Freeze-out Distributions Research Articles

Lévy walk of pions in heavy-ion collisions

The process of Lévy walk, i.e., movement patterns described by heavy-tailed random walks, plays a role in various phenomena, from chemical and microbiological systems through marine predators to climate change. Recent experiments have suggested that this phenomenon also appears in heavy-ion collisions. However, the theoretical interpretation supporting such findings is still debated. In high-energy collisions of heavy nuclei, the strongly interacting Quark Gluon Plasma is created, which, similarly to the early Universe, undergoes a rapid expansion and transition back to hadronic matter. In the subsequent expanding hadron gas, particles interact until kinetic freeze-out, when their momenta stop changing, and they freely transition toward the detectors. Measuring spatial freeze-out distributions is a crucial tool in understanding the dynamics of the created matter and the interactions among its constituents. In this paper, we introduce a three-dimensional analysis of the spatial freeze-out distribution of pions (the most abundant particles in such collisions). Utilising Monte-Carlo simulations of high-energy collisions, we show that the chain of processes ending in a final state pion has a step length distribution leading to Lévy-stable distributions. Subsequently, we show that simulated pion freeze-out distributions indeed exhibit heavy tails and can be described by a three-dimensional elliptically contoured symmetric Lévy-stable distribution.

Λ and Λ¯ Freeze-Out Distributions and Global Polarizations in Au+Au Collisions

The gold–gold collisions at sNN=7.7 and 11.5 GeV are simulated within the PHSD transport model. In each collision event, the spectator nucleons are separated and the fluidization procedure for the participants is performed. The local velocities are determined in the Landau frame and the kinematic and thermal vorticity fields are evaluated. We analyze the thermodynamic properties of the cells where Λs and Λ¯s were born or had their last interaction. Such cells contribute to the formation of the observed global polarization of hyperons induced by the thermal vorticity of the medium. The Λ¯ polarization signal is found to be mainly determined by hot, dense, and highly vortical cells at the earlier stage of the collision, whereas the Λ polarization signal is accumulated over the longer time and includes cells with lower vorticity. The calculated global polarizations for both Λs and Λ¯s agree well with the experimental finding by the STAR collaboration at energy sNN=11.5 GeV. For collisions at sNN=7.7 GeV, we can reproduce the STAR data for Λ hyperons, but significantly underpredict the observed global polarization of Λ¯. Furthermore, we consider the centrality dependence of the hyperon polarization in collisions at 7.7 GeV. It increases with an increase of centrality, reaches a maximum at 65–75% and then starts decreasing rapidly for peripheral collisions.

Deuteron and antideuteron coalescence in heavy-ion collisions: energy dependence of the formation geometry

We investigate the collision energy dependence of deuteron and antideuteron emission in the RHIC-BES low- to mid-energy range $\sqrt{s_{NN}} = 4.6-200$ GeV where the formation rate of antinuclei compared to nuclei is strongly suppressed. In the coalescence picture, this can be understood as bulk emission for nuclei in contrast to surface emission for antinuclei. By comparison with experimental data on the coalescence parameter $B_2$, we are able to extract the respective source geometries. This interpretation is further supported by results from the UrQMD transport model, and establishes the following picture: At low energies, nucleons freeze out over the total fireball volume, while antinucleons are annihilated inside the nucleon-rich fireball and can only freeze out on its surface. Towards higher energies, this annihilation effect becomes irrelevant (due to the decreasing baryochemical potential) and the system's freeze-out is driven by the mesons. Thus, the nucleon and antinucleon freeze-out distributions become similar with increasing energy.

Femtoscopic scales of particle-emitting source in small and large systems

The femtoscopy technique allows one to measure the spatial and temporal scales of the particle-emitting source produced in high-energy collisions. In non-central ultra-relativistic heavy-ion collisions, emitting source may be tilted in the reaction plane. The orientation of freeze-out distributions is interesting because it provides complementary information about quark-gluon matter properties. In the experiment, the tilt can be extracted by measuring femtoscopic radii as a function of the pair angle with respect to the first-order event plane.In this talk, we will present results of azimuthally sensitive femtoscopic analysis of Au+Au and Cu+Au collisions at . We will also present the transverse momentum and multiplicity dependence of identical pion femtoscopic radii from d+Au, 3He+Au collisions at . All data was obtained from the UrQMD model.

Estimation of pion-emitting source in symmetric and asymmetric collisions using the UrQMD model

The femtoscopy technique allows one to measure spatial and temporal characteristics of the particle-emitting source produced in high-energy collisions. In non-central ultrarelativistic heavy-ion collisions the emission source can be tilted in the reaction plane. In the current analysis, the orientation of freeze-out distributions with respect to the first-order event plane in symmetric (Au+Au) and asymmetric (Cu+Au) collisions at $$\sqrt {{s_{NN}}} = 200$$ GeV was studied using the UrQMD model to extract information about the emission source tilt. The effect of the initial geometry on the femtoscopic radii of small systems was measured at the same number of charged particles and transverse momentum was studied in d+Au and 3He+Au collisions at $$\sqrt {{s_{NN}}} = 200$$ GeV. The implications of the results are discussed.

Flow harmonics from self-consistent particlization of a viscous fluid

The quantitative extraction of quark-gluon plasma (QGP) properties from heavy-ion data, such as its specific shear viscosity $\ensuremath{\eta}/s$, typically requires comparison to viscous hydrodynamic or ``hybrid'' hydrodynamics + transport simulations. In either case, one has to convert the fluid to hadrons, yet without additional theory input the conversion is ambiguous for dissipative fluids. Here, shear viscous phase-space corrections calculated using linearized transport theory are applied in Cooper-Frye freeze-out to quantify the effects on anisotropic flow coefficients ${v}_{n}({p}_{T})$ at the energies available at both the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider. Expanding upon our previous flow harmonics studies [D. Molnar and Z. Wolff, Phys. Rev. C 95, 024903 (2017); Z. Wolff and D. Molnar, J. Phys.: Conf. Ser. 535, 012020 (2014)], we calculate pion and proton ${v}_{2}({p}_{T})$, ${v}_{4}({p}_{T})$, and ${v}_{6}({p}_{T})$, but here we incorporate a hadron gas that is chemically frozen below a temperature of 175 MeV and use hypersurfaces from realistic viscous hydrodynamic simulations. For additive quark model cross sections and relative phase-space corrections with ${p}^{3/2}$ momentum dependence rather than the quadratic Grad form, we find at moderately high transverse momentum noticeably higher ${v}_{4}({p}_{T})$ and ${v}_{6}({p}_{T})$ for protons than for pions. In addition, the value of $\ensuremath{\eta}/s$ deduced from elliptic flow data differs by nearly 50% from the value extracted using the naive ``democratic Grad'' form of freeze-out distributions. To facilitate the use of the self-consistent viscous corrections calculated here in hydrodynamic and hybrid calculations, we also present convenient parametrizations of the corrections for the various hadron species.

Bulk viscosity, chemical equilibration and flow at RHIC

We study the effects of bulk viscosity on p_T spectra and elliptic flow in heavy ion collisions at RHIC. We argue that direct effect of the bulk viscosity on the evolution of the velocity field is small, but corrections to the freezeout distributions can be significant. These effects are dominated by chemical non-equilibration in the hadronic phase. We show that a non-zero bulk viscosity in the range $\zeta/s \lsim 0.05$ improves the description of spectra and flow at RHIC.

TWO-PARTICLE CORRELATION IN HEAVY-ION COLLISIONS AT CSR ENERGY

The predictions of the two-particle correlation by using the relativistic quantum molecular dynamics model are presented for the heavy-ion reactions at HIRFL-CSR energy. The two-proton correlation function with the final state interaction is calculated with the Lednicky code for the U + U collisions at beam energy 520 A MeV. Applying the imaging technique, the relationship between the freeze-out spatial distributions and the results of correlation femtoscopy is investigated. We find that one can reliably reconstruct the source functions from the two-particle correlation functions with ignoring the degree of space-momentum correlations at this energy. The results are useful to the designing the hadron detector at CSR.

Freeze-out in Narrow and Wide Layers

The freeze-out of particles from a layer of finite thickness is discussed in a phenomenological kinetic model. The proposed model, based on the Modified Boltzman Transport Equation, is Lorentz invariant and can be applied equally well for the freeze-out layers with space-like and time-like normal vectors. It leads to non-equilibrated post freeze-out distributions. The dependence of the resulting distribution on the thickness of the layer is presented and discussed for a space-like freeze-out scenario.

Baryonic Effect on χcJ Suppression in Au+Au Collisionsat RHIC Energies

We predict that χcJ mesons at low transverse momentumin the central rapidity region are almost dissociatedby nucleons and antinucleons in hadronic matterproduced in central Au+Au collisionsat relativistic high-ion collider (RHIC) energies (sNN)1/2 = 130and 200 GeV. In the calculations thenucleon and antinucleon distributions in hadronic matter are results ofevolution from their freeze-out distributions which well fit theexperimental transverse momentum spectra of proton and antiproton.

New solutions to covariant nonequilibrium dynamics

New solutions of 3+1D covariant kinetic theory are presented for nuclear collisions in the energy domain Ecm ~ 200 AGeV. They are obtained using MPC, a new Monte-Carlo parton transport technique that employs very high parton subdivision that is necessary to preserve covariance. The transport results are compared with ideal hydrodynamics solutions. We show that the transport evolution differs significantly from hydrodynamics. In addition, we compare the transport freeze-out distributions to those obtained from ideal hydrodynamics with the Cooper-Frye isotherm freeze-out prescription. The transport freeze-out four-volume is shown to be sensitive to the reaction rates and deviates from both time-like and space-like freeze-out 3D hypersurfaces commonly assumed. In particular, we find that there does not exist a universal freeze-out temperature. Finally, the transverse momentum distributions are found to deviate by up to an order of magnitude from (Cooper-Frye frozen) hydrodynamics for a wide range of possible initial conditions and reaction rates at RHIC energies.

Relationship between particle freeze-out distributions and Hanbury Brown–Twiss radius parameters

The relationship between pion and kaon space-time freeze-out distributions and the Hanbury Brown--Twiss (HBT) radius parameters in high-energy nucleus-nucleus collisions is investigated. We show that the HBT radius parameters in general do not reflect the rms deviations of the single particle production points. Instead, the HBT radius parameters are most closely related to the curvature of the two-particle space-time relative position distribution at the origin. We support our arguments by studies with a dynamical model (RQMD 2.4).

Reaction dynamics in Pb + Pb at the CERN/SPS: From partonic degrees of freedom to freeze-out

We analyze the reaction dynamics of central Pb+Pb collisions at 160 GeV/nucleon. First we estimate the energy density e pile-up at mid-rapidity and calculate its excitation function: ε is decomposed into hadronic and partonic contributions. A detailed analysis of the collision dynamics in the framework of a microscopic transport model shows the importance of partonic degrees of freedom and rescattering of leading (di)quarks in the early phase of the reaction for E lab ⩾ 30GeV/nucleon . The energy density reaches up to 4 GeV/fm 3, 95% of which are contained in partonic degrees of freedom. It is shown that cells of hadronic matter, after t ≈ 2R/γν cm can be viewed as nearly chemically equilibrated. This matter never exceeds energy densities of ∼ 0.4 GeV/fm 3, i.e. a density above which the notion of separated hadrons loses its meaning. The final reaction stage is analyzed in terms of hadron ratios, freeze-out distributions and a source analysis for final state pions.