The effects of a finite system volume on thermodynamic quantities, such as the pressure, energy density, specific heat, speed of sound, conserved charge susceptibilities, and correlations, in hot and dense strongly interacting matter are studied within the parity-doublet chiral mean field model. Such an investigation is motivated by relativistic heavy-ion collisions, which create a blob of hot QCD matter of a finite volume, consisting of strongly interacting hadrons and potentially deconfined quarks and gluons. The effect of the finite volume of the system is incorporated by introducing lower momentum cutoffs in the momentum integrals appearing in the model, the numerical value of the momentum cutoff being related to the de Broglie wavelength of the given particle species. It is found that some of these quantities show a significant volume dependence, in particular, those sensitive to pion degrees of freedom, and the crossover transition is generally observed to become smoother in finite volume. These findings are relevant for the effective equation of state used in fluid dynamical simulations of heavy-ion collisions and efforts to extract the freeze-out properties of heavy-ion collisions with susceptibilities involving electric charge and strangeness.

India

Somenath Pal

Germany

Anton Motornenko

United States

Volodymyr Vovchenko

Abhijit Bhattacharyya

Jan Steinheimer

Horst Stoecker

Effect of finite volume on thermodynamics of quark-hadron matter

The time evolution of particle number fluctuations in nuclear collisions at intermediate energies (<math><mrow><msub><mi>E</mi><mi>lab</mi></msub><mo>=</mo><mn>1.23</mn></mrow><mtext>–</mtext><mn>10</mn><mrow><mi>A</mi><mspace width="0.16em"></mspace><mi>GeV</mi></mrow></math>) is studied by means of the UrQMD-3.5 transport model. The transport description incorporates baryonic interactions through a density-dependent potential. This allows for an implementation of a first-order phase transition including a mechanically unstable region at large baryon density. The scaled variance of the baryon and proton number distributions is calculated in the central cubic spatial volume of the collisions at different times. A significant enhancement of fluctuations associated with the unstable region is observed. This enhancement persists to late times, reflecting a memory effect for the fluctuations. The presence of the phase transition has a much smaller influence on the observable event-by-event fluctuations of protons in momentum space.

Ukraine

Oleh Savchuk

Roman V. Poberezhnyuk

Mark I. Gorenstein

Phase transition amplification of proton number fluctuations in nuclear collisions from a transport model approach

A set of different equations of state is implemented in the molecular dynamics part of a non-equilibrium transport simulation (UrQMD) of heavy-ion collisions. It is shown how different flow observables are affected by the density dependence of the equation of state. In particular, the effects of a phase transition at high density are explored, including an expected reduction in mean  $$m_T$$  <math> <msub> <mi>m</mi> <mi>T</mi> </msub> </math>  . We also show that an increase in  $$v_2$$  <math> <msub> <mi>v</mi> <mn>2</mn> </msub> </math>   is characteristic for a strong softening of the equation of state. The phase transitions with a low coexistence density,  $$n_{\text {CE}}&lt;4 n_0$$  <math> <mrow> <msub> <mi>n</mi> <mtext>CE</mtext> </msub> <mo>&lt;</mo> <mn>4</mn> <msub> <mi>n</mi> <mn>0</mn> </msub> </mrow> </math>  , show a distinct minimum in the slope of the directed flow as a function of the beam energy, which would be a clear experimental signal. By comparing our results with experimental data, we can exclude any strong phase transition at densities below  $$4n_0$$  <math> <mrow> <mn>4</mn> <msub> <mi>n</mi> <mn>0</mn> </msub> </mrow> </math>  .

Agnieszka Sorensen

Japan

Yasushi Nara

Volker Koch

Marcus Bleicher

The high-density equation of state in heavy-ion collisions: constraints from proton flow

It is shown that the initial compression in central heavy ion collisions at beam energies of  $$E_{\mathrm {lab}}=1-10A$$  <math> <mrow> <msub> <mi>E</mi> <mi>lab</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mn>10</mn> <mi>A</mi> </mrow> </math>   GeV depends dominantly on the underlying equation of state and only marginally on the model used for the dynamical description. To do so, a procedure to incorporate any equation of state in the UrQMD transport model is introduced. In particular we compare the baryon density, temperature and pressure evolution as well as produced entropy in a relativistic ideal hydrodynamics approach and the UrQMD transport model, where the same equation of state is used in both approaches. Not only is the compression similar if the same equation of state is used in either dynamical model, but it also strongly depends on the actual equation of state. These results indicate that the equation of state can be studied with observables which are sensitive to the initial compression phase and maximum compression achieved in heavy ion collisions at these beam energies.

Manjunath Omana Kuttan

A chiral mean-field equation-of-state in UrQMD: effects on the heavy ion compression stage

The thermal fit to preliminary HADES data of Au+Au collisions at <math><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><msub><mrow></mrow><mrow><mi>N</mi><mi>N</mi></mrow></msub></mrow></msub></mrow></msqrt><mo>=</mo><mn>2.4</mn></math> GeV shows two degenerate solutions at <math><mi>T</mi><mo>≈</mo><mn>50</mn></math> MeV and <math><mi>T</mi><mo>≈</mo><mn>70</mn></math> MeV. The analysis of the same particle yields in a transport simulation of the UrQMD model yields the same features, i.e. two distinct temperatures for the chemical freeze-out. While both solutions yield the same number of hadrons after resonance decays, the feeddown contribution is very different for both cases. This highlights that two systems with different chemical composition can yield the same multiplicities after resonance decays. The nature of these two minima is further investigated by studying the time-dependent particle yields and extracted thermodynamic properties of the UrQMD model. It is confirmed, that the evolution of the high temperature solution resembles cooling and expansion of a hot and dense fireball. The low temperature solution displays an unphysical evolution: heating and compression of matter with a decrease of entropy. These results imply that the thermal model analysis of systems produced in low energy nuclear collisions is ambiguous but can be interpreted by taking also the time evolution and resonance contributions into account.

Reinhard Stock

Ambiguities in the hadro-chemical freeze-out of Au+Au collisions at SIS18 energies and how to resolve them

Second-order susceptibilities <math><msubsup><mi>χ</mi><mrow><mi>i</mi><mi>j</mi></mrow><mn>11</mn></msubsup></math> of baryon, electric, and strangeness, <math><mi>B</mi></math>, <math><mi>Q</mi></math>, and <math><mi>S</mi></math>, charges are calculated in the chiral mean field (CMF) model and compared with available lattice QCD data. The susceptibilities are sensitive to the short-range repulsive interactions between different hadron species, especially to the hardcore repulsion of hyperons. Decreasing the hyperons size, as compared with the size of the nonstrange baryons, does improve significantly the agreement of the CMF model results with the lattice QCD data. The electric-charge-dependent susceptibilities are sensitive to the short-range repulsive volume of mesons. The comparison with lattice QCD data suggests that strange baryons, nonstrange mesons, and strange mesons have significantly smaller excluded volumes than nonstrange baryons. The CMF model with these modified hadron volumes allows for a mainly hadronic description of the QCD susceptibilities significantly above the chiral pseudocritical temperature. This improved CMF model, which is based on the lattice QCD data, has been used to study the properties of both cold QCD matter and neutron-star matter. The phase structure in both cases is essentially unchanged, i.e., a chiral first-order phase transition occurs at low temperatures <math><mrow><mo>(</mo><msub><mi>T</mi><mi>CP</mi></msub><mo>≈</mo><mn>17</mn><mspace width="4pt"></mspace><mi>MeV</mi><mo>)</mo></mrow></math>, and hyperons survive deconfinement to higher densities than nonstrange hadrons. The neutron-star maximal mass remains close to <math><mrow><mn>2.1</mn><msub><mi>M</mi><mo>⊙</mo></msub></mrow></math> and the mass-radius diagram is only modified slightly due to the appearance of hyperons and is in agreement with astrophysical observations.

Repulsive properties of hadrons in lattice QCD data and neutron stars

A method to determine the kinetic freeze-out temperature in heavy-ion collisions from measured yields of short-lived resonances is presented. The resonance production is treated in the framework of a thermal model with an evolution between chemical and kinetic freeze-outs. The yields of many short-lived resonances are suppressed at <math><mrow><mi>T</mi><mo>=</mo><msub><mi>T</mi><mi>kin</mi></msub><mo>&lt;</mo><msub><mi>T</mi><mi>ch</mi></msub></mrow></math>. We determine the values of <math><msub><mi>T</mi><mi>kin</mi></msub></math> and <math><msub><mi>T</mi><mi>ch</mi></msub></math> for various centralities in Pb-Pb collisions at <math><mrow><msqrt><msub><mi>s</mi><msub><mrow></mrow><mrow><mi>N</mi><mi>N</mi></mrow></msub></msub></msqrt><mo>=</mo><mn>2.76</mn></mrow></math> TeV by fitting the abundances of both the stable hadrons and the short-lived resonances such as <math><msup><mi>ρ</mi><mn>0</mn></msup></math> and <math><msup><mtext>K</mtext><mrow><mo>*</mo><mn>0</mn></mrow></msup></math>, which were measured by the ALICE collaboration. This allows us to extract the kinetic freeze-out temperature from the measured hadron and resonance yields alone, independent of assumptions about the flow velocity profile and the freeze-out hypersurface. The extracted <math><msub><mi>T</mi><mi>ch</mi></msub></math> values exhibit a moderate multiplicity dependence whereas <math><msub><mi>T</mi><mi>kin</mi></msub></math> drops, from <math><mrow><msub><mi>T</mi><mi>kin</mi></msub><mo>≃</mo><msub><mi>T</mi><mi>ch</mi></msub><mo>≃</mo><mn>155</mn><mspace width="4pt"></mspace><mi>MeV</mi></mrow></math> in peripheral collisions to <math><mrow><msub><mi>T</mi><mi>kin</mi></msub><mo>≃</mo><mn>110</mn><mspace width="4pt"></mspace><mi>MeV</mi></mrow></math> in 0%–20% central collisions. Predictions for other short-lived resonances are presented. A potential (non-)observation of a suppressed <math><mrow><msub><mi>f</mi><mn>0</mn></msub><mrow><mo>(</mo><mn>980</mn><mo>)</mo></mrow></mrow></math> meson yield will allow us to constrain the lifetime of that meson.

Carsten Greiner

Kinetic freeze-out temperature from yields of short-lived resonances

Using deep convolutional neural network (CNN), the nature of the QCD transition can be identified from the final-state pion spectra from hybrid model simulations of heavy-ion collisions that combines a viscous hydrodynamic model with a hadronic cascade “after-burner”. Two different types of equations of state (EoS) of the medium are used in the hydrodynamic evolution. The resulting spectra in transverse momentum and azimuthal angle are used as the input data to train the neural network to distinguish different EoS. Different scenarios for the input data are studied and compared in a systematic way. A clear hierarchy is observed in the prediction accuracy when using the event-by-event, cascade-coarse-grained and event-fine-averaged spectra as input for the network, which are about 80%, 90% and 99%, respectively. A comparison with the prediction performance by deep neural network (DNN) with only the normalized pion transverse momentum spectra is also made. High-level features of pion spectra captured by a carefully-trained neural network were found to be able to distinguish the nature of the QCD transition even in a simulation scenario which is close to the experiments.

Norway

China

Yi-Lun Du

Kai Zhou

Long-Gang Pang

Hong-Shi Zong

Xin-Nian Wang

Horst Stöcker

Identifying the nature of the QCD transition in relativistic collision of heavy nuclei with deep learning

The thermodynamic properties of high temperature and high density QCD matter are explored within the chiral SU(3)-flavor parity-doublet Polyakov-loop quark-hadron mean-field model, CMF. The quark sector of the CMF model is tuned to describe the <math><mrow><msub><mi>μ</mi><mi>B</mi></msub><mo>=</mo><mn>0</mn></mrow></math> thermodynamics data of lattice QCD. The resulting lines of constant physical variables as well as the baryon number susceptibilities are studied in some detail in the temperature–chemical-potential plane. The CMF model predicts three consecutive transitions: the nuclear first-order liquid-vapor phase transition, chiral symmetry restoration, and the crossover transition to a quark matter phase. All three phenomena are crossovers, for most of the <math><mrow><mi>T</mi><mtext>−</mtext><msub><mi>μ</mi><mi>B</mi></msub></mrow></math> plane. The deviations from the free ideal hadron gas baseline at <math><mrow><msub><mi>μ</mi><mi>B</mi></msub><mo>=</mo><mn>0</mn></mrow></math> and <math><mrow><mi>T</mi><mo>≈</mo><mn>100</mn><mtext>–</mtext><mn>200</mn></mrow></math> MeV can be attributed to remnants of the liquid-vapor first-order phase transition in nuclear matter. The chiral crossing transition determines the baryon fluctuations at much higher <math><mrow><msub><mi>μ</mi><mi>B</mi></msub><mo>≈</mo><mn>1.5</mn></mrow></math> GeV. At high baryon densities, <math><mrow><msub><mi>μ</mi><mi>B</mi></msub><mo>≈</mo><mn>2.4</mn></mrow></math> GeV, the behavior of fluctuations is controlled by crossover to quark matter. The CMF model also describe well the static properties of high <math><msub><mi>μ</mi><mi>B</mi></msub></math> neutron stars as well as recent neutron star merger observations. The effective equation of state presented here describes simultaneously lattice QCD results at <math><mrow><msub><mi>μ</mi><mi>B</mi></msub><mo>=</mo><mn>0</mn></mrow></math> as well as observed physical phenomena (nuclear matter and neutron star matter) at <math><mrow><mi>T</mi><mo>≅</mo><mn>0</mn></mrow></math> and high densities, <math><mrow><msub><mi>μ</mi><mi>B</mi></msub><mo>&gt;</mo><mn>1</mn></mrow></math> GeV.

Stefan Schramm

Equation of state for hot QCD and compact stars from a mean-field approach

Thermodynamic properties of systems with repulsive interactions are considered in the grand-canonical ensemble. The analytic structure of the excluded-volume model in the complex plane of the system chemical potential (fugacity) is elaborated, based on the fact that the pressure function can be given in terms of the Lambert <math><mi>W</mi></math> function. Even though the excluded-volume model has no phase transitions at real values of the chemical potential, it does exhibit a branch cut singularity in the complex plane, thus limiting the convergence range of the Taylor expansion in the chemical potential. Close similarities to analytic properties of the other models with repulsive interactions, such as a cluster expansion model, the mean-field model, and the ideal Fermi gas model, are pointed out. As an example, repulsive baryonic interactions in a hadron gas, with a focus on the fugacity/virial and Taylor expansion methods used in lattice QCD, are presented. The asymptotic behavior of the Fourier expansion coefficients in these various models suggests that the singular part of net baryonic density can to leading order be universally expressed in terms of polylogarithms.

Kirill Taradiy

Analytic structure of thermodynamic systems with repulsive interactions