Freeze-out Surface Research Articles

Correlated fluctuations near the QCD critical point

In this paper, we introduce a freeze-out scheme for the dynamical models near the QCD critical point through coupling the decoupled classical particles with the order parameter field. With a modified distribution function that satisfies specific static fluctuations, we calculate the correlated fluctuations of net protons on the hydrodynamic freeze-out surface. A comparison with recent STAR data shows that our model calculations could roughly reproduce energy dependent cumulant $C_4$ and $\kappa \sigma^2$ of net protons through tuning the related parameters. However, the calculated $C_2$ and $C_3$ with both Poisson and Binomial baselines are always above the experimental data due to the positive contributions from the static critical fluctuations. In order to qualitatively and quantitatively describe the experimental data, the dynamical critical fluctuations and more realistic non-critical fluctuation baselines should be investigated in the near future.

Indication of Differential Kinetic Freeze-out at RHIC and LHC Energies

The transverse momentum spectra at RHIC and LHC for A+A and p+p collisions are studied with Tsallis distributions in different approaches i.e. with and without radial flow. The information on the freeze-out surface in terms of freeze-out volume, temperature, chemical potential and radial flow velocities for different particle species are obtained. These parameters are found to show a systematic behavior with mass dependence. It is observed that the heavier particles freeze-out early as compared to lighter particles and freeze-out surfaces are different for different particles, which is a direct signature of mass dependent differential freeze-out. Further, we observe that the radial flow velocity decreases with increasing mass. This confirms the mass ordering behavior in collectivity observed in heavy-ion collisions. It is also observed that the systems created in peripheral heavy-ion collisions and in proton-proton collisions are of similar thermodynamic nature.

Indication of a Differential Freeze-Out in Proton-Proton and Heavy-Ion Collisions at RHIC and LHC Energies

The experimental data from the RHIC and LHC experiments of invariant pT spectra for most peripheral A+A and p+p collisions are analyzed with Tsallis distributions in different approaches. The information about the freeze-out surface in terms of freeze-out volume, temperature, chemical potential, and radial flow velocity for π+, K+, and p and their antiparticles is obtained. Furthermore, these parameters are studied as a function of the mass of the particles. A mass dependent differential freeze-out is observed which does not seem to distinguish between particles and their antiparticles. Furthermore, a mass-hierarchy in the radial flow is observed, meaning heavier particles suffer lower radial flow. Tsallis distribution function at finite chemical potential is used to study the mass dependence of chemical potential. The peripheral heavy-ion and proton-proton collisions at the same energies seem to be equivalent in terms of the extracted thermodynamic parameters.

Freezeout hypersurface at energies available at the CERN Large Hadron Collider from particle spectra: Flavor and centrality dependence

We extract the freezeout hypersurface in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=$ 2760 GeV at the CERN Large Hadron Collider by analysing the data on transverse momentum spectra within a unified model for chemical and kinetic freezeout. The study has been done within two different schemes of freezeout, single freezeout where all the hadrons freezeout together versus double freezeout where those hadrons with non-zero strangeness content have different freezeout parameters compared to the non-strange ones. We demonstrate that the data is better described within the latter scenario. We obtain a strange freezeout hypersurface which is smaller in volume and hotter compared to the non-strange freezeout hypersurface for all centralities with a reduction in $\chi^2/N_{df}$ around $40\%$. We observe from the extracted parameters that the ratio of the transverse size to the freezeout proper time is invariant under expansion from the strange to the non-strange freezeout surfaces across all centralities. Moreover, except for the most peripheral bins, the ratio of the non-strange and strange freezeout proper times is close to $1.3$.

Shear viscosity and phase diagram from Polyakov–Nambu–Jona-Lasinio model

We discuss a detailed study of the variation of shear viscosity, $\eta$, with temperature and baryon chemical potential within the framework of Polyakov$-$Nambu$-$Jona-Lasinio model. $\eta$ is found to depend strongly on the spectral width of the quasi-particles present in the model. The variation of $\eta$ across the phase diagram has distinctive features for different kinds of transitions. These variations have been used to study the possible location of the Critical End Point (CEP), and cross-checked with similar studies of variation of specific heat. Finally using a parameterization of freeze-out surface in heavy-ion collision experiments, the variation of shear viscosity to entropy ratio has also been discussed as a function of the center of mass energy of collisions.

Freeze-Out Parameters in Heavy-Ion Collisions at AGS, SPS, RHIC, and LHC Energies

We review the chemical and kinetic freeze-out conditions in high energy heavy-ion collisions for AGS, SPS, RHIC, and LHC energies. Chemical freeze-out parameters are obtained using produced particle yields in central collisions while the corresponding kinetic freeze-out parameters are obtained using transverse momentum distributions of produced particles. For chemical freeze-out, different freeze-out scenarios are discussed such as single and double/flavor dependent freeze-out surfaces. Kinetic freeze-out parameters are obtained by doing hydrodynamic inspired blast wave fit to the transverse momentum distributions. The beam energy and centrality dependence of transverse energy per charged particle multiplicity are studied to address the constant energy per particle freeze-out criteria in heavy-ion collisions.

Production of light nuclei in heavy-ion collisions within a multiple-freezeout scenario

We discuss the production of light nuclei in heavy ion collisions within a multiple freezeout scenario. Thermal parameters extracted from the fits to the observed hadron yields are used to predict the multiplicities of light nuclei. Ratios of strange to nonstrange nuclei are found to be most sensitive to the details of the chemical freezeout. The well-known disagreement between data of ${}_{\ensuremath{\Lambda}}^{3}\text{H}{/}^{3}\text{He}$ and $\overline{{}_{\ensuremath{\Lambda}}^{3}\text{H}{/}^{3}\text{He}}$ at $\sqrt{{s}_{NN}}=200$ GeV and models based on thermal as well as simple coalescence using a single chemical freezeout surface goes away when we let the strange and nonstrange hadrons freeze out at separate surfaces. At the CERN Large Hadron Collider energy of $\sqrt{{s}_{NN}}=2700$ GeV, multiple freezeout scenario within a thermal model provides a consistent framework to describe the yields of all measured hadrons and nuclei.

Sound edge of the quenching jets

When quenching jets deposit certain amounts of energy and momentum into ambient matter, part of it propagates in the form of shocks/sounds. The ``sound surface'', separating disturbed and undisturbed parts of the fireball, makes what we call the sound edge of jets. In this work we semianalytically study its shape, in various geometries. We further argue that since hadrons with in the kinematical range of ${p}_{\ensuremath{\perp}}\ensuremath{\sim}2\phantom{\rule{0.16em}{0ex}}\phantom{\rule{4pt}{0ex}}\mathrm{GeV}$ originate mostly from the ``rim'' of the fireball, near the maximum of the radial flow at the freeze-out surface, only the intersection of the ``sound surface'' with this ``rim'' would be observable. The resulting ``jet edge'' has a form of extra matter at the elliptic curve, in $\ensuremath{\Delta}\ensuremath{\phi},\ensuremath{\Delta}\ensuremath{\eta}$ coordinates, with radius $|\ensuremath{\Delta}\ensuremath{\phi}|\ensuremath{\sim}|\ensuremath{\Delta}\ensuremath{\eta}|\ensuremath{\sim}1$. In the case of large energy/momentum deposition $\ensuremath{\sim}100\phantom{\rule{0.16em}{0ex}}\phantom{\rule{4pt}{0ex}}\mathrm{GeV}$ we argue that the event should be considered as two subevents, with the interior of the ``sound surface'' having modified radial and directed flow. We further argue that in the kinematical range of ${p}_{\ensuremath{\perp}}\ensuremath{\sim}3\phantom{\rule{0.16em}{0ex}}\phantom{\rule{4pt}{0ex}}\mathrm{GeV}$ the effect of that can be large enough to be seen on an event-by-event basis. If so, this effect has the potential to become a valuable tool to address the geometry of jet production and quenching.

Viscous Flow in Heavy-Ion Collisions from RHIC to LHC

We present a systematic hydrodynamic study of the evolution of hadron spectra and their azimuthal anisotropy from the lowest collision energy studied at the Relativistic Heavy Ion Collider (RHIC), sqrt(s) = 7.7 A GeV, to the highest energy reachable at the Large Hadron Collider (LHC), sqrt(s) = 5500 A GeV. The energy dependence of the flow observables are quantitatively studied for both the Monte-Carlo Glauber and Monte-Carlo Kharzeev-Levin-Nardi (MC-KLN) models. For MC-Glauber model initial conditions with {\eta}/s = 0.08, the differential charged hadron elliptic flow v_2^{ch}(p_T, sqrt(s)) is found to exhibit a very broad maximum in the region 39 < sqrt(s) < 2760 A GeV. For MC-KLN initial conditions with {\eta}/s = 0.2, a similar "saturation" is not observed up to LHC energies. We emphasize that this "saturation" of elliptic flow arises from the interplay between radial flow and elliptic flow which shifts with sqrt(s) depending on the fluid's viscosity. By generalizing the definition of spatial eccentricity to isothermal hyper-surface, we also calculate {\epsilon}_x on the kinetic freeze-out surface at different collision energies.

Mixed harmonic charge dependent azimuthal correlations in Pb–Pb collisions at sNN=2.76TeV measured with the ALICE experiment at the LHC

Mixed harmonic charge dependent azimuthal correlations at mid-rapidity in Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV were measured with the ALICE detector at the LHC. A clear charge dependence for a series of correlations is observed both via the multi-particle cumulant and the event plane methods. Implications from these measurements for the possible effects of the local parity violation in QCD and for models which incorporate the azimuthal anisotropic flow and the local charge conservation on the kinetic freeze-out surface are discussed.

Jets, Bulk Matter, and their Interaction in Heavy Ion Collisions at the LHC

We discuss a theoretical scheme that accounts for bulk matter, jets, and the interaction between the two. The physical picture of our approach is the following: Initial hard scatterings result in mainly longitudinal flux tubes, with transversely moving pieces carrying the pt of the partons from hard scatterings. These flux tubes constitute eventually both bulk matter (which thermalizes, flows, and finally hadronizes) and jets, according to some criteria based on partonic energy loss. High energy flux tube segments will leave the fluid, providing jet hadrons via the usual Schwinger mechanism of flux-tube breaking caused by quark-antiquark production. But the jets may also be produced at the freeze-out surface. Here we assume that the quark-antiquark needed for the flux tube breaking is provided by the fluid, with properties (momentum, flavor) determined by the fluid rather than the Schwinger mechanism. Considering transverse fluid velocities up to 0.7c, and thermal parton momentum distributions, one may get a "push" of a couple of GeV to be added to the transverse momentum of the string segment. This will be a crucial effect for intermediate pt jet hadrons.

Separating jets from bulk matter in heavy ion collisions at the LHC

We discuss a theoretical scheme that accounts for bulk matter, jets, and the interaction between the two. The physical picture of our approach is the following: Initial hard scatterings result in mainly longitudinal flux tubes, with transversely moving pieces carrying the pt of the partons from hard scatterings. These flux tubes constitute eventually both bulk matter (which thermalizes, flows, and finally hadronizes) and jets, according to some criteria based on partonic energy loss. High energy flux tube segments will leave the fluid, providing jet hadrons via the usual Schwinger mechanism of flux-tube breaking caused by quark-antiquark production. But the jets may also be produced at the freeze-out surface. Here we assume that the quark-antiquark needed for the flux tube breaking is provided by the fluid, with properties (momentum, flavor) determined by the fluid rather than the Schwinger mechanism. Considering transverse fluid velocities up to 0.7c, and thermal parton momentum distributions, one may get a "push" of a couple of GeV to be added to the transverse momentum of the string segment. This will be a crucial effect for intermediate pt jet hadrons.

Collision energy dependence of viscous hydrodynamic flow in relativistic heavy-ion collisions

Using a (2+1)-d viscous hydrodynamical model, we study the dependence of flow observables on the collision energy ranging from sqrt(s)=7.7 A GeV at the Relativistic Heavy Ion Collider (RHIC) to sqrt(s)=2760 A GeV at the Large Hadron Collider (LHC). With a realistic equation of state, Glauber model initial conditions and a small specific shear viscosity eta/s = 0.08, the differential charged hadron elliptic flow v_2^{ch}(p_T,sqrt(s)) is found to exhibit a very broad maximum as a function of sqrt(s) around top RHIC energy, rendering it almost independent of collision energy for 39 < sqrt(s) < 2760 A GeV. Compared to ideal fluid dynamical simulations, this "saturation" of elliptic flow is shifted to higher collision energies by shear viscous effects. For color-glass motivated MC-KLN initial conditions, which require a larger shear viscosity eta/s = 0.2 to reproduce the measured elliptic flow, a similar "saturation" is not observed up to LHC energies, except for very low p_T. We emphasize that this "saturation" of the elliptic flow is not associated with the QCD phase transition, but arises from the interplay between radial and elliptic flow which shifts with sqrt(s) depending on the fluid's viscosity and leads to a subtle cancellation between increasing contributions from light and decreasing contributions from heavy particles to v_2 in the sqrt(s) range where v_2^{ch}(p_T,sqrt(s)) at fixed p_T is maximal. By generalizing the definition of spatial eccentricity epsilon_x to isothermal hyper-surfaces, we calculate epsilon_x on the kinetic freeze-out surface at different collision energies. Up to top RHIC energy, sqrt(s)=200 A GeV, the fireball is still out-of-plane deformed at freeze out, while at LHC energy the final spatial eccentricity is predicted to approach zero.

(3+1)D hydrodynamic simulation of relativistic heavy-ion collisions

We present music, an implementation of the Kurganov-Tadmor algorithm for relativistic 3+1 dimensional fluid dynamics in heavy-ion collision scenarios. This Riemann-solver-free, second-order, high-resolution scheme is characterized by a very small numerical viscosity and its ability to treat shocks and discontinuities very well. We also incorporate a sophisticated algorithm for the determination of the freeze-out surface using a three dimensional triangulation of the hypersurface. Implementing a recent lattice based equation of state, we compute ${p}_{T}$-spectra and pseudorapidity distributions for Au+Au collisions at $\sqrt{s}=200 \mathrm{GeV}$ and present results for the anisotropic flow coefficients ${v}_{2}$ and ${v}_{4}$ as a function of both ${p}_{T}$ and pseudorapidity $\ensuremath{\eta}$. We were able to determine ${v}_{4}$ with high numerical precision, finding that it does not strongly depend on the choice of initial condition or equation of state.

Shear viscosity to entropy density ratio in nuclear multifragmentation

Nuclear multifragmentation in intermediate-energy heavy-ion collisions has long been associated with liquid-gas phase transition. We calculate the shear viscosity to entropy density ratio $\ensuremath{\eta}/s$ for an equilibrated system of nucleons and fragments produced in multifragmentation within an extended statistical multifragmentation model. The temperature dependence of $\ensuremath{\eta}/s$ exhibits behavior surprisingly similar to that of ${\mathrm{H}}_{2}$O. In the coexistence phase of fragments and light particles, the ratio $\ensuremath{\eta}/s$ reaches a minimum of depth comparable to that for water in the vicinity of the critical temperature for liquid-gas phase transition. The effects of freeze-out volume and surface symmetry energy on $\ensuremath{\eta}/s$ in multifragmentation are studied.

Radiative energy loss andv2spectra for viscous hydrodynamics

This work investigates the first correction to the equilibrium phase-space distribution and its effects on spectra and elliptic flow in heavy-ion collisions. We show that the departure from equilibrium on the freeze-out surface is the largest part of the viscous corrections to ${v}_{2}({p}_{T})$. However, the momentum dependence of the departure from equilibrium is not known a priori, and it is probably not proportional to ${p}_{T}^{2}$ as has been assumed in hydrodynamic simulations. At high momentum in weakly coupled plasmas, it is determined by the rate of radiative energy loss and is proportional to ${p}_{T}^{3/2}$. The weaker ${p}_{T}$ dependence leads to straighter ${v}_{2}({p}_{T})$ curves at the same value of viscosity. Furthermore, the departure from equilibrium is generally species dependent. A species-dependent equilibration rate, with baryons equilibrating faster than mesons, can explain ``constituent quark scaling'' without invoking coalescence models.

Dynamical freeze-out condition in ultrarelativistic heavy ion collisions

We determine the decoupling surfaces for the hydrodynamic description of heavy ion collisions at RHIC and LHC by comparing the local hydrodynamic expansion rate with the microscopic pion-pion scattering rate. The pion ${p}_{T}$ spectra for nuclear collisions at BNL Relativistic Heavy Ion Collider (RHIC) and CERN Large Hadron Collider (LHC) are computed by applying the Cooper-Frye procedure on the dynamical-decoupling surfaces and compared with those obtained from the constant-temperature freeze-out surfaces. Comparison with RHIC data shows that the system indeed decouples when the expansion rate becomes comparable with the pion scattering rate. The dynamical decoupling based on the rates comparison also suggests that the effective decoupling temperature in central heavy ion collisions remains practically unchanged from RHIC to LHC.

Toward the AdS/CFT gravity dual for high energy collisions. II. The stress tensor on the boundary

In this second paper of the series, we calculate the stress tensor of excited matter, created by debris of high energy collisions at the boundary. The falling open strings, connected to receding charges, produce a nonzero stress tensor which we found analytically from time-dependent linearized Einstein equations in the bulk. It corresponds to exploding nonequilibrium matter: we discuss its behavior in some detail, including its internal energy density in a comoving frame and the 'freeze-out surfaces'. We then discuss what happens for the ensemble of strings.

Dissipative hydrodynamics in2+1dimensions

In $2+1$ dimensions, we simulated the hydrodynamic evolution of quark-gluon plasma (QGP) fluid with dissipation due to shear viscosity. Comparison of the evolution of ideal and viscous fluids, both initialized under the same conditions, e.g., same equilibration time, energy density and velocity profile, reveals that the dissipative fluid evolves slowly, cooling at a slower rate. Cooling slows even more at higher viscosities. The fluid velocities, however, evolve faster in a dissipative fluid than in an ideal fluid. The transverse expansion is also enhanced in dissipative evolution. For the same decoupling temperature, the freeze-out surface for a dissipative fluid is more extended than that for an ideal fluid. Dissipation produces entropy as a result of which particle production is increased. Particle production is increased as a result of the (i) the extension of the freeze-out surface and (ii) the change of the equilibrium distribution function to a nonequilibrium one, the latter effect being prominent at large transverse momentum. Compared to ideal fluid, transverse momentum distribution of pion production is considerably enhanced. Enhancement is greater at high ${p}_{T}$ than at low ${p}_{T}$. Pion production also increases with viscosity; the greater the viscosity, the greater the pion production. Dissipation also modifies the elliptic flow, which is reduced in viscous dynamics. Also, contrary to ideal dynamics where elliptic flow continues to increase with transverse momentum, in viscous dynamics elliptic flow tends to saturate at large transverse momentum. The analysis suggests that the initial conditions of the hot, dense matter produced in Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC), as extracted from ideal fluid analysis, can be changed significantly if the QGP fluid is viscous.

Nonideal particle distributions from kinetic freeze-out models

In fluid dynamical models the freeze-out of particles across a three-dimensional space-time hypersurface is discussed. The calculation of final momentum distribution of emitted particles is described for freeze-out surfaces, with both spacelike and timelike normals, taking into account conservation laws across the freeze-out discontinuity.