Central Nucleus-nucleus Collisions Research Articles

Use of the Meta-Analysis and Kolmogorov Criteria in the Finding of Singularities of a Nuclear Matter Created in Ultra-Relativistic Nuclear Collisions

Published theoretical data from several models – PHSD/HSD both with and without chiral symmetry restoration (CSR), applied to experimental data on nuclear collisions from BEVALAC/SIS to LHC energies were analyzed using meta-analysis and Kolmogorov criteria. This made it possible to localize possible features of nuclear matter created in central nucleus-nucleus collisions. Ignition of a drop of quark-gluon plasma (QGP) begins already at an energy of about √s<SUB>NN</SUB> = 2 GeV. The assessment showed that this QGP droplet occupies a small fraction, 15% (average radius of about 5.3 fm, if the fireball radius is 10 fm), of the total volume of the fireball created at √s<SUB>NN</SUB> = 2.7 GeV. A drop of exotic matter undergoes a split phase transition – separated boundaries of sharp (1<sup>st</sup> order) crossover and CSR in chiral limit, between QGP and Quarkyonic matter at an energy about √s<SUB>NN</SUB> = 3.5 GeV. The critical endpoint of 2<sup>nd</sup> order probably cannot be reached in nuclear collisions. The triple phase area occupies interval from √s<SUB>NN</SUB> =12 GeV to 15 GeV, the critical endpoint of 1<sup>st</sup> order – at around √s<SUB>NN</SUB> = 20 GeV. The boundary of smooth (2<sup>nd</sup> order) crossover transition with CSR in chiral limit between Quarkyonic matter and QGP was localized between √s<SUB>NN</SUB> = 9.3 GeV and 12 GeV, and between Hadronic and QGP in the interval from √s<SUB>NN</SUB> = 15 GeV to 20 GeV, the boundary of sharp (1<sup>st</sup> order) crossover transition with CSR in chiral limit between Hadronic matter and QGP was localized after √s<SUB>NN</SUB> = 20 GeV. The phase trajectory of the hadronic corona, enveloping the exotic droplet, always remains in the hadronic phase. The possible phase diagram of nuclear matter created in mid-central heavy ion collisions is also presented in the same energy range as for central collisions. Taking into account the quantum nature of the fireball created in nuclear collisions, emphasis is on the existence of events in central nuclear collisions at energy range from √s<SUB>NN</SUB> = 2 GeV to 2.76 TeV, at which no exotic matter is created and nuclear matter in the fireball remains in the hadronic phase throughout its (fireball) evolution.

Spinodal enhancement of fluctuations in nucleus-nucleus collisions

Subensemble Acceptance Method (SAM) [1, 2] is an essential link between measured event-by-event fluctuations and their grand canonical theoretical predictions such as lattice QCD. The method allows quantifying the global conservation law effects in fluctuations. In its basic formulation, SAM requires a sufficiently large system such as created in central nucleus-nucleus collisions and sufficient space-momentum correlations. Directly in the spinodal region of the First Order Phase Transition (FOPT) different approximations should be used that account for finite size effects. Thus, we present the generalization of SAM applicable in both the pure phases, metastable and unstable regions of the phase diagram [3]. Obtained analytic formulas indicate the enhancement of fluctuations due to crossing the spinodal region of FOPT and are tested using molecular dynamics simulations. A rather good agreement is observed. Using transport model calculations with interaction potential we show that the spinodal enhancement of fluctuations survives till the later stages of collision via the memory effect [4]. However, at low collision energies the space-momentum correlation is not strong enough for this signal to be transferred to second and third order cumulants measured in momentum subspace. This result agrees well with recent HADES data on proton number fluctuations at √SNN = 2.4 GeV which are found to be consistent with the binomial momentum space acceptance [5].

ψ(2S) production and nuclear modification factor in nucleus–nucleus collisions with ALICE

Charmonium production is sensitive to deconfinement in nucleusnucleus collisions. The production via regeneration within the QGP or at the phase boundary has been identified as an important ingredient for the description of the centrality and transverse momentum dependence (pT) of the J/ψ nuclear modification factor (RAA) at the LHC. ψ(2S) production relative to J/ψ is one possible discriminator between the two different regeneration scenarios. At the LHC. there is so far no significant observation of the ψ(2S) in central nucleus-nucleus collisions at low-pT, where regeneration is expected to play an important role. The combined Run 2 data set of ALICE allows one to extract a significant ψ(2S) signal in this kinematic region at forward rapidity, in the dimuon decay channel. In this contribution, we present for the first time results on the ψ(2S)-to-J/ψ single ratio and double ratio (to pp collisions) as well as the ψ(2S) nuclear modification factor, in Pb-Pb collisions at √SNN = 5.02 TeV. The ψ(2S)-to-J/ψ double ratio and ψ(2S) RAA are calculated using a new proton-proton reference with improved precision. Results are compared with model calculations.

Evolution of the statistical disintegration of finite nuclei toward high energy

We develop a statistical approach for the description of complex nuclei formation from dynamically produced baryons in high energy heavy-ion reactions. We consider a finite highly-excited expanding nuclear system formed after central nucleus-nucleus collisions. This system is sub-divided into primary equilibrated nucleon clusters. The final nuclei are produced after the decay of these excited clusters. By the successful comparison with the FOPI experimental data we prove the possibility of such a local equilibrium in nuclear matter with the temperature corresponding to the phase coexistence region. The regularities obtained in this new nuclei production mechanism are shown.

Deconfinement of Quarks and Gluons in Nucleus-nucleus Collisions

The energy dependence of hadron production in relativistic nucleus-nucleus collisions reveals the anomalies. They were predicted as the signals of the deconfinement phase transition and observed by NA49 collaboration in Pb + Pb collisions at the CERN SPS. This indicates the onset of the deconfinement in central nucleus-nucleus collisions at about 30 AGeV.

Coupling dynamical and statistical mechanisms for baryonic cluster production in nucleus collisions of intermediate and high energies

Central nucleus-nucleus collisions produce many new baryons and the nuclear clusters can be formed from these species. The phenomenological coalescence models were sufficiently good for description of light nuclei yields in a very broad range of collision energies. We demonstrate that in reality the coalescence process can be considered as 1) the formation of primary diluted excited baryon clusters and 2) their following statistical decay leading to the final cold fragment production. We argue that the formation of such excited systems from the interacting baryons is a natural consequence of the nuclear interaction at subnuclear densities resulting in the nuclear liquid-gas type phase transition in finite systems. In this way one can provide a consistent interpretation of the experimental fragment yields (FOPI data) including the important collision energy dependence in relativistic ion reactions. We investigate the regularities of this new kind of fragment production, for example, their yield, isospin, and kinetic energy characteristics. A generalization of such a clusterization mechanism for hypernuclear matter is suggested. The isotope yields and particle correlations should be adequate for studying these phenomena.

Influence of correlations between yields on the chemical freeze-out temperature

A statistical (thermal) model is applied to the description of hadron yields measured at central nucleus-nucleus collisions at the top RHIC energy sNN=200 GeV and the LHC energy sNN=2.76 TeV. In contrast to the previous analyzes a more general form of the least squares test statistic is used, which takes into account also possible correlations between different species of yields. In addition to hadrons also light nuclei are included in the fits. Because of the lack of data, a toy model is constructed where the correlation coefficients are just free parameters. Because of this the presented considerations are speculative and should be treated as an imperfect illustration of the problem. Within these limitations it is impossible to formulate any definite conclusion, it might be only mentioned that for the considered examples the dependence of the freeze-out temperature and baryon chemical potential on correlations turned out to be weak.

Chemical freeze-out conditions and fluctuations of conserved charges in heavy-ion collisions within a quantum van der Waals model

The chemical freeze-out parameters in central nucleus-nucleus collisions are extracted consistently from hadron yield data within the quantum van der Waals (QvdW) hadron resonance gas model. The beam energy dependences for skewness and kurtosis of net baryon, net electric, and net strangeness charges are predicted. The QvdW interactions in asymmetric matter, $Q/B \neq 0.5$, between (anti)baryons yield a non-congruent liquid-gas phase transition, together with a nuclear critical point (CP) with critical temperature of $T_c=19.5$ MeV. The nuclear CP yields the collision energy dependence of the skewness and the kurtosis to both deviate significantly from the ideal hadron resonance gas baseline predictions even far away, in $(T,\mu_B)$-plane, from the CP. These predictions can readily be tested by STAR and NA61/SHINE Collaborations at the RHIC BNL and the SPS CERN, respectively, and by HADES at GSI. The results presented here offer a broad opportunity for the search for signals of phase transition in dense hadronic matter at the future NICA and FAIR high intensity facilities.

Statistical hadron-gas treatment of systems created in proton-proton interactions at energies available at the CERN Super Proton Synchrotron

We analyze the newest data from the NA61/SHINE collaboration which, in addition to previous results on pions and kaons, include mean multiplicities of $p$, $\Lambda$, and $\phi$-mesons produced in inelastic proton-proton (p+p) interactions at $\sqrt{s_{NN}}=6.3-17.3$~GeV. The canonical ensemble formulation of the ideal hadron resonance gas (HRG) model is used with exact conservation of net baryon number $B=2$, electric charge $Q=2$, and strangeness $S=0$. The chemical freeze-out parameters in p+p interactions are obtained and compared to those in central nucleus-nucleus collisions. Several features of p+p interactions at the CERN SPS within a statistical model are studied: 1) the inclusion of the $\phi$-meson yields in thermal fits worsens significantly the fit quality; 2) the data show large event-by-event multiplicity fluctuations in inelastic p+p interactions which can not be explained by a single fireball described by a statistical model; 3) the fits within the canonical ensemble formulation of HRG do not give any improvement over the fits within the grand canonical ensemble formulation, i.e., there are no indications for existence of a single statistical system in p+p inelastic interactions in the considered energy range.

Energy dependent kinetic freeze-out temperature and transverse flow velocity in high energy collisions

Transverse momentum spectra of negative and positive pions produced at mid-(pseudo)rapidity in inelastic or non-single-diffractive proton-proton collisions and in central nucleus-nucleus collisions over an energy range from a few GeV to above 10 TeV are analyzed by a (two-component) blast-wave model with Boltzmann-Gibbs statistics and with Tsallis statistics respectively. The model results are in similarly well agreement with the experimental data measured by a few productive collaborations who work at the Heavy Ion Synchrotron (SIS), Super Proton Synchrotron (SPS), Relativistic Heavy Ion Collider (RHIC), and Large Hadron Collider (LHC), respectively. The energy dependent kinetic freeze-out temperature and transverse flow velocity are obtained and analyzed. Both the quantities have quick increase from the SIS to SPS, and slight increase or approximate invariability from the top RHIC to LHC. Around the energy bridge from the SPS to RHIC, the considered quantities in proton-proton collisions obtained by the blast-wave model with Boltzmann-Gibbs statistics show more complex energy dependent behavior comparing with the results in other three cases.

Energy and centrality dependent study of deconfinement phase transition in a color string percolation approach at RHIC energies

We take the experimental data for transverse momentum spectra of identified charged hadrons in different centrality classes for nucleus-nucleus (A+A) collisions at various Relativistic Heavy-Ion Collider (RHIC) energies measured by the STAR collaboration. We analyse these data in the framework of color string percolation model (CSPM) in order to extract various percolation parameters at different centralities at RHIC energies to study the effect of collision geometry and collision energy. We use these parameters to study the centrality dependent behaviour of initial temperature of the percolation cluster, energy density, average transverse momentum, shear viscosity to entropy density ratio ($\eta/s$) and trace anomaly for different energies at RHIC from $\sqrt{s_{\rm NN}}$ = 19.6 to 200 GeV. These observables are found to strongly depend on centrality at various collision energies. The critical percolation density, which is related to the deconfinement phase transition is achieved in the most central nucleus-nucleus collisions, while it fails in the peripheral collisions. A universal scaling is observed in color suppression factor and initial temperatures when studied as a function of charged particle pseudorapidity distribution scaled by nuclear overlap area at RHIC energies. The minimum of $\eta/s$ is observed in the most central collisions at $\sqrt{s_{\rm NN}}$ = 130 and 200 GeV.

Comparing Standard Distribution and Its Tsallis Form of Transverse Momenta in High Energy Collisions

The experimental (simulated) transverse momentum spectra of negatively charged pions produced at midrapidity in central nucleus-nucleus collisions at the Heavy-Ion Synchrotron (SIS), Relativistic Heavy-Ion Collider (RHIC), and Large Hadron Collider (LHC) energies obtained by different collaborations are selected by us to investigate, where a few simulated data are taken from the results of FOPI Collaboration which uses the IQMD transport code based on Quantum Molecular Dynamics. A two-component standard distribution and the Tsallis form of standard distribution are used to fit these data in the framework of a multisource thermal model. The excitation functions of main parameters in the two distributions are analyzed. In particular, the effective temperatures extracted from the two-component standard distribution and the Tsallis form of standard distribution are obtained, and the relation between the two types of effective temperatures is studied.

Higher moments of multiplicity fluctuations in a hadron-resonance gas with exact conservation laws

Higher moments of multiplicity fluctuations of hadrons produced in central nucleus-nucleus collisions are studied within the hadron-resonance gas model in the canonical ensemble. Exact conservation of three charges, baryon number, electric charge, and strangeness, is enforced in the large volume limit. Moments up to the forth order of various particles are calculated at SPS, RHIC and LHC energies. The asymptotic fluctuations within a simplified model with only one conserved charge in the canonical ensemble are discussed where simple analytical expressions for moments of multiplicity distributions can be obtained. Moments products of net-proton, net-kaon, and net-charge distributions in Au + Au collisions at RHIC energies are calculated. The pseudo-rapidity coverage dependence of net-charge fluctuation is discussed.

Observables and open problems for NICA

The restoration of chiral symmetry in hot dense nuclear systems in competition with a transition to deconfined matter in central nucleus-nucleus collisions at NICA energies is a central problem of nuclear physics. To explore these transitions we study the production of hadrons in nucleus-nucleus collisions from 4 to 160A GeV within the Parton-Hadron-String Dynamics (PHSD) transport approach that is extended to incorporate essentials aspects of chiral-symmetry restoration (CSR) in the hadronic sector (via the Schwinger mechanism) on top of the deconfinement phase transition as implemented in PHSD. The modeling of chiral-symmetry restoration in PHSD is driven by the pion-nucleon $\Sigma$ -term in the computation of the quark scalar condensate $\langle q \bar{q} \rangle$ that serves as an order parameter for CSR and is assumed to scale with the effective quark masses $ m_{s}$ and $ m_{q}$ . Furthermore, the nucleon scalar density $\rho_{s}$ , which also enters the computation of $\langle q \bar{q} \rangle$ , is evaluated within the nonlinear $\sigma$ - $ \omega$ model which is constrained by Dirac-Brueckner calculations and low-energy heavy-ion reactions. The essential impact of CSR is found in the Schwinger mechanism (for string decay) which fixes the ratio of strange to light quark production in the hadronic medium. We find that above $\sim 80$ A GeV the reaction dynamics of heavy nuclei is dominantly driven by partonic degrees-of-freedom such that traces of the chiral-symmetry restoration are hard to identify. Our studies support the conjecture of “quarkyonic matter” in heavy-ion collisions from about 5 to 40A GeV and suggest a microscopic explanation for the maximum in the $ K^{+}/\pi^{+}$ ratio at about 30A GeV which only shows up if in addition to CSR a deconfinement transition to partonic degrees-of-freedom is incorporated in the reaction dynamics.

Hadron multiplicities and chemical freeze-out conditions in proton-proton and nucleus-nucleus collisions

New results of the NA61/SHINE Collaboration at the CERN SPS on mean hadron multiplicities in proton-proton (p+p) interactions are analyzed within the transport models and the hadron resonance gas (HRG) statistical model. The chemical freeze-out parameters in p+p interactions and central Pb+Pb (or Au+Au) collisions are found and compared with each other in the range of the center of mass energy of the nucleon pair $\sqrt{s_{NN}}=3.2-17.3$ GeV. The canonical ensemble formulation of the HRG model is used to describe mean hadron multiplicities in p+p interactions and the grand canonical ensemble in central Pb+Pb and Au+Au collisions. The chemical freeze-out temperatures in p+p interactions are found to be larger than the corresponding temperatures in central nucleus-nucleus collisions.

Thermal Photon Radiation in High Multiplicity p+Pb Collisions at the Large Hadron Collider.

The collective behavior of hadronic particles has been observed in high multiplicity proton-lead collisions at the Large Hadron Collider, as well as in deuteron-gold collisions at the Relativistic Heavy-Ion Collider. In this work we present the first calculation, in the hydrodynamic framework, of thermal photon radiation from such small collision systems. Owing to their compact size, these systems can reach temperatures comparable to those in central nucleus-nucleus collisions. The thermal photons can thus shine over the prompt background, and increase the low p_{T} direct photon spectrum by a factor of 2-3 in 0%-1% p+Pb collisions at 5.02TeV. This thermal photon enhancement can therefore serve as a signature of the existence of a hot quark-gluon plasma during the evolution of these small collision systems, as well as validate hydrodynamic behavior in small systems.

Comment on “Investigation of Hadron Multiplicity and Hadron Yield Ratios in Heavy-Ion Collisions”

Oliinychenko, Bugaev, and Sorin [arXiv:1204.0103 [hep-ph]] considered the role of conservation laws in discussing possible weaknesses of thermal models which are utilized in describing the hadron multiplicities measured in central nucleus-nucleus collisions. They argued to analyze the criteria for chemical freeze-out and to conclude that none of them was robust. Based on this, they suggested a new chemical freeze-out criterion. They assigned to the entropy per hadron the ad hoc value 7.18 and supposed to remain unchanged over the whole range of the baryo-chemical potentials. Due to the unawareness of the recent literature, the constant entropy per hadron has been discussed in Refs. [Fizika B 18, 141 (2009), Europhys. Lett. 75, 420 (2006), Phys. Rev. C 85, 014908 (2012) and nucl-ph/1306.3291]. Furthermore, it has been shown that the constant entropy per hadron is equivalent to the constant entropy normalized to the cubic temperature, an earlier criterion for the chemical freeze-out introduced in Refs. [Europhys. Lett. 75, 420 (2006), Nucl. Phys. A 764, 387 (2006)]. In this comment, we list out the ignored literature, compare between the entropy-number density ratio and two criteria of averaged energy per averaged particle number and constant entropy per cubic temperature. All these criteria are confronted to the experimental results. The physics of constant entropy per number density is elaborated. It is concluded that this ratio cannot remain constant, especially at large chemical potentials related to the AGS and SIS energies.

Hadron-resonance gas at freeze-out: Reminder on the importance of repulsive interactions

An influence of the repulsive interactions on matter properties is considered within the excluded volume van der Waals hadron-resonance gas model. Quantitative results are presented for matter at the chemical freeze-out in central nucleus-nucleus collisions at relativistic energies. In particular, it is shown that repulsive interactions connected to non-zero size of created particles lead to a significant decrease of collision energy at which the net-baryon density has a maximum. A position of the transition point from baryon to meson dominated matter depends on the difference between baryon and meson hard-core radiuses.

Investigation of Hadron Multiplicities and Hadron Yield Ratios in Heavy Ion Collisions

We thoroughly discuss some weak points of the thermal model, which is traditionally used to describe the hadron multiplicities measured in the central nucleus-nucleus collisions. In particularly, the role of conservation laws and the values of hard-core radii along with the effects of the Lorentz contraction of hadron eigenvolumes and the hadronic surface tension are systematically studied. It is shown that, for the adequate description of hadron multiplicities, the conservation laws should be modified, whereas the conservation laws are not necessary at all for the description of hadron yield ratios. We analyzed the usual criteria for the chemical freeze-out and found that none of them is robust. A new chemical freeze-out criterion of constant entropy per hadron equals to 7.18 is suggested, and a novel effect of adiabatic chemical hadron production is discussed. Additionally, we found that the data for the center-of-mass energies above 10 GeV lead to the temperature of the nil hadronic surface tension coefficient of about T0 = 147 ± 7 MeV. This is a very intriguing result, since a very close estimate for such a temperature was obtained recently within an entirely different approach. We argue that these two independently obtained results evidence that the (tri)critical temperature of a QCD phase diagram is between 140 and 154 MeV. In addition, we suggest to consider the pion and kaon hardcore radii as new fitting parameters. Such an approach allows us, for the first time, to simultaneously describe the hadron multiplicities and the Strangeness Horn and to get a high-quality fit of the available experimental data.

Monte Carlo approach for hadron azimuthal correlations in high energy proton and nuclear collisions

We use a Monte Carlo approach to study hadron azimuthal angular correlations in high energy proton-proton and central nucleus-nucleus collisions at the BNL Relativistic Heavy Ion Collider (RHIC) energies at mid-rapidity. We build a hadron event generator that incorporates the production of $2\to 2$ and $2\to 3$ parton processes and their evolution into hadron states. For nucleus-nucleus collisions we include the effect of parton energy loss in the Quark-Gluon Plasma using a modified fragmentation function approach. In the presence of the medium, for the case when three partons are produced in the hard scattering, we analyze the Monte Carlo sample in parton and hadron momentum bins to reconstruct the angular correlations. We characterize this sample by the number of partons that are able to hadronize by fragmentation within the selected bins. In the nuclear environment the model allows hadronization by fragmentation only for partons with momentum above a threshold $p_T^{{\tiny{thresh}}}=2.4$ GeV. We argue that one should treat properly the effect of those partons with momentum below the threshold, since their interaction with the medium may lead to showers of low momentum hadrons along the direction of motion of the original partons as the medium becomes diluted.