate the charmonium and bottomonium production in $pp$ collisions using the Wigner densities formalism. The Wigner density of the quarkonia is approximated by analytical 3-D isotropic harmonic oscillator Wigner densities with the same root-mean-square radius given by the solution of the Schr\"odinger equation. This approach reproduces quite well the available experimental transverse momentum and rapidity distributions., Comment: Proceedings QM2023

Heavy-flavor hadrons produced in ultra-relativistic heavy-ion collisions are a sensitive probe for studying hadronization mechanisms of the quark-gluon-plasma. In this work, we survey how different transport models for the simulation of heavy-quark diffusion through a quark-gluon plasma in heavy-ion collisions implement hadronization and how this affects final-state observables. Utilizing the same input charm-quark distribution in all models at the hadronization transition, we find that the transverse-momentum dependence of the nuclear modification factor of various charm hadron species has significant sensitivity to the hadronization scheme. In addition, the charm-hadron elliptic flow exhibits a nontrivial dependence on the elliptic flow of the hadronizing partonic medium., Comment: 21 pages, 12 figures

Relativistic heavy-ion collisions produce a hot and dense nuclear matter, through which one can study the phase diagram of QCD. Open and hidden heavy flavors are promising probes to search for the properties of the hot and dense nuclear matter under extreme conditions. We present how the production and interactions of open and hidden heavy flavors in heavy-ion collisions are realized in the Parton-Hadron-String Dynamics, which is a non-equilibrium microscopic transport approach for the description of the dynamics of strongly interacting hadronic and partonic matter., Comment: 6 pages, 2 figures

The creation of a quark-gluon plasma (QGP) is expected in heavy ion collisions. It came as a surprise that proton-proton collisions at ultrarelativistic energies show as well a ``QGP-like'' behavior and signs of the creation of a fluid, although the corresponding system size is not more than a few cubic femtometers. Even more surprisingly, also heavy flavor particles seem to be part of the fluid or at least interact with it. In this paper, we will investigate in a quantitative way this ``collective behavior'' of heavy flavor, by employing the newly developed EPOS4HQ approach, which has proven to be compatible with basic experimental data of light flavor hadrons. We will investigate all observables, which may manifest collectivity, as particle spectra, elliptic flow, baryon-to-meson ratios, and two-particle correlations, and compare the results with experimental data. We will try to disentangle initial state effects, those being due to interactions between charm quarks and plasma partons, and final state effects (hadronization)., Comment: 9 pages, 14 figures

We present a new model for jet quenching from coherent radiation in a brick medium. The jet energy loss is simulated as a perturbative final-state vacuum parton shower followed by a medium-induced shower originating from elastic and radiative collisions with the medium constituents. Coherency is achieved by starting with trial gluons that act as field dressing of the initial jet parton. These are formed according to a Gunion-Bertsch seed. The QCD version of the LPM effect is attained by increasing the phase of the trial gluons through elastic scatterings with the medium. Above a phase threshold, the trial gluons will be realised and can produce coherent radiation themselves. The model has been implemented in a Monte Carlo code and has been validated by successfully reproducing the BDMPS-Z prediction for the energy spectrum. The realistic case with minimal assumptions are also produced and shown. In particular, we show the influence of various parameters on the energy spectrum and transverse momentum distribution, such as the in-medium quark masses, the energy transfer in the recoil process, and the phase accumulation criteria, especially for low and intermediate energy gluons. Future studies will allow for the interface with full simulations of the quark-gluon-plasma with hydrodynamic evolution, such as vHLLE, along with subsequent hadronisation of the jet partons in order to produce realistic distributions that can be directly compared to LHC and RHIC data., Comment: Proceedings for Hard Probes 2023 (Aschaffenburg, Germany, 26-31 March 2023). 6 pages, 8 figures

We study bottomonium $b\bar b$ production in pp collisions as well as in heavy-ion collisions, using a quantal density matrix approach. The initial bottom (anti)quarks are provided by the PYTHIA event generator. We solve the Schr\"odinger equation for the $b\bar b$ pair, identifying the potential with the free energy, calculated with lattice QCD, to obtain the temperature dependent $b\bar b$ density matrix as well as the dissociation temperature. The formation of bottomonium is given by projection of the bottomonium density matrix onto the density matrix of the system. With this approach we describe the rapidity and transverse momentum distribution of the $\Upsilon $(nS) in pp collisions at $\sqrt{s_{\rm NN}}=$ 5.02 TeV extending a similar calculation for the charmonium states \cite{Song:2017phm}. We employ the Remler formalism to study the $b\bar b$ production in heavy ion collisions in which the heavy quarks scatter elastically with partons from the quark gluon plasma (QGP). The elastic scattering of heavy (anti)quark in QGP is realized by the dynamical quasi-particle model (DQPM) and the expanding QGP is modeled by PHSD. We find that a reduction to 10 \% of the scattering cross section for a (anti)bottom quark with a QGP parton reproduces the experimental data. This suggests that due to color neutrality the scattering cross section of the small $b\bar b$ system with a parton is considerably smaller than twice the bottom-parton scattering cross section., Comment: 9 pages, 6 figures

The understanding of the mechanisms for the production of weakly bound clusters, such as a deuteron $d$, in heavy-ion reactions at mid-rapidity is presently one of the challenging problems which is also known as the "ice in a fire" puzzle. In this study we investigate the dynamical formation of deuterons within the Parton-Hadron-Quantum-Molecular Dynamics (PHQMD) microscopic transport approach and advance two microscopic production mechanisms to describe deuterons in heavy-ion collisions from SIS to RHIC energies: kinetic production by hadronic reactions and potential production by the attractive potential between nucleons. Differently to other studies, for the "kinetic" deuterons we employ the full isospin decomposition of the various $\pi NN\leftrightarrow \pi d$, $NNN\leftrightarrow N d$ channels and take into account the finite size properties of the deuteron by means of an excluded volume condition in coordinate space and by the projection onto the deuteron wave function in momentum space. We find that considering the quantum nature of the deuteron in coordinate and momentum space reduces substantially the kinetic deuteron production in a dense medium as encountered in heavy-ion collisions. If we add the "potential" deuterons by applying an advanced Minimum Spanning Tree (aMST) procedure, we obtain good agreement with the available experimental data from SIS energies up to the top RHIC energy., Comment: 35 pages, 24 figures

Using the Remler formalism for the creation of composed particles, we study charmonium production both in thermalized and thermalizing boxes, which contain charm and anticharm quarks. The thermalizing box studies include the lowering of the box temperature, the spatial diffusion of charm and anticharm quarks, which are initially confined in the central region, as well as the combination of both, what imitates heavy-ion collisions. Comparing numerical and analytical results we demonstrate that the rate of the original Remler formalism has to be supplemented by two rates to obtain, for $t\to \infty$, results, which are consistent with the statistical model predictions: i) a rate, which takes into account the temperature dependence of the Wigner density of the quarkonium during the expansion and, in the case that a heavy quark potential is not implemented in the Monte Carlo approach, ii) a rate which comes from the change of the relative distance between the heavy quark and antiquark. These results provide the basis for future applications of the Remler formalism to heavy-ion collisions., Comment: 9 pages, 5 figures

The nuclear equation of state (EOS) is at the center of numerous theoretical and experimental efforts in nuclear physics. With advances in microscopic theories for nuclear interactions, the availability of experiments probing nuclear matter under conditions not reached before, endeavors to develop sophisticated and reliable transport simulations to interpret these experiments, and the advent of multi-messenger astronomy, the next decade will bring new opportunities for determining the nuclear matter EOS, elucidating its dependence on density, temperature, and isospin asymmetry. Among controlled terrestrial experiments, collisions of heavy nuclei at intermediate beam energies (from a few tens of MeV/nucleon to about 25 GeV/nucleon in the fixed-target frame) probe the widest ranges of baryon density and temperature, enabling studies of nuclear matter from a few tenths to about 5 times the nuclear saturation density and for temperatures from a few to well above a hundred MeV, respectively. Collisions of neutron-rich isotopes further bring the opportunity to probe effects due to the isospin asymmetry. However, capitalizing on the enormous scientific effort aimed at uncovering the dense nuclear matter EOS, both at RHIC and at FRIB as well as at other international facilities, depends on the continued development of state-of-the-art hadronic transport simulations. This white paper highlights the essential role that heavy-ion collision experiments and hadronic transport simulations play in understanding strong interactions in dense nuclear matter, with an emphasis on how these efforts can be used together with microscopic approaches and neutron star studies to uncover the nuclear EOS., Comment: White paper prepared for the 2023 Long Range Plan. v3: Updated version as published in Progress in Particle and Nuclear Physics. Note: the published version does not include the executive summary; in the updated arXiv version, the executive summary is included as an appendix. v4: Corrected list of authors

Phase transitions in a non-perturbative regime can be studied by ab initio Lattice Field Theory methods. The status and future research directions for LFT investigations of Quantum Chromo-Dynamics under extreme conditions are reviewed, including properties of hadrons and of the hypothesized QCD axion as inferred from QCD topology in different phases. We discuss phase transitions in strong interactions in an extended parameter space, and the possibility of model building for Dark Matter and Electro-Weak Symmetry Breaking. Methodological challenges are addressed as well, including new developments in Artificial Intelligence geared towards the identification of different phases and transitions., Comment: 94 pages, 23 figures, GGI workshop "Phase Transitions in Particle Physics" review - v2: minor revisions and typo corrected, matches accepted version on PPNP

We investigate the capabilities of the Nambu--Jona-Lasinio model to describe and reproduce fundamental vacuum properties of Quantum Chromodynamics, notably the hadronic spectrum. Mesons are described as quark-antiquark bound states at the level of the random phase approximation of the Bethe-Salpeter equation, while baryons are characterized as quark-diquark bound states within the static approximation of the Faddeev equation. Within a Bayesian framework, we constrain the model by phenomenologically known quantities and study the implications on its parameters and predictions in vacuum, as well as the correlations between the two. We find that within our framework, the vacuum masses of mesons and baryons can be reasonably well reproduced. Scalar diquarks need to be significantly bound in order to correctly reproduce the masses of the baryon octet, therefore enforcing values of the scalar diquark coupling larger than what is suggested by the canonical Fierz values. These findings could have important implications on the phenomenology of strongly-interacting matter at high temperature and density as well as of compact star physics., Comment: 18 pages, 8 figures

We study the production of clusters and hypernuclei at midrapidity employing the Parton-Hadron-Quantum-Molecular-Dynamics (PHQMD) approach, a microscopic n-body transport model based on the QMD propagation of the baryonic degrees of freedom with density dependent 2-body potential interactions. In PHQMD the cluster formation occurs dynamically, caused by the interactions. The clusters are recognized by the Minimum Spanning Tree (MST) algorithm. We present the PHQMD results for cluster and hypernuclei formation in comparison with the available experimental data at relativistic energies. PHQMD allows to study the time evolution of formed clusters and the origin of their production, which helps to understand how such weakly bound objects are formed and survive in the rather dense and hot environment created in heavy-ion collisions. It offers therefore an explanation of the 'ice in the fire' puzzle. To investigate whether this explanation of the 'ice in the fire' puzzle applies only to the MST results we study also the deuterons production by coalescence. We embed MST and coalescence in the PHQMD and UrQMD transport approaches in order to obtain model independent results. We find that both clustering procedures give very similar results for the deuteron observables in the UrQMD as well as in the PHQMD environment. This confirms that our solution for the 'ice in the fire' puzzle is common to MST and coalescence and independent of the transport approach., Comment: 6 pages, 6 figures, Contribution to the SQM-2022 Proceedings

We present a new model for the creation of \J mesons in ultrarelativistic heavy ion collisions, which allows to follow the individual heavy quarks from their creation until the detector through the Quark Gluon Plasma (QGP), which is formed in these collisions and described by the EPOS2 event generator. The \cc quarks interact via a potential, based on results of lattice gauge calculations. The annihilation and creation of \J is described by a density matrix approach whose time evolution is studied in the expanding system. The comparison with PbPb data at $\sqrt{s}$=5.02 TeV shows that this model can describe simultaneously the nuclear modification factor $R_{AA}$ and the elliptic flow $v_2$ of the \J at low transverse momen, Comment: Computational error corrected. final version accepted by PRC

We investigate the hidden strange $\phi$ meson production in heavy-ion collisions from subthreshold ($E_{kin}\approx 1$ A GeV) to relativistic ($E_{kin}\approx 21$ A TeV) energies as well as its coupling to the open strange mesons (kaons, antikaons) and their productions. Our study is based on the off-shell microscopic Parton-Hadron-String Dynamics (PHSD) transport approach which is applicable for the dynamical description of strongly interacting hadronic and partonic degrees-of-freedom created in heavy-ion collisions. Implementing novel meson-baryon and meson-hyperon production channels for $\phi$ mesons, calculated within a T-matrix coupled channel approach based on the extended SU(6) chiral effective Lagrangian model, along with the collisional broadening of the $\phi$-meson in-medium spectral function, we find a substantial enhancement of $\phi$ meson production in heavy-ion collisions, especially at sub- and near-thresholds. This allows to describe the experimentally observed strong enhancement of the $\phi/K^-$ ratio at low energies without including hypothetical decays of heavy baryonic resonances to $\phi$ as in alternative approaches. Moreover, we show that in spite of a stronger contribution from enhanced $\phi$ to $K^-$ production, the majority of the experimental data for different A+A systems at low energies favor the scenario with in-medium modifications of the kaon and antikaon properties in the hot and dense environment. Moreover, we study the influence of the final state interactions of $K, \bar K$ mesons on the reconstruction of $\phi$'s by the by invariant mass method., Comment: 24 pages, 22 figures

Transport models are the main method to obtain physics information from low to relativistic-energy heavy-ion collisions. The Transport Model Evaluation Project (TMEP) has been pursued to test the robustness of transport model predictions in reaching consistent conclusions from the same type of physical model. Calculations under controlled conditions of physical input and set-up were performed with various participating codes. These included both calculations of nuclear matter in a box with periodic boundary conditions, and more realistic calculations of heavy-ion collisions. In this intermediate review, we summarize and discuss the present status of the project. We also provide condensed descriptions of the 26 participating codes, which contributed to some part of the project. These include the major codes in use today. We review the main results of the studies completed so far. They show, that in box calculations the differences between the codes can be well understood and a convergence of the results can be reached. These studies also highlight the systematic differences between the two families of transport codes, known as BUU and QMD type codes. However, when the codes were compared in full heavy-ion collisions using different physical models, as recently for pion production, they still yielded substantially different results. This calls for further comparisons of heavy-ion collisions with controlled models and of box comparisons of important ingredients, like momentum-dependent fields, which are currently underway. We often indicate improved strategies in performing transport simulations and thus provide guidance to code developers. Results of transport simulations of heavy-ion collisions from a given code will have more significance if the code can be validated against benchmark calculations such as the ones summarized in this review., Comment: 114 pages, 14 figures, 479 references, accepted for publication in Progress of Particle and Nuclear Phsics

The formation of deuterons in heavy-ion collisions at relativistic energies is investigated by employing two recently advanced models -- the Minimum Spanning Tree (MST) method and the coalescence model by embedding them in the PHQMD and the UrQMD transport approaches. While the coalescence mechanism combines nucleons into deuterons at the kinetic freeze-out hypersurface, the MST identifies the clusters during the different stages of time evolution. We find that both clustering procedures give very similar results for the deuteron observables in the UrQMD as well as in the PHQMD environment. Moreover, the results agree well with the experimental data on deuteron production in Pb+Pb collisions at $\sqrt{s_{NN}} = 8.8$ GeV (selected for the comparison of the methods and models in this study). A detailed investigation shows that the coordinate space distribution of the produced deuterons differs from that of the free nucleons and other hadrons. Thus, deuterons are not destroyed by additional rescattering.

We compare the microscopic transport models UrQMD, PHSD, PHQMD, and SMASH to make predictions for the upcoming Ag+Ag data at $E_\mathrm{lab}=1.58$~$A$GeV ($\sqrt{s_\mathrm{NN}}=2.55$~GeV) by the HADES collaboration. We study multiplicities, spectra and effective source temperatures of protons, $\pi^{\pm,0}$, $K^\pm$, the $\eta$, $\Lambda+\Sigma^0$ and the $\Xi^-$ within these models. Despite variations in the detailed implementation of the dynamics in the different models, the employed transport approaches all show consistent multiplicities of the bulk of investigated hadrons. The main differences are in the $\Xi^-$ production, which is treated differently between UrQMD/SMASH on one side employing high mass resonance states with explicit decays to $\mathrm{Resonance}\rightarrow \Xi+K+K$ in contrast to PHSD/PHQMD which account only non-resonant $\Xi$ production channels. A comparison of the spectra, summarized by effective source temperatures, shows that all models provide similar source temperatures around $T_\mathrm{source}=80-95$~MeV, and show substantial radial flow on the order of $\langle v_T\rangle=0.22c-0.3c$ even for such a small system., Comment: 13 pages, 11 figures

We extend the effective dynamical quasiparticle model (DQPM) - constructed for the description of non-perturbative QCD phenomena of the strongly interacting quark-gluon plasma (QGP) - to large baryon chemical potentials, $\mu_B$, including a critical end-point and a 1st order phase transition. The DQPM description of quarks and gluons is based on partonic propagators with complex selfenergies where the real part of the selfenergies is related to the quasiparticle mass and the imaginary part to a finite width of their spectral functions. In DQPM the determination of complex selfenergies for the partonic degrees of freedom at zero and finite $\mu_B$ has been performed by adjusting the entropy density to the lQCD data. The temperature-dependent effective coupling (squared) $g^2(T/T_c)$, as well as the parton effective masses and widths are based on this adjustment. The novel extended dynamical quasiparticle model, named "DQPM-CP", makes it possible to describe thermodynamical and transport properties of quarks and gluons in a wide range of $T$ and $\mu_B$, and reproduces the equation-of-state (EoS) of lQCD calculations in the crossover region of finite $T, \mu_B$. We apply a scaling ansatz for the strong coupling constant near the CEP, located at ($T^{CEP}$, $\mu^{CEP}_B) = (0.100, 0.960)$ GeV. We show the EoS as well as the speed of sound for $T>T_c$ and for a wide range of $\mu_B$, which can be of interest for hydrodynamical simulations. Furthermore, we consider two settings for the strange quark chemical potentials (I) $\mu_s=\mu_B/3$ and (II) $\mu_s=0$. The isentropic trajectories of the QGP matter are compared for these two cases. The phase diagram of DQPM-CP is close to PNJL calculations. The leading order pQCD transport coefficients of both approaches differ. This elucidates that the knowledge of the phase diagram alone is not sufficient to describe the dynamical evolution of QGP., Comment: 18 pages, 17 figures

We study cluster and hypernuclei production in heavy-ion collisions at relativistic energies employing the Parton-Hadron-Quantum-Molecular-Dynamics (PHQMD) approach, a microscopic n-body transport model based on the QMD propagation of the baryonic degrees of freedom with density dependent 2-body potential interactions. All other ingredients of PHQMD, including the collision integral and the treatment of the quark-gluon plasma (QGP) phase, are adopted from the Parton-Hadron-String Dynamics (PHSD) approach. In PHQMD the cluster formation occurs dynamically, caused by the interactions. The clusters are recognized by the Minimum Spanning Tree (MST) algorithm. We present the PHQMD results for cluster and hypernuclei formation in comparison with the available experimental data at AGS, SPS, RHIC-BES and RHIC fixed target energies. We also provide predictions on cluster production for the upcoming FAIR and NICA experiments. PHQMD allows to study the time evolution of formed clusters and the origin of their production, which helps to understand how such weakly bound objects are formed and survive in the rather dense and hot environment created in heavy-ion collisions. It offers therefore an explanation of the 'ice in the fire' puzzle., Comment: 25 pages, 33 figures, Fig. 13 updated

We study the in-medium effects in strangeness production in heavy-ion collisions at (sub-)\-threshold energies of 1 - 2 A GeV based on the microscopic Parton-Hadron-String Dynamics (PHSD) transport approach. The in-medium modifications of the antikaon $(\bar K = K^-, \bar K^0)$ properties are described via the self-consistent coupled-channel unitarized scheme based on a SU(3) chiral Lagrangian which incorporates explicitly the $s-$ and $p-$ waves of the kaon-nucleon interaction. This scheme provides the antikaon potential, spectral functions and reaction cross sections as well as their dependence on baryon density, temperature and antikaon momentum in the nuclear medium, which are incorporated in the off-shell dynamics of the PHSD. The in-medium modification of kaons $(K = K^+, K^0)$ are accounted via the kaon-nuclear potential, which is assumed to be proportional to the local baryon density. The manifestation of the medium effects in observables is investigated for the $K$ and ${\bar K}$ rapidity distributions, $p_T$-spectra as well as the polar and azimuthal angular distributions, direct ($v_1$) and elliptic ($v_2$) flow in C+C, Ni+Ni, and Au+Au collisions. We find - by comparison to experimental data from the KaoS, FOPI and HADES Collaborations - that the modifications of (anti)kaon properties in nuclear matter are necessary to explain the data in a consistent manner. Moreover, we demonstrate the sensitivity of kaon observables to the equation-of-state of nuclear matter., Comment: 38 pages, 26 figures, to be published in PRC

We calculate two transport coefficients -- the shear viscosity over entropy ratio $\eta/s$ and the ratio of the electric conductivity to the temperature $\sigma_0/T$ -- of strongly interacting quark matter within the extended $N_f=3$ Polyakov Nambu-Jona-Lasinio (PNJL) model along the crossover transition line for moderate values of baryon chemical potential $0 \leq \mu_B \leq 0.9$ GeV as well as in the vicinity of the critical endpoint (CEP) and at large baryon chemical potential $\mu_B=1.2$ GeV, where the first-order phase transition takes place. The evaluation of the transport coefficients is performed on the basis of the effective Boltzmann equation in the relaxation time approximation. We employ two different methods for the calculation of the quark relaxation times: i) using the averaged transition rate defined via thermal averaged quark-quark and quark-antiquark PNJL cross sections and ii) using the 'weighted' thermal averaged quark-quark and quark-antiquark PNJL cross sections. The $\eta/s$ and $\sigma_0/T$ transport coefficients have a similar temperature and chemical potential behavior when approaching the chiral phase transition for the both methods for the quark relaxation time, however, the differences grow with increasing temperature. We demonstrate the effect of the first-order phase transition and of the CEP on the transport coefficients in the deconfined QCD medium., Comment: 16 pages, 21 figures, 4 tables

We report on a benchmark calculation of the in-medium radiative energy loss of low-virtuality jet partons within the EPOS3-Jet framework. The radiative energy loss is based on an extension of the Gunion-Bertsch matrix element for a massive projectile and a massive radiated gluon. On top of that, the coherence (LPM effect) is implemented by assigning a formation phase to the trial radiated gluons in a fashion similar to the approach in JHEP 07 (2011), 118, by Zapp, Stachel and Wiedemann. In a calculation with a simplified radiation kernel, we reproduce the radiation spectrum reported in the approach above. The radiation spectrum produces the LPM behaviour $dI/d\omega\propto\omega^{-1/2}$ up to an energy $\omega=\omega_c$, when the formation length of radiated gluons becomes comparable to the size of the medium. Beyond $\omega_c$, the radiation spectrum shows a characteristic suppression due to a smaller probability for a gluon to be formed in-medium. Next, we embed the radiative energy loss of low-virtuality jet partons into a more realistic "parton gun" calculation, where a stream of hard partons at high initial energy $E_\text{ini}=100$ GeV and initial virtuality $Q^2=E^2$ passes through a box of QGP medium with a constant temperature. At the end of the box evolution, the partons are hadronized using Pythia 8, and the jets are reconstructed with the FASTJET package. We find that the full jet energy loss in such scenario approaches a ballpark value reported by the ALICE collaboration. However, the calculation uses a somewhat larger value of the coupling constant $\alpha_s$ to compensate for the missing collisional energy loss of the low-virtuality jet partons., Comment: Hard Probes 2020 proceedings (online at Austin (TX), USA, June 1-5, 2020). 5 pages, 2 figures

EPOS3-Jet is an integrated framework for jet modelling in heavy ion collisions, where the initial hard (jet) partons are produced along with soft (medium) partons in the initial state EPOS approach. The jet partons then propagate in the hydrodynamically expanding medium. The energy and momentum lost by the jet partons is added to the hydrodynamic medium via the source terms. The full evolution proceeds in a concurrent mode, without separating hydrodynamic and jet parts. In this report, we examine the medium recoil effects in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV LHC energy in the EPOS3-Jet framework., Comment: proceedings of Strangeness in Quark Matter 2019 conference (Bari, Italy, 10-15 June 2019). 4 pages, 1 figure

In this article we investigate how the drag coefficient $A$ and $\hat{q}$, the transverse momentum transfer by unit length, of charm quarks are modified if the QGP is not in complete thermal equilibrium using the dynamical quasi-particle model (DQPM) which reproduces both, the equation-of-state of the QGP and the spatial diffusion coefficient of heavy quarks as predicted by lattice QCD calculations. We study three cases: a) the QGP has an anisotropic momentum distribution of the partons which leads to an anisotropic pressure b) the QGP partons have higher or lower kinetic energies as compared to the thermal expectation value, and c) the QGP partons have larger or smaller pole masses of their spectral function as compared to the pole mass from the DQPM at the QGP temperature. In the last two cases we adjust the number density of partons to obtain the same energy density as in an equilibrated QGP. In the first scenario we find that if the transverse pressure exceeds the longitudinal one for small heavy quark momenta $A$ becomes larger and $\hat{q}$ smaller as compared to an isotropic pressure. For heavy quarks with large momentum both, $A$ and $\hat{q}$ , approach unity. If the partons have less kinetic energy or a smaller pole mass as compared to a system in equilibrium charm quarks lose more energy. In the former case $\hat{q}$ decreases whereas in the latter case it increases for charm quark with a low or intermediate transverse momentum. Thus each non-equilibrium scenario affects $A$ and $\hat{q}$ of charm quarks in a different way. The modifications in our scenarios are of the order 20-50\% at temperatures relevant for heavy ion reactions. These modifications have to be considered if one wants to determine these coefficients by comparing heavy ion data with theoretical predictions from viscous hydrodynamics or Langevin equations., Comment: 18 pages, 12 figures

We extend the SU(3) (Polyakov) Nambu Jona-Lasinio in two ways: We introduce the next to leading order contribution (in $N_c$) in the partition function. This contribution contains explicit mesonic terms. We introduce a coupling between the gluon field and the quark degrees of freedom which goes beyond a simple rescaling of the critical temperature. With both these improvements we can reproduce, for vanishing chemical potentials, the lattice results for the thermal properties of a strongly interacting system like pressure, energy density, entropy density, interaction measure and the speed of sound. Also the expansion parameter towards small but finite chemical potentials agrees with the lattice results. Extending the calculations to finite chemical potentials (what does not require any new parameter) we find a first order phase transition up to a critical end point of $T_{CEP}= 110\ MeV$ and $\mu_q = 320\ MeV$. For very large chemical potentials, we find agreement with pQCD calculations. We calculate the mass of mesons and baryons as a function of temperature and chemical potential and the transition between the hadronic and the chirally restored phase. These calculations provide an equation of state in the whole $T,\mu$ plane an essential ingredient for dynamical calculations of ultra-relativistic heavy ion collisions but also for the physics of neutron stars and neutron star collisions.

Central lead-lead collisions at the LHC energies may pose a particular challenge for jet identification as multiple jets are produced per each collision event. We simulate the jet evolution in central Pb-Pb events at $\sqrt{s_{\rm NN}} = 2.76$ GeV collision energy with EPOS3 initial state, which typically contains multiple hard scatterings in each event. Therefore the partons from different jets have a significant chance to overlap in momentum space. We find that 30% of the jets with $p_\perp > 50$ GeV, identified by the standard anti-$k_\perp$ jet finding algorithm with jet cone size R=0.3, contain `intruder' particles from overlapping generator-level jets. This fraction increases with increasing beam energy and increasing R. The reconstructed momentum of the jet differs from that of the modelled jet by the loss due to jet partons which are outside of the jet cone and by the gain due to intruder partons. The sum of both may be positive or negative. These intruder partons particularly affect the radial jet momentum distribution because they contribute mostly at large angles $\Delta r$ with respect to the jet centre. The study stresses the importance of the jet overlap effect emerging in central lead-lead collisions at the LHC energies, while being negligible in peripheral PbPb or $p$Pb/$pp$ collisions., Comment: 7 pages, 10 figures; version accepted for Physical Review C

The EPOS-HQ model is a framework designed for predicting heavy-flavor observables both in p-p, p-A and A-A collisions. It results from the integration of the MC$@_s$HQ and EPOS3 codes and should supersede predictions made with each of these two. In this contribution, we briefly present the new ingredients of the EPOS-HQ model as well as some preliminary results. From the comparison with experimental data, we derive some direction of improvement for the near future., Comment: Proceedings of Hard Probes 2018 conference in Aix Les Bains (France)

The energy-loss of hard probes within the hot and dense medium of a quark gluon plasma (QGP) can be described by theoretical models based on radiative energy loss as well as combinations of collisional and radiative energy loss. In a search for observables that allow to disentangle these energy-loss mechanisms, we introduced a set of effective models that allows to investigate the consequences on jets of both types of jet-medium interactions within a consistent framework. We particularly studied angular jet-broadening via angular two-particle correlations. Distinguishing contributions from pairs at different scales of particle momenta, we found qualitative differences between radiative and collisional approaches., Comment: proceedings for a seminar talk at the "Hard Probes 2018" conference in Aix Les Bains, 4 pages, 1 figure

We report on the first results for jet observables from a time-like parton cascade integrated with hydrodynamic evolution within the EPOS3-HQ framework. The hard (jet) partons are produced along with soft partons in the initial state EPOS approach. The soft partons, represented by strings, melt into a thermalized medium which is described by a 3 dimensional event-by-event viscous hydrodynamic approach. The jet partons then propagate in the hydrodynamically expanding medium. The total jet energy gets progressively `degraded' when the partons reaching a thermal energy scale are melted into the hydrodynamic medium via the source terms. The full evolution proceeds in a parallel mode, without separating the thermalized and jet parts. We demonstrate how the transverse expansion of the medium affects the jet structure, and how the medium itself is affected by the jet recoil., Comment: talk at Hard Probes 2018 conference (Aix-Les-Bains, France, 30 September - 5 October, 2018)

Several transport models have been employed in recent years to analyze heavy-flavor meson spectra in high-energy heavy-ion collisions. Heavy-quark transport coefficients extracted from these models with their default parameters vary, however, by up to a factor of 5 at high momenta. To investigate the origin of this large theoretical uncertainty, a systematic comparison of heavy-quark transport coefficients is carried out between various transport models. Within a common scheme devised for the nuclear modification factor of charm quarks in a brick medium of a quark-gluon plasma, the systematic uncertainty of the extracted drag coefficient among these models is shown to be reduced to a factor of 2, which can be viewed as the smallest intrinsic systematical error band achievable at present time. This indicates the importance of a realistic hydrodynamic evolution constrained by bulk hadron spectra and of heavy-quark hadronization for understanding the final heavy-flavor hadron spectra and extracting heavy-quark drag coefficient. The transverse transport coefficient is less constrained due to the influence of the underlying mechanism for heavy-quark medium interaction. Additional constraints on transport models such as energy loss fluctuation and transverse-momentum broadening can further reduce theoretical uncertainties in the extracted transport coefficients., Comment: 20 pages in ReVTex with 11 figures, final version to appear in PRC

Energy-loss studies of hard particle probes produced in heavy ion collisions have often been used to get information on the interactions within the medium of a quark-gluon plasma (QGP). However, with the study of in-medium energy-loss of individual particles alone, it remains still ambiguous, whether the occured decrease in particle energy is caused by predominantly radiative or collisional energy-loss mechanisms. Focusing on the in-medium energy-loss of hard jet-partons, we propose additional studies of the angular jet-structure as a means to further constrain the energy-loss mechanisms.

In this talk we will discuss the recent advances in describing heavy-quark dynamics in the quark-gluon plasma (QGP), which evolves hydrodynamically. Special emphasis is put on the collective flow of the heavy-quarks with the medium constituents, for which we present our latest results obtained within the MC@sHQ+EPOS2 model at $\sqrt{s}=5$~TeV., Comment: Proceedings for the 17th International Conference on Strangeness in Quark Matter (SQM 2017), July 10-15 2017, Utrecht, The Netherlands

We describe two independent frameworks which provide unambiguous determinations of the deconfinement and the decoupling conditions of a relativistic gas at finite temperature. First, we use the Polyakov-Nambu-Jona-Lasinio model to compute meson and baryon masses at finite temperature and determine their melting temperature as a function of their strangeness content. Second, we analyze a simple expanding gas within a Friedmann-Robertson-Walker metric, which admits a well-defined decoupling mechanism. We examine the decoupling time as a function of the particle mass and cross section. We find evidences of an inherent dependence of the hadronization and freeze-out conditions on flavor, and on mass and cross section, respectively., Comment: 4 pages, 3 figures. Contribution to the proceedings of the 17th International Conference on Strangeness in Quark Matter (SQM2017), Utrecht, the Netherlands, 10-15 July 2017

We present an analysis of the comparison between 2nd and 3rd flow harmonics of $\pi$, protons and D mesons produced in ultrarelativistic heavy ion collisions. We advocate that such an analysis could turn out to be a good strategy in order to quantify the off-equilibrium dynamics of heavy flavor at lower transverse momentum $p_T$., Comment: QM 2017 proceedings

$J/\psi$ observables of p+p collisions at $\sqrt{s}=$ 200 GeV and 2.76 TeV are calculated using the PYTHIA event generator for the production of $c$ and $\bar c$ and the Wigner density formalism. The charm quark momentum from PYTHIA is tuned in such a way that the transverse momentum and rapidity distribution correspond to the Fixed-Order Next-to-Leading Logarithm (FONLL) calculations and hence to the experimental data for open charm mesons. Using the Wigner density of the charmonium wave function we calculate for each charm quark pair the probability to form a charmonium. As a result, the experimental data on the total $J/\psi$ yield, its rapidity and transverse momentum distribution as well as the fractions of feed-down from excited states of charmonium are reproduced. Applying the same approach to relativistic heavy-ion collisions, we find, if quark gluon plasma (QGP) effects are ignored, a considerable enhancement of the primordial $J/\psi$'s., Comment: 9 pages, 7 figures

We study the equation of state of QCD using an improved version of the three-flavor Polyakov-Nambu-Jona-Lasinio model beyond the mean-field approximation. It incorporates the effects of unquenched quarks into the Polyakov-loop effective potential, as well as mesonic contributions to the grand-canonical potential. We study in full detail the calculation of the thermodynamical potential in this approach and compare the resulting pressure and entropy density with the most-recent lattice-QCD calculations at zero baryochemical potential. Finally, we present some exploratory results at finite chemical potential which include the phase diagram of the model, the quark and meson masses, and finally, the thermodynamical pressure., Comment: 44 pages, 23 figures. Small improvements and more explanations added. Reference list updated. Comparison with recent lattice-QCD results incorporated. Version accepted by the Physical Review C journal

We discuss the quark masses and the elastic $q\bar q$ 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., Comment: Proceedings Discovery Physics at the LHC, December 4-9, 2016 Protea Hotel, Kruger Gate, SA