It is shown that the hadronic phase in ultra-relativistic heavy ion collisions can be used to understand the properties of the $$f_0(980)$$ resonance. In particular it is shown that the centrality dependence of the $$f_0(980)/\pi $$ and $$f_0(980)/\phi $$ ratios depends strongly on the $$f_0(980)\rightarrow {\overline{K}}+K$$ branching ratio and whether the $$f_0(980)$$ is produced as a $$\left| {\overline{q}}q \right\rangle $$ or $$\left| {\overline{s}}s \right\rangle $$ state. These conclusions are drawn from calculations within the partial chemical equilibrium of the HRG model within Thermal-FIST as well as with the fully non-equilibrium hybrid-transport approach UrQMD. Our findings show how the hadronic phase in heavy ion collisions can be used for studies of exotic hadron properties otherwise possible only in dedicated experiments such as PANDA.

Germany

Tom Reichert

Jan Steinheimer

United States

Volodymyr Vovchenko

Thailand

Christoph Herold

Ayut Limphirat

Marcus Bleicher

The structure of the $$f_0(980)$$ from system size dependent hadronic resonance ratios in p + p, p + Pb, and Pb + Pb collisions at the LHC

This work presents a formalism to compute spatial <math><mi>n</mi></math>-point correlations of a conserved charge density in a large thermal system in the canonical ensemble, with explicit results presented up to fourth order. The resulting correlators contain local and balancing terms expressed through the grand-canonical susceptibilities for any equation of state. The new formalism is used to introduce a Gaussian local baryon number conservation in (spatial) rapidity in heavy-ion collisions at CERN Large Hadron Collider conditions through a modulation of the balancing term. Connection to the conservation volume <math><msub><mi>V</mi><mi>c</mi></msub></math> approach is established, indicating that the latter is appropriate for observables within a limited range around midrapidity. Quantitative analysis of the experimental data of the ALICE Collaboration on net proton cumulants in central Pb-Pb collisions at <math><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>5.02</mn></mrow></math> TeV shows significant evidence for local baryon conservation.

Density correlations under global and local charge conservation

This work studies the influence of an external magnetic field on hadron yields and fluctuations in a hadron resonance gas by performing calculations within an updated version of the open-source thermal-fist package. The presence of the magnetic field has a sizable influence on certain hadron yield ratios. Most notably, it leads to enhanced <math><mrow><mi>p</mi><mo>/</mo><mi>π</mi></mrow></math> and suppressed <math><mrow><mi>n</mi><mo>/</mo><mi>p</mi></mrow></math> ratios, which may serve as a magnetometer in heavy-ion collisions. By attributing the centrality dependence of the <math><mrow><mi>p</mi><mo>/</mo><mi>π</mi></mrow></math> ratio in Pb-Pb collisions at 5.02 TeV measured by the ALICE Collaboration entirely to the magnetic field, its maximal strength at freezeout is estimated to be <math><mrow><mi>e</mi><mi>B</mi><mo>≃</mo><mn>0.12</mn><mspace width="4pt"></mspace><msup><mrow><mi>GeV</mi></mrow><mn>2</mn></msup><mo>≃</mo><mn>6.3</mn><msubsup><mi>m</mi><mi>π</mi><mn>2</mn></msubsup></mrow></math> in peripheral collisions. The magnetic field also enhances various conserved charge susceptibilities, which is qualitatively consistent with recent lattice QCD data and is driven in the HRG model by the increase of hadron densities. However, the variances of hadrons do not show any enhancement when normalized by the means, therefore, measurements of second-order fluctuations in heavy-ion collisions appear to offer limited additional information about the magnetic field relative to mean multiplicities.

Magnetic field effect on hadron yield ratios and fluctuations in a hadron resonance gas

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

Anton Motornenko

Abhijit Bhattacharyya

Horst Stoecker

Effect of finite volume on thermodynamics of quark-hadron matter

Molecular dynamics simulations are performed for a finite nonrelativistic system of particles with Lennard-Jones potential. We study the effect of liquid-gas mixed phase on particle number fluctuations in coordinate subspace. A metastable region of the mixed phase, the so-called nucleation region, is analyzed in terms of a noninteracting cluster model. Large fluctuations due to spinodal decomposition are observed. They arise due to the interplay between the size of the acceptance region and that of the liquid phase. These effects are studied with a simple geometric model. The model results for the scaled variance of particle number distribution are compared with those obtained from the direct molecular dynamic simulations.

Ukraine

Volodymyr A. Kuznietsov

Oleh Savchuk

Roman V. Poberezhnyuk

Mark I. Gorenstein

Molecular dynamics analysis of particle number fluctuations in the mixed phase of a first-order phase transition

We study the equation of state of a mixture of (quasi-)free constituent quarks and nucleons with hard-core repulsion at zero temperature. Two opposite scenarios for the realization of the Pauli exclusion principle are considered: (i) a Fermi sea of quarks surrounded by a shell of baryons – the quarkyonic matter, and (ii) a Fermi sea of nucleons surrounded by a shell of quarks which we call baryquark matter. In both scenarios, the sizes of the Fermi sea and shell are fixed through energy minimization at fixed baryon number density. While both cases yield a qualitatively similar transition from hadronic to quark matter, we find that baryquark matter is energetically favored in this setup and yields a physically acceptable behavior of the speed of sound without the need to introduce an infrared regulator. In order to retain the theoretically more appealing quarkyonic matter as the preferred form of dense QCD matter will thus require modifications to the existing dynamical generation mechanisms, such as, for example, the introduction of momentum-dependent nuclear interactions.

Volker Koch

Quarkyonic or baryquark matter? On the dynamical generation of momentum space shell structure

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.

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

This work incorporates the effect of short-range repulsion between particles into the Cooper-Frye hadron sampling procedure. This is achieved by means of a rejection sampling step, which prohibits any pair of particles from overlapping in the coordinate space, effectively modeling the effect of hard-core repulsion. The new procedure—called the fist sampler—is based on the package thermal-fist. It is used here to study the effect of excluded volume on cumulants of the (net-)proton number distribution in central collisions of heavy ions in a broad collision energy range in conjunction with exact global conservation of baryon number, electric charge, and strangeness. The results are compared with earlier calculations based on analytical approximations, quantifying the accuracy of the latter at different collision energies. An additional advantage of the new method over the analytic approaches is that it offers the flexibility provided by event generators, making it straightforwardly extendable to other observables.

Cooper-Frye sampling with short-range repulsion

The centrality dependence of the <math><mi>p</mi><mo>/</mo><mi>π</mi></math> ratio measured by the ALICE Collaboration in 5.02 TeV Pb-Pb collisions indicates a statistically significant suppression with the increase of the charged particle multiplicity once the centrality-correlated part of the systematic uncertainty is eliminated from the data. We argue that this behavior can be attributed to baryon annihilation in the hadronic phase. By implementing the <math><mi>B</mi><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>↔</mo><mn>5</mn><mi>π</mi></math> reaction within a generalized partial chemical equilibrium framework, we estimate the annihilation freeze-out temperature at different centralities, which decreases with increasing charged particle multiplicity and yields <math><msub><mrow><mi>T</mi></mrow><mrow><mi>ann</mi></mrow></msub><mo>=</mo><mn>132</mn><mo>±</mo><mn>5</mn></math> MeV in 0-5% most central collisions. This value is considerably below the hadronization temperature of <math><msub><mrow><mi>T</mi></mrow><mrow><mi>had</mi></mrow></msub><mo>∼</mo><mn>160</mn></math> MeV but above the thermal (kinetic) freeze-out temperature of <math><msub><mrow><mi>T</mi></mrow><mrow><mi>kin</mi></mrow></msub><mo>∼</mo><mn>100</mn></math> MeV. Baryon annihilation reactions thus remain relevant in the initial stage of the hadronic phase but freeze out before (pseudo-)elastic hadronic scatterings. One experimentally testable consequence of this picture is a suppression of various light nuclei to proton ratios in central collisions of heavy ions.

Centrality dependence of proton and light nuclei yields as a consequence of baryon annihilation in the hadronic phase

We develop a framework to relate proton number cumulants measured in heavy-ion collisions within a momentum space acceptance to the susceptibilities of baryon number, assuming that particles are emitted from a fireball with uniform distribution of temperature and baryochemical potential, superimposed on a hydrodynamic flow velocity profile. The rapidity acceptance dependence of proton cumulants measured by the HADES Collaboration in <math><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>NN</mi></mrow></msub></mrow></msqrt><mo>=</mo><mn>2.4</mn></math> GeV Au-Au appears to be consistent with thermal emission of nucleons from a grand-canonical heat bath, with the extracted baryon number susceptibilities exhibiting an hierarchy <math><msubsup><mrow><mi>χ</mi></mrow><mrow><mn>4</mn></mrow><mrow><mi>B</mi></mrow></msubsup><mo>≫</mo><mo>−</mo><msubsup><mrow><mi>χ</mi></mrow><mrow><mn>3</mn></mrow><mrow><mi>B</mi></mrow></msubsup><mo>≫</mo><msubsup><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>B</mi></mrow></msubsup><mo>≫</mo><msubsup><mrow><mi>χ</mi></mrow><mrow><mn>1</mn></mrow><mrow><mi>B</mi></mrow></msubsup></math>. Naively, this could indicate large non-Gaussian fluctuations that might point to the presence of the QCD critical point close to the chemical freeze-out at <math><mi>T</mi><mo>∼</mo><mn>70</mn></math> MeV and <math><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>∼</mo><mn>850</mn><mo>−</mo><mn>900</mn></math> MeV. However, the description of the experimental data at large rapidity acceptances becomes challenging once the effect of exact baryon number conservation is incorporated, suggesting that more theoretical and experimental studies are needed to reach a firm conclusion.