Parton-Hadron-Quantum-Molecular Dynamics

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.

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.

The formation of weakly bound clusters in the hot and dense environment at midrapidity is one of the surprising phenomena observed experimentally in heavy-ion collisions from a low center of mass energy of a few GeV up to a ultra-relativistic energy of several TeV. Three approaches have been advanced to describe the cluster formation: coalescence at kinetic freeze-out, cluster formation during the entire heavy-ion collision by potential interaction between nucleons and deuteron production by hadronic reactions. We identify experimental observables, which can discriminate these production mechanisms for deuterons.

The origin of weakly bound objects like clusters and hypernuclei, observed in heavy-ion collisions, is of theoretical and experimental interest. It is in the focus of the experiments at RHIC and LHC since it is not evident how such weakly bound objects can survive in an environment whose hadronic decay products point to a temperature of the order of 150 MeV. It is as well one of the key research topics in the future facilities of FAIR and NICA which are under construction in Darmstadt (Germany) and Dubna (Russia), respectively. We present here first results on the cluster dynamics within the model-independent cluster recognition library "phase-space Minimum Spanning Tree" (psMST) applied to different transport approaches: PHQMD, PHSD, SMASH and UrQMD. The psMST is based on the "Minimum Spanning Tree" (MST) algorithm for the cluster recognition which exploits correlations in coordinate space, and it is extended to correlations of baryons in the clusters in momentum space. We show the sensitivity of the cluster formation on the microscopic realization of the n-body dynamics and on the potential interactions in heavy-ion collisions.

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.

The study of the nuclear equation-of-state (EoS) is a one of the primary goals of experimental and theoretical heavy-ion physics. The comparison of recent high statistics data from the STAR Collaboration with transport models provides a unique possibility to address this topic in a yet unexplored energy domain. Employing the microscopic N-body Parton-Hadron-Quantum-Molecular Dynamics (PHQMD) transport approach, which allows to describe the propagation and interactions of hadronic and partonic degrees of freedom including cluster and hyper-nucleus formation and dynamics, we investigate the influence of different EoS on bulk observables, the multiplicity, p_T and rapidity distributions of protons, \Lambdas and clusters up to A=4 as well as their influence on the collective flow. We explore three different EoS: two static EoS, dubbed 'soft' and 'hard', which differ in the compressibility modulus, as well as a soft momentum dependent EoS. We find that a soft momentum dependent EoS reproduces most baryon and cluster observables, including the flow observables, quantitatively, however, hard EOS show a similar trend.