To assess the degree of equilibration of the matter created in heavy-ion reactions at low to intermediate beam energies, a hadronic transport approach (SMASH) is employed. By using a coarse-graining method, we compute the energy momentum tensor of the system at fixed time steps and evaluate the degree of isotropy of the diagonal terms and the relative magnitude of the off-diagonal terms. This study focuses mostly on Au+Au collisions in the energy range $\sqrt{s_{\rm NN}}$ = 2.4-7.7 GeV, but central collisions of lighter ions like C+C, Ar+KCl and Ag+Ag are considered as well. We find that the conditions concerning local equilibration for a hydrodynamic description are reasonably satisfied in a large portion of the system for a significant amount of time (several fm/c) when considering the average evolution of many events, yet they are rarely fulfilled on an event by event basis. This is relevant for the application of hybrid approaches at low beam energies as they are or will be reached by the HADES experiment at GSI, the future CBM experiment at FAIR as well as the beam energy scan program at RHIC.
Within Israel-Stewart's theory of dissipative hydrodynamics, we have analyzed ALICE data for the centrality dependence of charged particles multiplicity, elliptic flow and $p_T$ spectra in $\sqrt{s}_{NN}$=2.76 TeV Pb+Pb collisions and obtained the temperature dependence of the QGP viscosity over the entropy ratio ($\etas$). If temperature dependence of $\etas$ is parameterized as $\etas=α\frac{T-T_c}{T_c}+\frac{1}{4π}$, experimental data favor $α$ in the range 0-0.2. $α\geq 0.4$ is not favored by the data. Experimental data in $\sqrt{s}_{NN}$=200 GeV Au+Au collisions however, prefer $α$=0.4.
In the Israel-Stewart's theory of second order hydrodynamics, we have simulated $\sqrt{s}$=2.76 TeV Pb+Pb collisions. ALICE data for the centrality dependence of charged particles multiplicity, $p_T$ spectra in 0-5% collisions, centrality dependence of integrated and differential elliptic flow are analysed. Analysis indicate that while ALICE data on charged particles multiplicity or $p_T$ spectra do not demand any viscosity, viscosity is demanded by the elliptic flow data. From a simulataneous fit to all the data sets, viscosity to entropy ratio in $\sqrt{s}_{NN}$=2.76 TeV Pb+Pb collisions is …
In Israel-Stewart's theory of dissipative hydrodynamics, we have analyzed the recent ALICE data for the centrality dependence of charged particle multiplicity, centrality dependence of integrated elliptic flow and 0-5% charged particles $p_T$ spectra in $\sqrt{s}_{NN}$=2.76 TeV Pb+Pb collisions and determined the initial or the thermalisation time. Analysis indicate that the ALICE data disfavor very early thermalsiation $τ_i$=0.2 fm, or very late thermalsation $τ_i$= 4fm. Data are best explained for thermalisation time $τ_i=0.88^{-0.14}_{+0.68}$ fm.
Taking into account of entropy generation during evolution of a viscous fluid, we have estimated inverse Knudsen number, ideal hydrodynamic limit for elliptic flow and QGP viscosity to entropy ratio in $\sqrt{s}$=62 and 200 GeV Cu+Cu/Au+Au collisions. Viscosity to entropy ratio is estimated as $η/s=0.17\pm 0.10\pm 0.20$, the first error is statistical, the second one is systematic. In a central Au+Au collision, inverse Knudsen number is $\approx 2.80\pm 1.63$, which presumably small for complete equilibration. In peripheral collisions it is even less. Ideal hydrodynamic limit for elliptic flow…
The transverse momentum spectra for direct photons produced in Pb-Pb collisions at the LHC, including thermal (hydrodynamics) and prompt (pQCD) emissions are presented.
The single inclusive charged hadron pT spectra in Pb-Pb collisions at the LHC, predicted by a combined hydrodynamics+perturbative QCD (pQCD) approach are presented.
We review the formulation of Landau hydrodynamics and find that the rapidity distribution of produced particles in the center-of-mass system should be more appropriately modified as dN/dy \exp[\sqrt{y_b^2-y^2}], where y_b=\ln[\sqrt{s_{NN}}/m_p] is the beam nucleon rapidity, instead of Landau's original distribution, dN/dy(Landau) \exp[\sqrt{L^2-y^2}], where L=\ln[\sqrt{s_{NN}}/2m_p]. The modified distribution agrees better with experimental dN/dy data than the original Landau distribution and can be represented well by the Gaussian distribution, dN/dy(Gaussian) \exp[-y^2/2L]. Past successes of…
Single particle spectra as well as elliptic flow in Cu+Cu collisions at $\sqrt{s_{NN}}=200$ GeV are investigated within a hadronic cascade model and an ideal hydrodynamic model. Pseudorapidity distribution and transverse momentum spectra for charged hadrons are surprisingly comparable between these two models. However, a large deviation is predicted for the elliptic flow. The forthcoming experimental data will clarify the transport and thermalization aspects of matter produced in Cu+Cu collisions.
In hydrodynamical modeling of ultrarelativistic heavy-ion collisions, the freeze-out is typically assumed to take place at a surface of constant temperature or energy density. A more physical approach is to assume that freeze-out takes place at a surface of constant Knudsen number. We evaluate the Knudsen number as a ratio of the expansion rate of the system to the pion scattering rate, and apply the constant Knudsen number freeze-out criterion to ideal hydrodynamical description of heavy-ion collisions at RHIC ($\sqrt{s_\mathrm{NN}}=200$ GeV) and the LHC ($\sqrt{s_\mathrm{NN}}=2760$ GeV) ener…
Direct photon production, in $\sqrt{s_{NN}}$=200 GeV Au+Au and in $\sqrt{s_{NN}}$=2.76 TeV Pb+Pb collisions, are studied in a hydrodynamic model. Ideal hydrodynamic model, initialised to reproduce experimentally charged particle spectra in RHIC and LHC energy, also reproduces the PHENIX and ALICE measurements for the direct photon spectra in Au+Au collisions at RHIC and Pb+Pb collisions at LHC. The model however produces less elliptic flow than in experiment. Discrepancy between experiment and hydrodynamic simulation is comparatively less in Pb+Pb collisions at LHC than in Au+Au collisions at …
The matter created in central p+p, p+Pb and Pb+Pb collisions at sqrt{s}=5.02 TeV is simulated event-by-event using the superSONIC model, which combines pre-equilibrium flow, viscous hydrodynamic evolution and late-stage hadronic rescatterings. Employing a generalization of the Monte Carlo Glauber model where each nucleon possesses three constituent quarks, superSONIC describes the experimentally measured elliptic and triangular flow at central rapidity in all systems using a single choice for the fluid parameters, such as shear and bulk viscosities. This suggests a common hydrodynamic origin o…
We calculate flow observables with the NeXSPheRIO ideal hydrodynamic model and make the first comparison to the complete set of mid-rapidity flow measurements made by the PHENIX collaboration in top energy Au+Au collisions. A simultaneous calculation of v_2, v_3, v_4, and the first event-by-event calculation of quadrangular flow defined with respect to the v_2 event plane (v_4{Psi_2}) gives good agreement with measured values, including the dependence on both transverse momentum and centrality. This provides confirmation that the collision system is indeed well described as a quark-gluon plasm…
Based on a hydrodynamical model, we compare 130 GeV/$A$ Au+Au collisions at RHIC and 17 GeV/$A$ Pb+Pb collisions at SPS. The model well reproduces the single-particle distributions of both RHIC and SPS. The numerical solution indicates that huge amount of collision energy in RHIC is mainly used to produce a large extent of hot fluid rather than to make a high temperature matter; longitudinal extent of the hot fluid in RHIC is much larger than that of SPS and initial energy density of the fluid is only 5% higher than the one in SPS. The solution well describes the HBT radii at SPS energy but sh…
Centrality dependence of charged particles multiplicity, transverse momentum spectra, integrated and differential elliptic flow, in $\sqrt{s}_{NN}$=200 GeV Au+Au collisions are analyzed using event by event ideal hydrodynamics. Monte-Carlo Glauber model of initial condition, constrained to reproduce experimental charged particle's multiplicity in 0-10% Au+Au collisions, reasonably well reproduces all the experimental observables, e.g. centrality dependence of charged particles multiplicity, integrated and differential elliptic flow. Model predictions for higher flow harmonics, $v_3$, $v_4$ how…
Using the (2+1)-dimensional viscous hydrodynamic code VISH2+1, we present systematic studies of the dependence of pion and proton transverse momentum spectra and their elliptic flow in 200 A GeV Au+Au collisions on the parameters of the hydrodynamic model (thermalization time, initial entropy density distribution, decoupling temperature, equation of state, and specific shear viscosity eta/s). We identify a tension between the slope of the proton spectra, which (within hydrodynamic simulations that assume a constant shear viscosity to entropy density ratio) prefer larger eta/s values, and the s…
The recently measured correlations between the flow angles associated with higher harmonics in the anisotropic flow generated in relativistic heavy-ion collisions are shown to be of hydrodynamic origin. The correlation strength is found to be sensitive to both the initial conditions and the shear viscosity of the expanding fireball medium.
Landau hydrodynamics is a plausible description for the evolution of the dense hot matter produced in high-energy heavy-ion collisions. We review the formulation of Landau hydrodynamics to pave the way for its application in high-energy heavy-ion collisions. It is found that Landau's rapidity distribution needs to be modified to provide a better quantitative description. In particular, the rapidity distribution in the center-of-mass system should be more appropriately given as dN/dy \exp{\sqrt{y_b^2-y^2}}, where y_b=\ln{\sqrt{s_NN}/m_p} is the beam nucleon rapidity, instead of Landau's origina…
The first calculation of triangular flow $v_3$ in Au+Au collisions at $\sqrt{s_{\rm NN}}=200A$ GeV from an event-by-event (3+1)-d transport+hydrodynamics hybrid approach is presented. As a response to the initial triangularity $ε_3$ of the collision zone, $v_3$ is computed in a similar way to the standard event-plane analysis for elliptic flow $v_2$. It is found that the triangular flow exhibits weak centrality dependence and is roughly equal to elliptic flow in most central collisions. We also explore the transverse momentum and rapidity dependence of $v_2$ and $v_3$ for charged particles as …
In high energy collisions of heavy-ions, experimental findings of collective flow are customarily associated with the presence of a thermalized medium expanding according to the laws of hydrodynamics. Recently, the ATLAS, CMS and ALICE experiments found signals of the same type and magnitude in ultrarelativistic proton-proton collisions. In this study, the state-of-the-art hydrodynamic model SONIC is used to simulate the systems created in p+p collisions. By varying the size of the second-order transport coefficients, the range of applicability of hydrodynamics itself to the systems created in…
Flow signatures in experimental data from relativistic ion collisions are usually interpreted as a fingerprint of the presence of a hydrodynamic phase during the evolution of these systems. In this work, flow signatures arising from event-by-event viscous hydrodynamics are compared to those arising from event-by-event non-interacting particle dynamics (free-streaming), both followed by a late-stage hadronic cascade, in d+Au, 3He+Au at sqrt(s)=200 GeV and p+Pb collisions at sqrt(s)=5 TeV, respectively. For comparison, also Pb+Pb collisions at sqrt(s)=2.76 TeV are simulated. It is found that non…
We study the effect of separate chemical and kinetic freeze-outs to the ideal hydrodynamical flow in Au+Au collisions at RHIC (sqrt(s_NN) = 200 GeV energy). Unlike in earlier studies we explore how these effects can be counteracted by changes in the initial state of the hydrodynamical evolution. We conclude that the reproduction of pion, proton and antiproton yields necessitates a chemical freeze-out temperature of T = 150 MeV instead of T = 160 - 170 MeV motivated by thermal models. Unlike previously reported, this lower temperature makes it possible to reproduce the p_T-spectra of hadrons if…
We revisit the use of ideal hydrodynamics to describe bulk- and multistrange-hadron observables in nuclear collisions at the Relativistic Heavy Ion Collider. Toward this end we augment the 2+1-dimensional code "AZHYDRO" by employing (a) an equation of state based on recent lattice-QCD computations matched to a hadron-resonance gas with chemical decoupling at $T_{\rm ch}\simeq$160\,MeV, (b) a compact initial density profile, (c) an initial-flow field including azimuthal anisotropies, and (d) a sequential kinetic decoupling of bulk ($π$, $K$, $p$) and multistrange ($ϕ$, $Ξ$, $Ω$) hadrons at $T\s…
Combining the hydrodynamic model (Hydro code) and the transport model (PACIAE model), we present the Hydro-PACIAE hybrid model. We use the Hydro-PACIAE hybrid model to calculate Au+Au collisions at $\sqrt{s_{NN}}$=130 GeV and Pb+Pb collisions at $\sqrt{s_{NN}}$=2.76 TeV. The obtained pseudo-rapidity and transverse momentum distributions well reproduce the experimental data. This shows that the Hydro-PACIAE hybrid model is useful to describe the ultrarelativistic Heavy Ion Collisions at RHIC and LHC Energies. We used the hybrid model to calculate the elliptical flow for the Pb+Pb collisions at …
It is shown that a simultaneous comparison of both elliptic and triangular flow from (2+1)-dimensional viscous fluid dynamics with recent measurements in Pb+Pb collisions at the Large Hadron Collider (LHC) favors a small specific shear viscosity (eta/s)_QGP approximately equal to 1/(4pi) for the quark-gluon plasma. Using this viscosity value, the relative magnitude of the elliptic and triangular flow is well described with Monte-Carlo Glauber (MC-Glauber) initial conditions while Monte-Carlo Kharzeev-Levin-Nardi (MC-KLN) initial conditions require twice as large viscosity to reproduce the elli…
Hydrodynamic simulations are used to make predictions for the integrated elliptic flow coefficient v_2 in sqrt(s)=5.5 TeV lead-lead and sqrt(s)=14 TeV proton-proton collisions at the LHC. We predict a 10% increase in v_2 from RHIC to Pb+Pb at LHC, and v_2 ~ 0 in p+p collisions unless eta/s < 0.08.
A new set of equations for relativistic viscous hydrodynamics that captures both weak-coupling and strong-coupling physics to second order in gradients has been developed recently. We apply this framework to bulk physics at RHIC, both for standard (Glauber-type) as well as for Color-Glass-Condensate initial conditions and show that the results do not depend strongly on the values for the second-order transport coefficients. Results for multiplicity, radial flow and elliptic flow are presented and we quote the ratio of viscosity over entropy density for which our hydrodynamic model is consisten…
We present a dynamical description of (anti)proton number fluctuations cumulants and correlation functions in central Au-Au collisions at $\sqrt{s_{\rm NN}} = 7.7-200$ GeV by utilizing viscous hydrodynamics simulations. The cumulants of proton and baryon number are calculated in a given momentum acceptance analytically, via an appropriately extended Cooper-Frye procedure describing particlization of an interacting hadron resonance gas. The effects of global baryon number conservation are taken into account using a generalized subensemble acceptance method. The experimental data of the STAR col…
We analyze single particle momentum spectra and interferometry radii in central Au+Au collisions at RHIC within a hydro-inspired parametrization accounting for continuous hadron emission through the whole lifetime of hydrodynamically expanding fireball. We found that a satisfactory description of the data is achieved for a physically reasonable set of parameters when the emission from non space-like sectors of the enclosed freeze-out hypersurface is fairly long: $ 9$ fm/c. This protracted surface emission is compensated in outward interferometry radii by positive $r_{out} - t$ correlations tha…
We compute the longitudinal hydrodynamic flow in ultrarelativistic heavy ion collisions at $\sqrt{s}$ = 5500 GeV by using boost non-invariant initial conditions following from perturbative QCD. The transfer of entropy and energy from the central region to larger rapidities caused by boost non-invariance is determined and the associated decrease in the lifetime of the system is estimated.
We implement a Langevin approach for the transport of charm quarks in the UrQMD (hydrodynamics + Boltzmann) hybrid model. Due to the inclusion of event-by-event fluctuations and a full (3+1) dimensional hydrodynamic evolution, this approach provides a more realistic model for the evolution of the matter produced in heavy ion collisions as compared to simple homogeneous fireball expansions usually employed. As drag and diffusion coefficients we use a resonance approach for elastic heavy-quark scattering and assume a decoupling temperature of the charm quarks from the hot medium of 130 MeV. A co…
We explore the possibility of observing elliptic flow in low multiplicity events in central pp collisions at LHC energy, $\sqrt{s}$=14 TeV. It is assumed that the initial interactions produces a number of hot spots. Hydrodynamical evolution of two or more hot spots can generate sufficiently large elliptic flow to be accessible experimentally in 4-th order cumulant analysis.
Identical-particle (pion and kaon) femtoscopy in Pb$-$Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV with Therminator2 modeled with (3+1)D viscous hydrodynamics
Indian Institute of Technology Bombay（印度理工学院孟买分校）；University of Tsukuba（筑波大学）
利用 (3+1)D 粘性流体动力学和 THERMINATOR 2 代码研究 Pb-Pb 碰撞中介子和 K 介子的费米简缩，发现半径随对偶动量增加而减小，表明强集体性。
Following the Boz$\dot{\textrm{e}}$k-Wyskiel parametrization tilted initial condition, an alternative way to construct a longitudinal tilted fireball based on the Glauber collision geometry is presented. This longitudinal tilted initial condition combined with the Ideal-CLVisc (3 + 1)D hydrodynamic model, a nonvanishing directed flow coefficient $v_{1}$ in a wide rapidity range is observed. After comparing the model's results with experimentally observed data of directed flow coefficient $v_{1}(η)$ from $\sqrt{s_{NN}}$ = 200 GeV Cu + Cu, Au + Au collisions at RHIC energy to $\sqrt{s_{NN}}$ = 2…
This study presents generalization of the Landau hydrodynamic solution for multiparticle production applied to non-central relativistic heavy ion collisions. Obtained results shows longitudinal scaling of elliptic flow $v_2$ as a function of rapidity shifted by beam rapidity ($y-y_{beam}$) for different energies ($\sqrt{s_{NN}}=62.4$ GeV and 200 GeV) and for different systems (Au-Au and Cu-Cu). It is argued, that the elliptic flow and its longitudinal scaling is due to the initial transverse energy density distribution and initial longitudinal thickness effect.
Under the assumption that a quark-gluon plasma droplet is produced and its evolution can be described by hydrodynamics in p + A collisions, $γ$-triggered hadron spectra are studied within a next-to-leading-order perturbative QCD parton model with the medium-modified parton fragmentation functions. The initial conditions and space-time evolution of the small QGP droplet are provided by the superSONIC hydrodynamic model simulations and parton energy loss in such a medium is described by the high-twist (HT) approach. The scaled jet transport coefficient $\hat{q}/T^3$ in this HT approach is extrac…
We study deuteron production using no-coalescence hydrodynamic + transport simulations of central AuAu collisions at $\sqrt{s_{NN}} = 7 - 200$ GeV. Deuterons are sampled thermally at the transition from hydrodynamics to transport, and interact in transport dominantly via $πp n \leftrightarrow πd$ reactions. The measured proton, Lambda, and deuteron transverse momentum spectra and yields are reproduced well for all collision energies considered. We further provide a possible explanation for the measured minimum in the energy dependence of the coalescence parameter, $B_2(\sqrt{s_{NN}})$ as well …
In an ideal hydrodynamic model, with an equation of state where the confinement-deconfinement transition is a cross-over at $T_{co}=196 MeV$, we have simulated $\sqrt{s}$=200 GeV Au+Au collisions. Simultaneous description of the experimental charged particle's $p_T$ spectra and elliptic flow require that in central (0-10%) Au+Au collisions, initial energy density scales with the binary collision number density. In less central collisions, experimental data demand scaling with the participant density. Simulation studies also indicate that in central collisions viscous effects are minimal.
Direct photon emission in heavy-ion collisions is calculated within a relativistic micro+macro hybrid model and compared to the microscopic transport model UrQMD. In the hybrid approach, the high-density part of the collision is calculated by an ideal 3+1-dimensional hydrodynamic calculation, while the early (pre-equilibrium-) and late (rescattering-) phase are calculated with the transport model. We study both models with Au+Au-collisions at \sqrt{s_NN} = 200 GeV and compare the results to experimental data published by the PHENIX collaboration.
We carry out simulations using a multiphase transport (AMPT) model to describe the observed flow signatures in $\sqrt{s_{NN}}=2.76$ TeV Pb-Pb collisions. Especially, we calculate the flow fluctuations of $v_2$ in terms of cumulant ratios and the standardized skewness. Based on event-by-event AMPT simulations, we study the linear and cubic response relation between $v_2$ and $\varepsilon_2$. We found that the observed response relation is compatible to what has been noticed in hydrodynamic modelings, with similar dependence on shear viscosity. Besides, this response relation is not sensitive to…
Causal viscous hydrodynamic fits to experimental data for pion and kaon transverse momentum spectra from central Au+Au collisions at \sqrt{s_{NN}}=200 GeV are presented. Starting the hydrodynamic evolution at 1 fm/c and using small values for the relaxation time, reasonable fits up to moderate ratios η/s\simeq 0.4 can be obtained. It is found that a percentage of roughly 50 η/s to 75 η/s of the final meson multiplicity is due to viscous entropy production. Finally, it is shown that with increasing viscosity, the ratio of HBT radii R_{out}/R_{side} approaches and eventually matches the experime…
Results from the RHIC and LHC experiments show, that in relativistic heavy ion collisions, a new state of matter, a strongly interacting perfect fluid is created. Accelerating, exact and explicit solutions of relativistic hydrodynamics allow for a simple and natural description of this medium. A finite rapidity distribution arises from these solutions, leading to an advanced estimate of the initial energy density of high energy collisions. These solutions can be utilized to describe various aspects of proton-proton collisions, as originally suggested by Landau. We show that an advanced estimat…
We predict the elliptic flow parameter v_2 in U+U collisions at sqrt{s_{NN}}=200 GeV and in Pb+Pb collisions at sqrt{s_{NN}} = 2.76 TeV using a hybrid model in which the evolution of the quark gluon plasma is described by ideal hydrodynamics with a state-of-the-art lattice QCD equation of state, and the subsequent hadronic stage by a hadron cascade model.
High-energy nuclear collisions produce a nonequilibrium plasma of quarks and gluons which thermalizes and exhibits hydrodynamic flow. There are currently no practical frameworks to connect the early particle production in classical field simulations to the subsequent hydrodynamic evolution. We build such a framework using nonequilibrium Green's functions, calculated in QCD kinetic theory, to propagate the initial energy-momentum tensor to the hydrodynamic phase. We demonstrate that this approach can be easily incorporated into existing hydrodynamic simulations, leading to stronger constraints …
In this paper, our goal is to make a simultaneous analysis of the high- and low-P_T parts of the charged-hadron P_T spectrum measured by the ALICE collaboration in central Pb-Pb collisions at sqrt{s}=2.76 TeV at the Large Hadron Collider (LHC), based on models which have been successfully applied and constrained in Au-Au collisions at Relativistic Heavy Ion Collider (RHIC). For the hydrodynamical modeling with which we obtain the low-P_T spectrum, we have computed the initial conditions based on perturbative QCD (pQCD) minijet production and saturation. The sensitivity of the obtained charged-…
The femtoscopy correlation radii for d-Au collisions at $200$GeV are calculated in the hydrodynamic model and compared to PHENIX collaboration data. For asymmetric systems, such as d-Au or p-Pb collisions, the correlation radius $R_{out-long}$ is estimated and predicted to be non-zero. It appears due to different lifetimes of the parts of the fireball at positive and negative rapidities. Azimuthally sensitive Hanbury Brown-Twiss analysis with respect to the second order event plane shows a significant angular dependence of the radii. It reflects the strong azimuthal asymmetry of the d-Au sourc…
Background: A component of azimuth correlations from high-energy heavy ion collisions varying as $\cos(2ϕ)$ and denoted by symbol $v_2$ is conventionally interpreted to represent "elliptic flow," a hydrodynamic manifestation of the initial-state åoverlap geometry. Several numerical methods are used to estimate $v_2$, resulting in various combinations of "flow" and "nonflow" that reveal systematic biases in the $v_2$ estimates. QCD jets contribute strongly to azimuth correlations and specifically to the $\cos(2ϕ)$ component. Purpose: We question the extent of jet-related ("nonflow") bias in and…
The rapidity distribution and transverse spectra of most copious particles such as pions, Kaons and antiprotons from central Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV and central Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV have been investigated in the framework of Landau hydrodynamical model. With a more realistic choice of freeze-out condition and the employment of lattice equation of state, we find transverse expansion of the collision systems is important to explain the observed data. With the increase of collision energy from RHIC to LHC, transverse flow becomes more and more important…
