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We suggest to explore an entirely new method to experimentally and theoretically study the phase diagram of strongly interacting matter based on the triple nuclear collisions (TNC). We simulated the TNC using the UrQMD 3.4 model at the beam center-of-mass collision energies $\sqrt{s_{NN}} = 200$ GeV and $\sqrt{s_{NN}} = 2.76$ TeV. It is found that in the most central and simultaneous TNC the initial baryonic charge density is about 3 times higher than the one achieved in the usual binary nuclear collisions at the same energies. As a consequence, the production of protons and $\Lambda$-hyperons is increased by a factor of 2 and 1.5, respectively. Using the MIT Bag model equation we study the evolution of the central cell in TNC and demonstrate that for the top RHIC energy of collision the baryonic chemical potential is 2-2.5 times larger than the one achieved in the binary nuclear collision at the same type of reaction. Based on these estimates, we show that TNC offers an entirely new possibility to study the QCD phase diagram at very high baryonic charge densities., Comment: Summary of the talk given at the Online Conference "Strangeness in Quark Matter 2021"

Here we develop an original approach to investigate the grand canonical partition function of the multicomponent mixtures of Boltzmann particles with hard-core interaction in finite and even small systems of the volumes above 20 fm$^3$. The derived expressions of the induced surface tension equation of state are analyzed in details. It is shown that the metastable states, which can emerge in the finite systems with realistic interaction, appear at very high pressures at which the hadron resonance gas, most probably, is not applicable at all. It is shown how and under what conditions the obtained results for finite systems can be generalized to include into a formalism the equation for curvature tension. The applicability range of the obtained equations of induced surface and curvature tensions for finite systems is discussed and their close relations to the equations of the morphological thermodynamics are established. The hadron resonance gas model on the basis of the obtained advanced equation of state is worked out. Also, this model is applied to analyze the chemical freeze-out of hadrons and light nuclei with the number of (anti-)baryons not exceeding 4, including the most problematic ratios of hyper-triton and its antiparticle. Their multiplicities were measured by the ALICE Collaboration in the central lead-lead collisions at the center-of-mass energy $\sqrt{s_{\rm NN}} =$ 2.76 TeV., Comment: 24 pages, 3 figures and 1 table

We present a summary of the recent results obtained with the novel hadron resonance gas model with the multicomponent hard-core repulsion which is extended to describe the mixtures of hadrons and light (anti-, hyper-)nuclei. A very accurate description is obtained for the hadronic and the light nuclei data measured by STAR at the collision energy $\sqrt{s_{NN}} =200$ GeV and by ALICE at $\sqrt{s_{NN}} =2.76$ TeV. The most striking result discussed here is that for the most probable chemical freeze-out scenario for the STAR energy the found parameters allow us to reproduce the values of the experimental ratios $S_3$ and $\overline{S}_3$ without fitting., Comment: 6 pages, 3 figures

Here we develop a new strategy to analyze the chemical freeze-out of light (anti)nuclei produced in high energy collisions of heavy atomic nuclei within an advanced version of the hadron resonance gas model. It is based on two different, but complementary approaches to model the hard-core repulsion between the light nuclei and hadrons. The first approach is based on an approximate treatment of the equivalent hard-core radius of a roomy nuclear cluster and pions, while the second approach is rigorously derived here using a self-consistent treatment of classical excluded volumes of light (anti)nuclei and hadrons. By construction, in a hadronic medium dominated by pions, both approaches should give the same results. Employing this strategy to the analysis of hadronic and light (anti)nuclei multiplicities measured by ALICE at $\sqrt{s_{NN}} =2.76$ TeV and by STAR at $\sqrt{s_{NN}} =200$ GeV, we got rid of the existing ambiguity in the description of light (anti)nuclei data and determined the chemical freeze-out parameters of nuclei with high accuracy and confidence. At ALICE energy the nuclei are frozen prior to the hadrons at the temperature $T = 175.1^{+2.3}_{-3.9}$ MeV, while at STAR energy there is a single freeze-out of hadrons and nuclei at the temperature $T = 167.2 \pm 3.9$ MeV. We argue that the found chemical freeze-out volumes of nuclei can be considered as the volumes of quark-gluon bags that produce the nuclei at the moment of hadronization., Comment: 15 pages, 4 figures, 3 tables

From the analysis of light (anti)nuclei multiplicities that were measured recently by the ALICE collaboration in Pb+Pb collisions at the center-of-mass collision energy $\sqrt{s_{NN}} =2.76$ TeV there arose a highly non-trivial question about the excluded volume of composite particles. Surprisingly, the hadron resonance gas model (HRGM) is able to perfectly describe the light (anti)nuclei multiplicities under various assumptions. Thus, one can consider the (anti)nuclei with a vanishing hard-core radius (as the point-like particles) or with the hard-core radius of proton, but the fit quality is the same for these assumptions. It is clear, however, that such assumptions are unphysical. Hence we obtain a formula for the classical excluded volume of loosely bound light nuclei consisting of A baryons. To implement a new formula into the HRGM we have to modify the induced surface tension concept to treat the hadrons and (anti)nuclei on the same footing. We perform a simultaneous analysis of hadronic and (anti)nuclei multiplicities measured by the ALICE collaboration. The HRGM with the induced surface tension allows us to verify different assumptions on the values of hard-core radii and different scenarios of chemical freeze-out of light (anti)nuclei. It is shown that the unprecedentedly high quality of fit $\chi^2_{tot}/dof \simeq 0.769$ is achieved, if the chemical freeze-out temperature of hadrons is about $T_h=150$ MeV, while the one for all (anti)nuclei is $T_A=174-175.2$ MeV., Comment: 15 pages, 2 figures

The multiplicities of light (anti)nuclei were measured recently by the ALICE collaboration in Pb+Pb collisions at the center-of-mass collision energy $\sqrt{s_{NN}} =2.76$ TeV. Surprisingly, the hadron resonance gas model is able to perfectly describe their multiplicities under various assumptions. For instance, one can consider the (anti)nuclei with a vanishing hard-core radius (as the point-like particles) or with the hard-core radius of proton, but the fit quality is the same for these assumptions. In this paper we assume the hard-core radius of nuclei consisting of $A$ baryons or antibaryons to follow the simple law $R(A) = R_b (A)^\frac{1}{3}$, where $R_b$ is the hard-core radius of nucleon. To implement such a relation into the hadron resonance gas model we employ the induced surface tension concept and analyze the hadronic and (anti)nuclei multiplicities measured by the ALICE collaboration. The hadron resonance gas model with the induced surface tension allows us to verify different scenarios of chemical freeze-out of (anti)nuclei. It is shown that the most successful description of hadrons can be achieved at the chemical freeze-out temperature $T_h=150$ MeV, while the one for all (anti)nuclei is $T_A=168.5$ MeV. Possible explanations of this high temperature of (anti)nuclei chemical freeze-out are discussed., Comment: 6 pages, 1 figure

The chemical freeze-out irregularities found with the most advanced hadron resonance gas model and possible signals of two QCD phase transitions are discussed. We found that the center-of-mass collision energy range of tricritical endpoint of QCD phase diagram is [9; 9.2] GeV which is consistent both with QCD inspired exactly solvable model and with experimental findings., Comment: 6 pages, 2 figures

In this work we discuss a novel approach to model the hadronic and nuclear matter equations of state using the induced surface tension concept. Since the obtained equations of state, classical and quantum, are among the most successful ones in describing the properties of low density phases of strongly interacting matter, they set strong restrictions on the possible value of the hard-core radius of nucleons. Therefore, we perform a detailed analysis of its value which follows from hadronic and nuclear matter properties and find the most trustworthy range of its values: the hard-core radius of nucleons is 0.30--0.36 fm. A comparison with the phenomenology of neutron stars implies that the hard-core radius of nucleons has to be temperature and density dependent., Comment: 12 pages, 4 figures, references added, typos corrected

In this contributions we discuss the novel version of hadron resonance gas model which is based on the induced surface tension concept. Also we present new arguments in favor of a hypothesis that the chiral symmetry restoration transition in central nuclear collisions may occur at the center of mass energies 4.3-4.9 GeV and that the deconfinement phase transition may occur at the center of mass energies 8.8-9.2 GeV. These arguments are based on the unique thermostatic properties of the mixed phase and the ones of an exponential mass spectrum of hadrons., Comment: 10 pages, 4 figures

We present a summary of possible signals of the chiral symmetry restoration and deconfinement phase transitions which may be, respectively, probed at the center of mass collision energies at 4.3-4.9 GeV and above 8.7-9.2 GeV. It is argued that these signals may evidence for an existence of the tricritical endpoint of QCD phase diagram at the collision energy around 8.7-9.2 GeV. The equation of state of hadronic matter with the restored chiral symmetry is discussed and the number of bosonic and fermionic degrees of freedom is found., Comment: 5 pages

Using the most advanced formulation of the hadron resonance gas model we analyze the two sets of irregularities found at chemical freeze-out of central nuclear-nuclear collisions at the center of mass energies 3.8-4.9 GeV and 7.6-9.2 GeV. In addition to previously reported irregularities at the collision energies 4.9 GeV and 9.2 GeV we found sharp peaks of baryonic charge density. Also we analyze the collision energy dependence of the modified Wroblewski factor and the strangeness suppression factor. Based on the thermostatic properties of the mixed phase of a 1-st order phase transition and the ones of the Hagedorn mass spectrum we explain, respectively, the reason of observed chemical equilibration of strangeness at the collision energy 4.9 GeV and above 8.7 GeV. It is argued that the both sets of irregularities possibly evidence for two phase transitions, namely, the 1-st order transition at lower energy range and the 2-nd order transition at higher one. In combination with a recent analysis of the light nuclei number fluctuations we conclude that the center of mass collision energy range 8.8-9.2 GeV may be in the nearest vicinity of the QCD tricritical endpoint. The properties of the phase existing between two phase transitions are revealed and discussed., Comment: 24 pages, 6 figures, to appear in PEPAN Lett

Here we present a physically transparent generalization of the multicomponent Van der Waals equation of state in the grand canonical ensemble. For the one-component case the third and fourth virial coefficients are calculated analytically. It is shown that an adjustment of a single model parameter allows us to reproduce the third and fourth virial coefficients of the gas of hard spheres with small deviations from their exact values. A thorough comparison of the compressibility factor and speed of sound of the developed model with the one and two component Carnahan-Starling equation of state is made. It is shown that the model with the induced surface tension is able to reproduce the results of the Carnahan-Starling equation of state up to the packing fractions 0.2-0.22 at which the usual Van der Waals equation of state is inapplicable. At higher packing fractions the developed equation of state is softer than the gas of hard spheres and, hence, it breaks causality in the domain where the hadronic description is expected to be inapplicable. Using this equation of state we develop an entirely new hadron resonance gas model and apply it to a description of the hadron yield ratios measured at AGS, SPS, RHIC and ALICE energies of nuclear collisions. The achieved quality of the fit per degree of freedom is about 1.08. We confirm that the strangeness enhancement factor has a peak at low AGS energies, while at and above the highest SPS energy of collisions the chemical equilibrium of strangeness is observed. We argue that the chemical equilibrium of strangeness, i.e. $\gamma_s \simeq 1$, observed above the center of mass collision energy 4.3 GeV may be related to the hadronization of quark gluon bags which have the Hagedorn mass spectrum, and, hence, it may be a new signal for the onset of deconfinement.

We develop a novel formulation of the hadron-resonance gas model which, besides a hard-core repulsion, explicitly accounts for the surface tension induced by the interaction between the particles. Such an equation of state allows us to go beyond the Van der Waals approximation for any number of different hard-core radii. A comparison with the Carnahan-Starling equation of state shows that the new model is valid for packing fractions 0.2-0.22, while the usual Van der Waals model is inapplicable at packing fractions above 0.1-0.11. Moreover, it is shown that the equation of state with induced surface tension is softer than the one of hard spheres and remains causal at higher particle densities. The great advantage of our model is that there are only two equations to be solved and it does not depend on the various values of the hard-core radii used for different hadronic resonances. Using this novel equation of state we obtain a high-quality fit of the ALICE hadron multiplicities measured at center-of-mass energies of 2.76 TeV per nucleon. Furthermore, using the traditional hadron-resonance gas model with multi-component hard-core repulsion and the novel one we investigate the recently suggested model in which the proper volume of a hadron is proportional to its mass. We find that the high-temperature maximum of $\chi^2/ndf$ observed in the latter model always appears in the region located far above the limit of its applicability., Comment: More results are presented, new figures and new section are added; the list of authors is updated

We present an elaborate version of the hadron resonance gas model with the combined treatment of separate chemical freeze-outs for strange and non-strange hadrons and with an additional $\gamma_{s}$ factor which accounts for the remaining strange particle non-equilibration. Within suggested approach the parameters of two chemical freeze-outs are connected by the conservation laws of entropy, baryonic charge, third isospin projection and strangeness. The developed model enables us to perform a high-quality fit of the hadron multiplicity ratios measured at AGS, SPS and RHIC with $\chi^2/dof \simeq 0.93$. A special attention is paid to a successful description of the Strangeness Horn. The well-known problem of selective suppression of $\bar \Lambda $ and $\bar \Xi$ hyperons is also discussed. The main result is that for all collision energies the $\gamma_{s}$ factor is about 1 within the error bars, except for the center of mass collision energy 7.6 GeV at which we find about 20\% enhancement of strangeness. Also we confirm an existence of strong jumps in pressure, temperature and effective number of degrees of freedom at the stage of strange particle chemical freeze-out, when the center of mass collision energy changes from 4.3 to 4.9 GeV. We argue that these irregularities may signal about the quark-hadron phase transition., Comment: 15 pages. This is greatly improved and essentially extended version of arXiv:1312.5149. The title and list of authors are undated

Here we present several remarkable irregularities at chemical freeze-out which are found using an advanced version of the hadron resonance gas model. The most prominent of them are the sharp peak of the trace anomaly existing at chemical freeze-out at the center of mass energy 4.9 GeV and two sets of highly correlated quasi-plateaus in the collision energy dependence of the entropy per baryon, total pion number per baryon, and thermal pion number per baryon which we found at the center of mass energies 3.8-4.9 GeV and 7.6-10 GeV. The low energy set of quasi-plateaus was predicted a long time ago. On the basis of the generalized shock-adiabat model we demonstrate that the low energy correlated quasi-plateaus give evidence for the anomalous thermodynamic properties inside the quark-gluon-hadron mixed phase. It is also shown that the trace anomaly sharp peak at chemical freeze-out corresponds to the trace anomaly peak at the boundary between the mixed phase and quark gluon plasma. We argue that the high energy correlated quasi-plateaus may correspond to a second phase transition and discuss its possible origin and location. Besides we suggest two new observables which may serve as clear signals of these phase transformations., Comment: 14 pages, 4 figures, new signals of QGP formation are suggested