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Effects of bulk viscosity and hadronic rescattering in heavy ion collisions at energies available at the BNL Relativistic Heavy Ion Collider and at the CERN Large Hadron Collider
Abstract
We describe ultrarelativistic heavy ion collisions at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider with a hybrid model using the IP-Glasma model for the earliest stage and viscous hydrodynamics and microscopic transport for the later stages of the collision. We demonstrate that within this framework the bulk viscosity of the plasma plays an important role in describing the experimentally observed radial flow and azimuthal anisotropy simultaneously. We further investigate the dependence of observables on the temperature below which we employ the microscopic transport description.
... For shear viscosity, we assume a constant shear viscosity over entropy ratio η/s = 0.08 or η/s = 0.16 [45]. For bulk viscosity, we use the temperature-dependent parametrization of ζ/s(T ) by the McGill group [42,46,47]. We perform particlization following the Cooper-Frye prescription [19] on a freezeout hypersurface at T = 130 MeV (corresponding to an energy density 0.18 GeV/fm 3 ). ...
... Note, finally, that there is some arbitrariness in the choice of the viscous correction to the momentum distribution at freeze-out [49][50][51]. We choose the Chapman-Enskog prescription [42,47]. Fig. 1 (a) displays spectra of unindentified charged particles. ...
... One sees that hydrodynamics generally underestimates the transverse momentum of protons compared to that of pions and kaons. It is a well-known feature which can be improved [47] by taking into account hadronic rescatterings after the end of the hydrodynamic evolution [60,61]. Fig. 2 (b) presents our predictions for v 0 (p T )/v 0 of identified particles. ...
Event-by-event fluctuations in the initial stages of ultrarelativistic nucleus-nucleus collisions depend little on rapidity. The hydrodynamic expansion which occurs in later stages then gives rise to correlations among outgoing particles which depend weakly on their relative rapidity. Azimuthal correlations, through which anisotropic flow () is defined, have been the most studied. Here we study a new observable introduced in 2020 by Schenke, Shen and Teaney and dubbed , which quantifies the relative change in the spectrum induced by a fluctuation. We describe how it can be measured. Using hydrodynamic simulations, we make quantitative predictions for of charged and identified hadrons. We then discuss how relates to two phenomena which have been measured: The increase of the mean transverse momentum in ultracentral collisions, and the event-by-event fluctuations of the transverse momentum per particle . We show that determines the dependence of these quantities on the cuts implemented in the analysis. We quantitatively explain the rise of observed by ATLAS as the upper -cut is increased from 2 to 5~GeV/c.
... While shear viscosity primarily affects collective behaviour and momentum anisotropy, bulk viscosity retards the overall rate of radial expansion and hence reduces average momentum of the produced particles. In literature hydrodynamic simulations of heavy-ion collisions including both the shear and bulk viscous corrections have been performed with various initial conditions [20][21][22][23][24][25][26][27][28][29][30][31]. The studies demonstrate that bulk viscosity can have a visible effect on the bulk observables of heavy-ion collisions at RHIC and LHC. ...
... Simulations with MUSIC hydrodynamical model with IP-Glasma initial conditions [29], have shown that inclusion of a finite bulk viscosity coefficient leads to a better description of the integrated ansiotropic flow coefficients (v n ) in in ultra-central Pb-Pb collisions at LHC, while reducing η/s by 32% from 0.22 to 0.15. An improved agreement is also observed between the realistic hybrid simulations [30,31] using MUSIC+UrQMD model with IP-Glasma initial conditions and a multitude of integrated and differential measurements from Pb-Pb collisions at LHC and Au-Au collisions at RHIC, in presence of bulk viscosity. Inclusion of finite bulk viscosity of the order ζ /s 0.3 near the QCD phase transition, can simultaneously describe the centrality dependence of multiplicity and < p T > of pions, kaons and protons and reduces the shear viscosity by almost 50% in order to preserve the model agreement with the measured harmonic flow coefficients. ...
In this article, we reexamine the formulation for extraction of Knudsen number ( K ), the ratio of shear viscosity to entropy density ( η / s ), within the incomplete thermalization scenario, using eccentricity scaling of elliptic flow ( v 2 ) of final state hadrons. Data on centrality dependence of charged hadron v 2 in Xe–Xe and Pb–Pb collisions, measured by ALICE and CMS collaborations at LHC are analyzed for this purpose. Results have been compared using two different models of collision namely Glauber Monte Carlo and TRENTO. The measured v 2 , even for s NN = 5.02 TeV most central Pb–Pb collisions is found to be below the ideal hydrodynamic limit by at least 15 % . Extracted η / s of the medium exhibit heavy dependence on the employed initial conditions. Impact of the Pade approximants based alternative formulation of the functional relation between v 2 and K are also investigated in detail. Our studies reconfirm the importance of clarifying the initial state configuration as well as the inbuilt ambiguities in employing the transport approach based on incomplete equilibrium in a strongly coupled regime at LHC.
... [hep-ph] 4 Mar 2025 momentum of the produced particles. In literature hydrodynamic simulations of heavy-ion collisions including both the shear and bulk viscous corrections have been performed with various initial conditions [20][21][22][23][24][25][26][27][28][29][30][31]. ...
... Simulations with MU-SIC hydrodynamical model with IP-Glasma initial conditions [29], have shown that inclusion of a finite bulk viscosity coefficient leads to a better description of the integrated ansiotropic flow coefficients (v n ) in in ultra-central Pb-Pb collisions at LHC, while reducing η/s by 32% from 0.22 to 0.15. An improved agreement is also observed between the realistic hybrid simulations [30,31] using MU-SIC+UrQMD model with IP-Glasma initial conditions and a multitude of integrated and differential measurements from Pb-Pb collisions at LHC and Au-Au collisions at RHIC, in presence of bulk viscosity. Inclusion of finite bulk viscosity of the order ζ/s ≃ 0.3 near the QCD phase transition, can simultaneously describe the centrality dependence of multiplicity and < p T > of pions, kaons and protons and reduces the shear viscosity by almost 50% in order to preserve the model agreement with the measured harmonic flow coefficients. ...
In this article, we reexamine the formulation for extraction of Knudsen number (K), the ratio of shear viscosity to entropy density (), within the incomplete thermalization scenario, using eccentricity scaling of elliptic flow () of final state hadrons. Data on centrality dependence of charged hadron in Xe-Xe and Pb-Pb collisions, measured by ALICE and CMS collaborations at LHC are analyzed for this purpose. Results have been compared using two different models of collision namely Glauber Monte Carlo and TRENTO. The measured , even for TeV most central Pb-Pb collisions is found to be below the ideal hydrodynamic limit by at least . Extracted of the medium exhibit heavy dependence on the employed initial conditions. Impact of the Pade approximants based alternative formulation of the functional relation between and K are also investigated in detail. Our studies reconfirm the importance of clarifying the initial state configuration as well as the inbuilt ambiguities in employing the transport approach based on incomplete equilibrium in a strongly coupled regime at LHC.
... At the forward rapidity where the temperature becomes small, the behavior of η/s in the hadronic phase affects the elliptic flow [22,24]. Now not only the shear viscosity but also the bulk viscosity are included in relativistic viscous hydrodynamic simulations [25][26][27][28][29][30][31][32][33][34][35]. Generally bulk viscosity reduces the growth of radial flow in hydrodynamic expansion. ...
... Generally bulk viscosity reduces the growth of radial flow in hydrodynamic expansion. In computations with IP-Glasma initial condition, finite bulk viscosity is important for explanation of experimental data, for example, mean p T [32,33,35]. However, the evaluation of the effect of bulk viscosity in the calculation of particle distribution in the Cooper-Frye formula is not fixed yet. ...
Using our developed new relativistic viscous hydrodynamics code, we investigate the temperature dependence of shear and bulk viscosities from comparison with the ALICE data: single particle spectra and collective flows of Pb+Pb TeV collisions at the Large Hadron Collider. We find that from the comprehensive analyses of centrality dependence of single particle spectra and collective flows we can extract detailed information on the quark-gluon plasma bulk property, without the information being smeared by the final state interactions.
... There have been several attempts using lattice QCD techniques to compute the plasma's shear viscosity for a pure gluon system [19][20][21][22]. On the other hand, extensive phenomenological studies were able to show that the hadronic observables measured from heavy-ion collisions are sensitive to the viscosities in the QGP [14,[23][24][25][26][27][28]. There have been many studies using hydrodynamics in heavy-ion collision simulations to estimate the specific shear viscosity η/s for the QGP [23,24,[29][30][31]. ...
... Our model provides a good description of the STAR measurements for pions and kaons, while slightly underestimating the proton and anti-proton mean p T but still within the experimental uncertainties. The averaged transverse momenta of protons is more sensitive to the scattering cross sections and baryon-anti-baryon annihilation processes in the hadronic transport model [28]. For the mid-rapidity observables at √ s NN = 19.6 ...
This work presents a Bayesian inference study for relativistic heavy-ion collisions in the Beam Energy Scan program at the Relativistic Heavy-Ion Collider. The theoretical model simulates event-by-event (3+1)D collision dynamics using hydrodynamics and hadronic transport theory. We analyze the model's 20-dimensional posterior distributions obtained using three model emulators with different accuracy and demonstrate the essential role of training an accurate model emulator in the Bayesian analysis. Our analysis provides robust constraints on the Quark-Gluon Plasma's transport properties and various aspects of (3+1)D relativistic nuclear dynamics. By running full model simulations with 100 parameter sets sampled from the posterior distribution, we make predictions for -differential observables and estimate their systematic theory uncertainty. A sensitivity analysis is performed to elucidate how individual experimental observables respond to different model parameters, providing useful physics insights into the phenomenological model for heavy-ion collisions.
... One instance of the aforementioned simulation codes is MUSIC [24][25][26][27]. In this case, the expressions for the various transport coefficients required in the simulations were determined using calculations for an ultrarelativistic singlecomponent gas [28]. ...
... Similar relations were derived for the HRG model, see Eqs. (25), (26), and (29). We further note that similar asymptotic expressions, derived for a single component gas [28], are often used in fluid-dynamical simulations of heavy-ion collisions [25][26][27]. We note that the introduction of a temperature dependence mass to recover QCD thermodynamic modified qualitatively the asymptotic expressions for most of these transport coefficients. ...
We calculate all transport coefficients of second order transient hydrodynamics in two effective kinetic theory models: a hadron-resonance gas and a quasiparticle model with thermal masses tuned to reproduce QCD thermodynamics. We compare the corresponding results with calculations for an ultrarelativistic single-component gas, that are widely employed in hydrodynamic simulations of heavy ion collisions. We find that both of these effective models display a qualitatively different normalized bulk viscosity, when compared to the calculation for the single-component gas. Indeed, ζ/[τΠ(ε0 + P0)] ≃ 16.91(1/3 − c 2 s) 2 , for the hadron-resonance gas model, and ζ/[τΠ(ε0 + P0)] ≃ 5(1/3−c 2 s) for the quasiparticle model. Differences are also observed for many second-order transport coefficients, specially those related to the bulk viscous pressure. The transport coefficients derived are shown to be consistent with fundamental linear stability and causality conditions.
... The investigation of ultrarelativistic heavy-ion collisions motivates the study of various transport phenomena [1][2][3][4][5][6][7][8]. In particular, the description of the quark-gluon plasma phase (QGP), a fluid in which quarks and gluons are deconfined, is performed in terms of relativistic dissipative hydrodynamic models [9][10][11][12][13][14]. Hydrodynamics describes the long-time, long-wavelength behavior of the conserved quantities of a given system. ...
... Given the assumptions Eqs. (14) and (15), the Fourier-space evolution of the perturbations around local equilibrium in this scenario is given by ...
Using an analytical result for the eigensystem of the linearized collision term for a classical system of massless scalar particles with quartic self-interactions, we show that the shear-stress linear response function possesses a branch-cut singularity that covers the whole positive imaginary semi-axis. This is demonstrated in two ways: (1) by truncating the exact, infinite linear system of linear equations for the rank-two tensor modes, which reveals the cut touching the origin; and (2) by employing the Trotterization techniques to invert the linear response problem. The former shows that the first pole tends towards the origin and the average separation between consecutive poles tends towards zero as power laws in the dimension of the basis. The latter allows one to obtain the response function in closed form in terms of Tricomi hypergeometrical functions, which possess a branch-cut on the above-mentioned semi-axis. This suggests that the presence of a cut along the imaginary frequency axis of the shear stress correlator, inferred from previous numerical analyses of weakly coupled scalar λφ 4 theories, does not arise due to quantum statistics but instead emerges from the fundamental properties of this system's interactions.
... The primary objective of our Bayesian analysis is to determine these six model parameters simultaneously, allowing them to vary within predefined intervals (see Table I). These intervals are based on physical considerations and knowledge from previous studies [23,25,32,61,62]. It is worth mentioning that we have confirmed a posteriori that the optimal values fall within these intervals rather than on their boundaries, and, in cases where no clear convergence was obtained, larger intervals were employed. ...
... Furthermore, the inclusion of the hyperon data leads to an increase in the chemical freeze-out temperature. This finding is consistent with previous observations using hydrodynamic simulations [23,61], suggesting that strange and Table II. The configuration involving only pions and kaons is depicted in a lighter color, reflecting the lack of convergence to a single minimum in the MCMC procedure for this specific setup. ...
A phenomenological analysis of the experimental measurements of transverse momentum spectra of identified charged hadrons and strange hyperons in Pb-Pb and Xe-Xe collisions at the CERN Large Hadron Collider (LHC) is presented. The analysis is based on the relativistic fluid dynamics description implemented in the numerically efficient FluiduM approach. Building on our previous work, we separate in our treatment the chemical and kinetic freeze-outs, and incorporate the partial chemical equilibrium to describe the late stages of the collision evolution. This analysis makes use of Bayesian inference to determine key parameters of the quark-gluon plasma (QGP) evolution and its properties including the shear and bulk viscosity to entropy ratios, the initialization time, the initial entropy density, and the freeze-out temperatures. The physics parameters and their posterior probabilities are extracted using a global search in multidimensional space with modern machine learning tools, such as ensembles of neural networks. We employ our newly developed fast framework to assess systematic uncertainties in the extracted model parameters by systematically varying key components of our analysis.
... The primary objective of our Bayesian analysis is to determine these six model parameters simultaneously, allowing them to vary within predefined intervals (see Tab. I). These intervals are based on physical considerations and knowledge from previous studies [23,25,32,61,62]. It is worth mentioning that we have confirmed a posteriori that the optimal values fall within these intervals rather than on their boundaries, and in cases where no clear convergence was obtained, larger intervals were employed. ...
... Furthermore, the inclusion of the Λ hyperon data leads to an increase in the chemical freeze-out temperature. This finding is consistent with previous observations using hydrodynamic simulations [23,61], suggesting that strange and multi-strange baryons are more sensitive to changes in the transition temperature between the fluid evolution and the hadronic transport phases. This aligns with proposals in the literature indicating that strange hadrons may undergo chemical freeze-out earlier than non-strange particles [76][77][78][79]. ...
A phenomenological analysis of the experimental measurements of transverse momentum spectra of identified charged hadrons and strange hyperons in \PbPb and \XeXe collisions at the LHC is presented. The analysis is based on the relativistic fluid dynamics description implemented in the numerically efficient \fluidum approach. Building on our previous work, we separate in our treatment the chemical and kinetic freeze-out, and incorporate the partial chemical equilibrium to describe the late stages of the collision evolution. This analysis makes use of Bayesian inference to determine key parameters of the QGP evolution and its properties including the shear and bulk viscosity to entropy ratios, the initialisation time, the initial entropy density, and the freeze-out temperatures. The physics parameters and their posterior probabilities are extracted using a global search in multidimensional space with modern machine learning tools, such as ensembles of neural networks. We employ our newly developed fast framework to assess systematic uncertainties in the extracted model parameters by systematically varying key components of our analysis.
... This difference arises because electromagnetic emission is more heavily weighted toward the hottest regions (i.e. with a higher power of T [70]) than the energy density weightings used in defining v prefrz r . In contrast, hadronic observables capture the final-state expansion: v frz r reflects conditions at chemical freezeout, while v kin r additionally accounts for hadronic acceleration between chemical and kinetic freezeout [71,72]. Figure 3 thus encapsulates the continuous development of radial flow, with each observable providing sensitivity to a different stage of the system's evolution. ...
We present a novel multimessenger approach to extract the effective radial flow of the quark-gluon plasma (QGP) by jointly analyzing thermal photon and dilepton spectra in heavy-ion collisions. A key feature of this method is that it circumvents the need for an unmeasurable reference -- the temperature extracted from the photon spectrum in the absence of flow -- by establishing a linear correlation between it and the dilepton-inferred temperature within a calibrated framework. By leveraging the complementary sensitivities of photons and dileptons, we define an effective radial flow observable that reflects early-time collectivity and expansion dynamics. We find that this observable exhibits a strong correlation with the spacetime-averaged radial velocity of the QGP, providing it with clear physical meaning as a measure of collective expansion. Together with previous results linking dilepton temperatures to initial QGP conditions, our work establishes a consistent framework for electromagnetic tomography of the QGP, offering direct access to its early-time dynamics.
... In the hydrodynamic model, the impact of shear and bulk viscosities, η and ζ, on finalstate observables has been extensively studied [111,119,120,123,[236][237][238][239][240][241][242][243][244][245][246]. The values of η/s and ζ/s (where s is the entropy density), are quantitatively extracted through model-todata comparisons [122,189,[247][248][249][250]. ...
This thesis aims to elucidate the role of initial baryon stopping and its diffusion in heavy-ion collisions (HIC) using hydrodynamic model. In this regard, we have studied the observable-directed flow () of identified hadrons, particularly the of baryons and antibaryons, as well as the splitting observed between them in detail. We propose a new ansatz for the initial baryon distribution. By employing this initial baryon deposition model alongside a tilted energy distribution as inputs to a hybrid framework, we successfully describe the rapidity-odd of identified hadrons, including the elusive baryon-antibaryon splitting of across a wide range of . Our model, incorporating baryon stopping and it's subsequent diffusion within a relativistic hydrodynamic framework and employing a crossover equation of state derived from lattice QCD calculations, establishes a non-critical baryonic baseline. Moreover, we demonstrate that recent STAR measurements of the centrality and system-size dependence of splitting between oppositely charged hadrons-attributed to electromagnetic field effects-are significantly influenced by background contributions from baryon stopping and its diffusion. Furthermore, we show that the rapidity dependence of the splitting of the rapidity-even component of between p and is highly sensitive to the initial baryon deposition scheme. If measured experimentally, this could constraint the rapidity dependence of the initial baryon deposition profile. Moreover, it could offer valuable phenomenological insights into the baryon junction picture and help refine constraints on the baryon diffusion coefficient of the medium. Notably, utilizing this phenomenologically successful baryon deposition model, we present the first estimation of the baryon diffusion coefficient for the strongly interacting QCD matter created in HIC.
... Lattice QCD calculations face numerical challenges [328][329][330]. Nevertheless, many theoretical predictions support a non-vanishing shear viscosity over entropy ratio η/s [47,331,332], although many lQCD approaches have to limit themselves to pure gluon systems [332][333][334][335]. On the other hand, many phenomenological studies have succeeded in showing that the hadronic observables measured from heavy-ion collisions are sensitive to the viscosities in the QGP [177,239,242,323,[336][337][338]. In the default approach, collision energy dependent constant values for η/s are chosen, the value of which can be found in [221]. ...
This thesis presents a comprehensive study of transport coefficients in relativistic heavy‐ion collisions using a multi‐stage hybrid simulation framework. The core model, SMASH-vHLLE-Hybrid, integrates the SMASH hadronic transport code for early non‐equilibrium dynamics with (3+1)D viscous hydrodynamics (vHLLE) for the hot, dense phase, followed by Cooper–Frye particlization and hadronic afterburner in SMASH . We assess the sensitivity of anisotropic flow observables to three distinct initial‐state models—IP-Glasma, TRENTo, and SMASH—to quantify model‐dependence in the extraction of shear viscosity . Building on this, we introduce a parametrization of shear viscosity η/s(ϵ,ρ) as a function of energy density and net baryon density, demonstrating that incorporating µB‐dependence can reduce uncertainties arising from particlization criteria . A Bayesian inference framework, accelerated by Gaussian Process emulators, is employed to fit experimental data across beam energies, yielding posterior distributions for temperature‐ and baryochemical‐potential‐dependent transport coefficients. The analysis indicates that η/s reaches a minimum near the QCD transition temperature and increases at lower temperatures, while ζ/s remains nonzero with a broad inferred range . These findings highlight the pivotal roles of initial‐state fluctuations and detailed viscosity parametrizations in hybrid models and provide constraints on the µB‐dependence of η/s and ζ/s from heavy‐ion collision data. The results pave the way for future studies employing more differential observables and refined initial‐state characterizations to tighten constraints on QCD transport properties.
... The effects of hadronic rescattering on elliptic flow have been studied in both the UrQMD model and the hydrodynamic + cascade hybrid frameworks, showing satisfactory agreement with experimental results [25,26]. However, these studies consistently reveal that hadronic rescattering can significantly enhance elliptic flow, particularly in low transverse momentum and peripheral collisions, diverging from the AMPT model results presented in this study. ...
We investigate how hadronic scattering cross sections σH of the hadronic transport processes shape charged hadron observables in Au + Au collisions at sNN=200GeV using the AMPT (A Multi-Phase Transport) model. By adjusting cross sections, we find that larger σH reduces midrapidity charged hadron multiplicity and flattens transverse momentum spectra. While anisotropic flow is secondarily affected by σH due to its dominance by partonic stage dynamics, HBT radii for pions and kaons exhibit strong sensitivity to σH, with elastic and inelastic pion scattering driving spatial expansion. HBT radii of kaons further depend on inelastic interactions with pions, yet increasing kaon cross sections enhances kaon HBT radii without altering pion HBT radii, revealing distinct rescattering mechanisms. These results resolve the HBT underestimation in default AMPT simulations and establish critical constraints for refining transport models and quantifying hadronic viscosity in relativistic heavy-ion collisions.
... Overall, careful tuning of parameters is necessary to simultaneously describe various observables. In this context, it would also be desirable to include simulating many accelerated strongly interacting hadrons (SMASH) as an afterburner, since p T -differential observables in particular are expected to be sensitive to hadronic rescattering effects [92][93][94][95]. The results presented in this paper are intended to highlight the potential of our approach, and we prefer to postpone further tuning until after the afterburner is incorporated. ...
Subnuclear fluctuations in the initial state of heavy-ion collisions impact not only transverse long-range correlations of small systems, but also the creation of longitudinal structures, seen in particle detectors as longitudinal decorrelation observables. In this work, we study the emergence of long-range rapidity correlations in nuclear collisions based on the 3D resolved initial state model, and for the first time, connect it to experimental observables using the 3 + 1 D viscous hydrodynamics framework CLVisc. We include different sources of fluctuations at the nucleon and subnucleon level and study the effects of these additional fluctuation sources on the longitudinal structure of relevant observables, such as the flow decorrelations and directed flow.
Published by the American Physical Society 2025
... We vary T 0 across the range [0.23, 0.666] GeV in increments of 0.004 GeV, while σ is varied over [4.25, 5.06] fm with a step size of 0.028 fm. For each (T 0 , σ) combination, we solve the ideal hydrodynamic evolution and find freeze-out hypersurfaces [21] for various freeze-out temperatures T f using the MUSIC hydrodynamic code [22][23][24][25] . The final-state particles are obtained by sampling particles from these hypersurfaces using the Cooper-Frye procedure [26,27] and performing decays for unstable hadrons. ...
The mean transverse momentum of hadrons has been observed experimentally and in numerical simulations to have a power-law dependence on the hadronic multiplicity N in ultracentral relativistic heavy-ion collisions: . It has been put forward that this exponent is the speed of sound of quark-gluon plasma measured at a temperature determined from . We study step by step the connection between (i) the energy and entropy of hydrodynamic simulations and (ii) experimentally measurable observables. We show that an argument based on energy and entropy should yield an exponent equal to the pressure over energy density , rather than the speed of sound . We discuss the importance of the ``effective volume'' needed for the thermodynamics arguments. Our results indicate that the agreement of with rather than is accidental.
... There have been several attempts using lattice QCD techniques to compute the plasma's shear viscosity for a pure gluon system [31][32][33][34]. On the other hand, extensive phenomenological studies were able to show that the hadronic observables measured from heavy-ion collisions are sensitive to the viscosities in the QGP [14,24,[35][36][37][38][39]. There have been many studies using hydrodynamics in heavy-ion collision simulations to estimate the specific shear viscosity η/s for the QGP [24,35,[40][41][42]. ...
This study aims to apply statistical learning, specifically Bayesian inference, to the (3+1)D SMASH-vHLLE-hybrid model using initial conditions generated by the SMASH transport code itself, with the objective of constraining model parameters and gaining deeper insight on the temperature and baryochemical potential dependence of both the shear and the bulk viscosity. This study is performed in the hybrid approach SMASH-vHLLE, composed of the hadronic transport approach SMASH and the (3+1)D viscous hydrodynamic code vHLLE. A Bayesian framework is employed, utilizing Markov Chain Monte Carlo (MCMC) sampling to explore the parameter space. The analysis compares model predictions against experimental observables, including particle yields, momentum and flow coefficients both at midrapidity as well as in forward and backward direction. We find that the SMASH-vHLLE-hybrid framework, using hadronic initial conditions for Au+Au collisions at different beam energies, can reproduce a variety of experimental observables at midrapidity and forward/backward rapidities. Notably, the preferred posterior distribution suggests a near-vanishing specific shear viscosity in the high-temperature QGP phase, combined with moderate-to-large bulk viscosity around the phase transition region, although the constraints on baryochemical potential dependence are weak. Our findings reveal that a hadronic initial condition constrains the evolution more strictly at intermediate energies, making parameters such as the hydrodynamic onset time highly sensitive. Intriguingly, the extracted shear viscosity differs substantially from previous Bayesian analyses, motivating further systematic studies with higher-statistics data sets and refined modeling assumptions.
... This is to be expected, as the smaller size and shorter lifetime of less central events amplify the effects of weaker pressure gradients. It is known that v 2 tends to decrease with greater shear and bulk viscosities [46][47][48][49], so one can interpret quark chemical equilibration as effectively increasing these viscosities. In this work, we did not vary Π and π µν with the quark fugacity, but this result highlights the necessity of doing so in future studies. ...
The early stage of a heavy-ion collision is marked by rapid entropy production and the transition from a gluon saturated initial condition to a plasma of quarks and gluons that evolves hydrodynamically. However, during the early times of the hydrodynamic evolution, the chemical composition of the QCD medium is still largely unknown. We present a study of quark chemical equilibration in the (Q)GP using a novel model of viscous hydrodynamic evolution in partial chemical equilibrium. Motivated by the success of gluon saturated initial condition models, we initialize the QCD medium as a completely gluon dominated state. Local quark production during the hydrodynamic phase is then simulated through the evolution of time-dependent fugacities for each independent quark flavor, with the timescales set as free parameters to compare different rates of equilibration. We present the results of complete heavy-ion collision simulations using this partial chemical equilibrium model, and show the effects on hadronic and electromagnetic observables. In particular, we show that the development of flow is sensitive to the equilibration timescale, providing an empirical way to probe the chemical equilibration of the QCD medium.
... In this study, the specific shear viscosity is taken as 0.16, the temperature dependence of bulk viscosity is taken from Ref. [26], and the equation of state is taken from the HotQCD Collaboration [60]. When the temperature of the QGP fluid cell drops down to the freezeout temperature ( =150 MeV), the momentum of the thermal hadrons is obtained using the Cooper-Frye prescription, ...
We study the transverse momentum ( ) differential anisotropic flow and flow fluctuation in Pb+Pb collisions at =5.02 TeV at the LHC. A (3+1)-dimensional CLVisc hydrodynamics framework with fluctuating TRENTO (or AMPT) initial conditions is utilized to simulate the space-time evolution of the quark-gluon plasma (QGP) medium. The effects of shear viscosity and the sub-nucleon structure on anisotropic flow and flow fluctuation are analyzed. Our result shows that shear viscosity tends to suppress both flow coefficients ( , , and ) and flow fluctuation ( ) owing to its smearing effect on local density fluctuation. The flow coefficients appear to be insensitive to the sub-nucleon structure, whereas the flow fluctuation tends to be suppressed by the sub-nucleon structure in central collisions but enhanced in peripheral collisions. After taking into account the sub-nucleon structure effect, our numerical result can qualitatively describe the relative flow fluctuations ( , ) measured by the ALICE Collaboration at the LHC. We further investigate the effects of shear viscosity, sub-nucleon structure, and initial condition model on the flow angle and flow magnitude decorrelations ( , ) using the four-particle correlation method. We find that the flow decorrelation effect is typically stronger in central collisions than in peripheral collisions. The flow angle decorrelation is found to be insensitive to the shear viscosity and sub-nucleon structure, whereas the flow magnitude decorrelation shows quite different behaviors when using the TRENTO and AMPT initial condition models. Our study sheds light on the anisotropic flow, transport properties, and initial structure of the QGP created in high-energy nuclear collisions.
... Consequently, MUSIC's results depend on the choice of second-order transport coefficients, a dependence discussed in App. C. We use the typical prescription for the second-order transport coefficients in MUSIC, e.g. τ π = 5η/(ϵ + P ) (see [22,60,61] and App. C for details). ...
We conduct a numerical study of relativistic viscous fluid dynamics in the Density Frame for one-dimensional fluid flows. The Density Frame is a formulation of relativistic viscous hydrodynamics that is first-order in time, requires no auxiliary fields, and has no non-hydrodynamic modes. We compare our results to QCD kinetic theory simulations and find excellent agreement within the regime of applicability of hydrodynamics. Additionally, the Density Frame results remain well-behaved and robust near the boundary of applicability. We also compare our findings to the second-order-in-time hydrodynamic theory developed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK) and a well-known M\"uller-Israel-Stewart-type hydrodynamics code, MUSIC, which is commonly used to simulate heavy-ion collisions.
... high energy heavy-ion collisions carried out at the Large Hadron Collider (LHC) and the Relativistic Heavy Ion Collider (RHIC) create a new state of matter, the quark-gluon plasma (QGP) [1,2]. QGP is fluid-like, which makes the theoretical modeling based on hydrodynamics [3][4][5][6][7][8][9][10][11] remarkably successful. Most contemporary studies implement a so-called hybrid approach, where event-by-event an initial entropy distribution [12][13][14][15][16][17][18][19][20][21] is followed by viscous relativistic hydrodynamic evolution [22][23][24][25][26][27][28], which dovetails into relativistic hadronic transport [29][30][31][32]. ...
We train a generative diffusion model (DM) to simulate ultra-relativistic heavy-ion collisions from end to end. The model takes initial entropy density profiles as input and produces two-dimensional final particle spectra, successfully reproducing integrated and differential observables. It also captures higher-order fluctuations and correlations. These findings suggest that the generative model has successfully learned the complex relationship between initial conditions and final particle spectra for various shear viscosities, as well as the fluctuations introduced during initial entropy production and hadronization stages, providing an efficient framework for resource-intensive physical goals. The code and trained model are available at https://huggingface.co/Jing-An/DiffHIC/tree/main.
... by projecting Eq. (5) along the flow velocity u μ (first equation) and orthogonal to it (second equation). We solve these equations numerically with MUSIC [39][40][41][42]. The equation of state is again a constant speed of sound one: P = c 2 s ε. ...
We introduce a minimal model of ultracentral heavy-ion collisions to study the relation between the speed of sound of the produced plasma and the final particles' energy and multiplicity. We discuss how the particles' multiplicity N tot and average energy E tot / N tot is related to the speed of sound c s by c s 2 = d ln ( E tot / N tot ) / d ln N tot if the fluid is inviscid, its speed of sound is constant and all final particles can be measured. We show that finite rapidity cuts on the particles' multiplicity N and energy E introduce corrections between c s 2 and d ln ( E / N ) / d ln N that depend on the system's lifetime. We study analytically these deviations with the Gubser hydrodynamic solution, finding that, for ultrarelativistic bosons, they scale as the ratio of the freeze-out temperature T FO over the maximum initial temperature of the fluid T 0 ; the nonthermodynamic aspect of these corrections is highlighted through their dependence on the system's initial conditions.
Published by the American Physical Society 2024
... We have used three different parametrizations of bulk viscosity as a function of temperature [64]. The first one, dubbed as "Parametrization I" was introduced in Ref. [65]: ...
We have studied the spin polarization of Λ hyperons in heavy ion collisions at center-of-mass energies s NN = 200 GeV and s NN = 5.02 TeV carried out at RHIC and LHC colliders. We have calculated the mean spin vector at local thermodynamic equilibrium, including all known first-order terms in the gradients of the thermo-hydrodynamic fields, assuming that the hadronization hypersurface has a uniform temperature. We have also included the feed-down contributions to the polarization of Λ stemming from the decays of polarized Σ ∗ and Σ 0 hyperons. The obtained results are in good agreement with the data. In general, the component of the spin vector along the global angular momentum, orthogonal to the reaction plane, shows strong sensitivity to the initial longitudinal flow velocity. Furthermore, the longitudinal component of the spin vector turns out to be very sensitive to the bulk viscosity of the plasma at the highest LHC energy. Therefore, the azimuthal dependence of spin polarization can effectively constrain the initial hydrodynamic conditions and the transport coefficients of the quark gluon plasma.
... (5) along the flow velocity u µ (first equation) and orthogonal to it (second equation). We solve these equations numerically with MUSIC [36][37][38][39]. The equation of state is again a constant speed of sound one: P = c 2 s ε. ...
We introduce a minimal model of ultracentral heavy-ion collisions to study the relation between the speed of sound of the produced plasma and the final particles' energy and multiplicity. We discuss how the particles' multiplicity and average energy is related to the speed of sound by if the fluid is inviscid, its speed of sound is constant and all final particles can be measured. We show that finite rapidity cuts on the particles' multiplicity N and energy E introduce corrections between and that depend on the system's lifetime. We study analytically these deviations with the Gubser hydrodynamic solution, finding that, for ultrarelativistic bosons, they scale as the ratio of the freezeout temperature over the maximum initial temperature of the fluid ; the non-thermodynamic aspect of these corrections is highlighted through their dependence on the system's initial conditions.
... Previous work has largely been devoted to understanding the properties (Alford & Harris 2019;) and the potential appearance of bulk viscosity Hammond et al. 2021; in the remnant or studying the idealized limit of perfect β-equilibrium (Ardevol-Pulpillo et al. 2019;Hammond et al. 2023). While the effects of microphysical viscosity in neutron star merger simulations have largely been ignored, they have been well studied in the related context of dense matter formed by heavy-ion collisions (Monnai & Hirano 2009;Bozek 2010;Song & Heinz 2010;Dusling & Schäfer 2012;Noronha-Hostler et al. 2013;Ryu et al. 2015Ryu et al. , 2018; see also Romatschke & Romatschke 2019 for a review). ...
In nuclear matter in isolated neutron stars, the flavor content (e.g., proton fraction) is subject to weak interactions, establishing flavor ( β -)equilibrium. However, there can be deviations from this equilibrium during the merger of two neutron stars. We study the resulting out-of-equilibrium dynamics during the collision by incorporating direct and modified Urca processes (in the neutrino-transparent regime) into general-relativistic hydrodynamics simulations with a simplified neutrino transport scheme. We demonstrate how weak-interaction-driven bulk viscosity in postmerger simulations can emerge and assess the bulk viscous dynamics of the resulting flow. We further place limits on the impact of the postmerger gravitational-wave strain. Our results show that weak-interaction-driven bulk viscosity can potentially lead to a phase shift of the postmerger gravitational-wave spectrum, although the effect is currently on the same level as the numerical errors of our simulation.
... Experimental observations of hadrons, such as charged pions, kaons, and protons, are computed by combining decay contributions from short-lived primary resonances with the initial thermal abundances. While direct decay freezeout often provides a satisfactory fit to the data [30][31][32], it overlooks potential hadron rescattering and regeneration processes, which can be accounted for through the inclusion of hadronic after-burners [33,34]. An alternative simplification involves fitting the thermal spectra of pions, kaons, and protons directly to the observed particle spectra. ...
We investigate the transverse momentum spectra of identified particles at 7 and 13 TeV in pp collisions in the framework of the blast wave model with Tsallis statistics (TBW). Based on experimental data by ALICE Collaboration, we observe that the model describes the p T spectra well with the common Tsallis temperature (T) and flow velocity (β T ) but separate non-extensive parameters (q) for baryons and mesons. The parameter dependence on multiplicity as well as on collision energy is investigated, and a strong dependence on the former while a weak dependence on the latter is reported. The extracted parameters in this work consist of the initial temperature (T i ), the average transverse momentum (〈p T 〉), the Tsallis temperature (T), the flow velocity (β T ), and the non-extensive parameter (q). These parameters are found to increase a little with increasing energy, however, they (except the parameter q) decrease significantly with decreasing multiplicity. We observe that β T drops to zero at high multiplicity , while, T and q do not change their behavior. Furthermore, our analysis explore the correlations among different parameters, including associations with the charged particle multiplicity per unit pseudorapidity ( 〈dNch/dη〉 ). The correlations between T and β T , T and 〈dNch/dη〉 , β T and 〈dNch/dη〉 , T i and 〈p T 〉 and T i and 〈dNch/dη〉 demonstrates a positive relationship, while, the correlation between T and q − 1, and q − 1 and 〈dNch/dη〉 is negative. Finally, we implement an extra flow correction on the T parameter. Our findings reveal that the Doppler-corrected temperature parameter aligns closely with the T in scenarios with lower multiplicities. However, as the multiplicity increases, a noticeable divergence emerges between these parameters, indicating a widening separation between them.
... The importance of the bulk viscosity in the hydrodynamic evolution of quark gluon plasma has been emphasized in Refs. [51][52][53]. Our framework provides a direct control over this first-order transport coefficient through a choice of matching condition via b 0 . ...
Bhatnagar–Gross–Krook (BGK) collision kernel is employed in the Boltzmann equation to formulate relativistic dissipative hydrodynamics. In this formulation, we find that there remains freedom of choosing a matching condition that affects the scalar transport in the system. We also propose a new collision kernel which, unlike BGK collision kernel, is valid in the limit of zero chemical potential and derive relativistic first-order dissipative hydrodynamics using it. We study the effects of this new formulation on the coefficient of bulk viscosity.
... We will present the DNMR theory for the case where n, J , and Q are absent, so in particular all functions of ϱ, n will be functions of ϱ only, since this is the case treated in Theorems 6.14 and 6.18. This is also the situation that has been the primary focus of investigation in studies of the quark-gluon plasma [261]. We will, nevertheless, also mention some general results valid for the full set of equations derived in [81]. ...
We review some recent developments in mathematical aspects of relativistic fluids. The goal is to provide a quick entry point to some research topics of current interest that is accessible to graduate students and researchers from adjacent fields, as well as to researches working on broader aspects of relativistic fluid dynamics interested in its mathematical formalism. Instead of complete proofs, which can be found in the published literature, here we focus on the proofs' main ideas and key concepts. After an introduction to the relativistic Euler equations, we cover the following topics: a new wave-transport formulation of the relativistic Euler equations tailored to applications; the problem of shock formation for relativistic Euler; rough (i.e., low-regularity) solutions to the relativistic Euler equations; the relativistic Euler equations with a physical vacuum boundary; relativistic fluids with viscosity. We finish with a discussion of open problems and future directions of research.
... The collision of the two color glass condensates generates gluon fields [25,26] which are evolved in time with the classical Yang-Mills equations. This model is known for its success in describing a wide range of heavy-ion measurements with a limited set of parameters [2,23,[27][28][29][30][31][32]. ...
In ultrarelativistic heavy-ion collisions, a plasma of deconfined quarks and gluons is formed within 1~fm/c of the nuclei's impact. The complex dynamics of the collision before ~fm/c is often described with parametric models, which affect the predictivity of calculations. In this work, we perform a systematic analysis of LHC measurements from Pb-Pb collisions, by combining an \emph{ab-initio} model of the early stage of the collisions with a hydrodynamic model of the plasma. We obtain state-of-the-art constraints on the shear and bulk viscosity of quark-gluon plasma. We mitigate the additional cost of the ab-initio initial conditions by combining Bayesian model averaging with transfer learning, allowing us to account for important theoretical uncertainties in the hydrodynamics-to-hadron transition. We show that, despite the apparent strong constraints on the shear viscosity, metrics that balance the model's predictivity with its degree of agreement with data do not prefer a temperature-dependent specific shear viscosity over a constant value. We validate the model by comparing with discriminating observables not used in the calibration, finding excellent agreement.
... First, the Müller-Israel-Stewart equations have been very successful in the construction of phenomenological models of the quark-gluon plasma. With the help of sophisticated numerical simulations (see, e.g., [45]), these models are able to reproduce, to a great degree of accuracy, many of the experimentally observed properties of the quark-gluon plasma [13]. Because of this, they are currently the most used equations in the study of viscous effects in relativistic fluids [13]. ...
We consider equations of Müller–Israel–Stewart type describing a relativistic viscous fluid with bulk viscosity in four-dimensional Minkowski space. We show that there exists a class of smooth initial data that are localized perturbations of constant states for which the corresponding unique solutions to the Cauchy problem break down in finite time. Specifically, we prove that in finite time such solutions develop a singularity or become unphysical in a sense that we make precise. We also show that in general Riemann invariants do not exist in 1+1 dimensions for physically relevant equations of state and viscosity coefficients. Finally, we present a more general version of a result by Y. Guo and A.S. Tahvildar-Zadeh: We prove large-data singularity formation results for perfect fluids under very general assumptions on the equation of state, allowing any value for the fluid sound speed strictly less than the speed of light.
... For the final decoupling stage of the fireball evolution, the hadrons sampled from the particlization surface are fed into the hadronic Boltzmann transport code SMASH [54], which allows the hadrons to rescatter and the unstable resonances to decay and to be recreated in hadronic interactions, until the system becomes so dilute and collisions so rare that first the chemical composition and then the momentum distributions fall out of equilibrium and eventually freeze out [62][63][64][65][66][67][68][69]. To obtain sufficient particle statistics at limited computational cost, we limit the full hydrodynamic runs to a representative sample of the initial-state quantum fluctuations between 200 and 1600 hydro events, distributed over all collision centralities, per design point in parameter space (see App. A), but oversample the switching hypersurface for each hydro event many times until a sufficient number of emitted hadrons has been generated for good statistical precision of all observables of interest [7][8][9][10][11][12][13][14][15][16][17][18]. ...
Due to large pressure gradients at early times, standard hydrodynamic model simulations of relativistic heavy-ion collisions do not become reliable until O(1)\,fm/c after the collision. To address this one often introduces a pre-hydrodynamic stage that models the early evolution microscopically, typically as a conformal, weakly interacting gas. In such an approach the transition from the pre-hydrodynamic to the hydrodynamic stage is discontinuous, introducing considerable theoretical model ambiguity. Alternatively, fluids with large anisotropic pressure gradients can be handled macroscopically using the recently developed Viscous Anisotropic Hydrodynamics (VAH). In high-energy heavy-ion collisions VAH is applicable already at very early times, and at later times transitions smoothly into conventional second-order viscous hydrodynamics (VH). We present a Bayesian calibration of the VAH model with experimental data for Pb--Pb collisions at the LHC at \sqrts{}=2.76\,TeV. We find that the VAH model has the unique capability of constraining the specific viscosities of the QGP at higher temperatures than other previously used models.
While the abundances of the final state hadrons in relativistic heavy-ion collisions are rather well described by the thermal particle production, the shape of the transverse momentum, , distribution below MeV/c, is still poorly understood. We propose a procedure to quantify the model-to-data differences using Bayesian inference techniques, which allows for consistent treatment of the experimental uncertainties and tests the completeness of the available hydrodynamic frameworks. Using relativistic fluid framework FluiduM with PCE coupled to TrENTo initial state and FastReso decays, we analyze distribution of identified charged hadrons measured in heavy-ion collisions at top RHIC and the LHC energies and identify an excess of pions produced below MeV/c. Our results provide new input for the interpretation of the pion excess as either missing components in the thermal particle yield description or as an evidence for a different particle production mechanism.
We compute the homogeneous limit of non-hydrodynamic quasinormal modes (QNM's) of a phenomenologically realistic Einstein-Maxwell-Dilaton (EMD) holographic model for the Quark-Gluon Plasma (QGP) that is able to: i) {\it quantitatively} describe state-of-the-art lattice results for the QCD equation of state and higher order baryon susceptibilities with 2+1 flavors and physical quark masses up to highest values of the baryon chemical potential currently reached in lattice simulations; ii) describe the nearly perfect fluidity of the strongly coupled QGP produced in ultrarelativistic heavy ion collisions; iii) give a very good description of the bulk viscosity extracted via some recent Bayesian analyzes of hydrodynamical descriptions of heavy ion experimental data. This EMD model has been recently used to predict the location of the QCD critical point in the QCD phase diagram, which was found to be within the reach of upcoming low energy heavy ion collisions. The lowest quasinormal modes of the SO(3) rotationally invariant quintuplet, triplet, and singlet channels evaluated in the present work provide upper bounds for characteristic equilibration times describing how fast the dense medium returns to thermal equilibrium after being subjected to small disturbances. We find that the equilibration times in the different channels come closer to each other at high temperatures, although being well separated at the critical point. Moreover, in most cases, these equilibration times decrease with increasing baryon chemical potential while keeping temperature fixed.
State-of-the-art simulations of high-energy nuclear collisions rely on hybrid setups, involving in particular a pre-equilibrium stage to let the system evolve from a far-from-equilibrium initial condition towards a near-equilibrated state after which fluid dynamics can be applied meaningfully. A known issue is the mismatch between the equation of state in the fluid-dynamical evolution and the effective one in the previous stage, which leads to discontinuities at the interface between the two models. Here we introduce a new matching prescription at this interface, based on the entropy, and we compare it with the standard one relying on local energy conservation. We study the behavior of various quantities at the switching time between the models and investigate a number of final-state hadronic observables. For the latter, we show that they are not modified significantly by the choice of matching prescription, provided an appropriate normalization is chosen for the initial state. In turn, our approach reduces sizeably the ratio of bulk over thermodynamic pressure at the beginning of the fluid-dynamical stage.
We review some recent developments in mathematical aspects of relativistic fluids. The goal is to provide a quick entry point to some research topics of current interest that is accessible to graduate students and researchers from adjacent fields, as well as to researches working on broader aspects of relativistic fluid dynamics interested in its mathematical formalism. Instead of complete proofs, which can be found in the published literature, here we focus on the proofs’ main ideas and key concepts. After an introduction to the relativistic Euler equations, we cover the following topics: a new wave-transport formulation of the relativistic Euler equations tailored to applications; the problem of shock formation for relativistic Euler; rough (i.e., low-regularity) solutions to the relativistic Euler equations; the relativistic Euler equations with a physical vacuum boundary; relativistic fluids with viscosity. We finish with a discussion of open problems and future directions of research.
We review recent theoretical developments relevant to heavy-ion experiments carried out within the Beam Energy Scan program at the Relativistic Heavy Ion Collider. Our main focus is on the description of the dynamics of systems created in heavy-ion collisions and establishing the necessary connection between the experimental observables and the QCD phase diagram.
Quantum fluctuations plays an essential role in forming the collective flow of hadrons observed in relativistic heavy-ion collisions. Event-by-event fluctuations of the collective flow can arise from various sources, such as the fluctuations in the initial geometry, hydrodynamic expansion, hadronization, and hadronic evolution of the nuclear matter, while the exact contribution from each source is still an open question. Using a (3+1)-dimensional relativistic hydrodynamic model coupled to a Monte Carlo Glauber initial condition, Cooper-Frye particlization and a hadronic transport model, we explore the system-size and shape dependencies of the collective-flow fluctuations in Au+Au, Cu+Au, and O+O collisions at sNN=200 GeV. The particle yields, mean transverse momenta, two-particle and four-particle cumulant elliptic flows (v2{2} and v2{4}) from our calculation agree with the currently existing data from RHIC. Different centrality dependencies of the flow fluctuations, quantified by the v2{4}/v2{2} ratio, are found for different collision systems due to their different sizes and shapes. By comparing v2{4}/v2{2} between different hadron species, and comparing v2{4}/v2{2} to the initial state geometric fluctuations quantified by the cumulant eccentricity ratio ɛ2{4}/ɛ2{2}, we find that while the initial state fluctuations are the main source of the v2 fluctuations in large collision systems, other sources like nonlinear hydrodynamic response, hadronization, and hadronic afterburner can significantly affect the v2 fluctuations in small systems.
A global Bayesian analysis of relativistic Pb+Pb collisions at sNN=2.76TeV is performed, using a multistage model consisting of an ip-glasma initial state, a viscous fluid dynamical evolution, and a hadronic transport final state. The observables considered are from the soft sector hadronic final state. Posterior and maximum a posteriori parameter distributions that pertain to the ip-glasma and hydrodynamic phases are obtained, including the shear and bulk specific viscosity of strong interacting matter. The first use of inference with transfer learning in heavy-ion analyses is presented, together with Bayes model averaging.
In ultrarelativistic heavy-ion collisions, a plasma of deconfined quarks and gluons is formed within 1 fm/c of the nuclei’s impact. The complex dynamics of the collision before ≈1 fm/c is often described with parametric models, which affect the predictivity of calculations. In this work, we perform a systematic analysis of LHC measurements from Pb-Pb collisions, by combining an ab initio model of the early stage of the collisions with a hydrodynamic model of the plasma. We obtain state-of-the-art constraints on the shear and bulk viscosity of quark-gluon plasma. We mitigate the additional cost of the ab initio initial conditions by combining Bayesian model averaging with transfer learning, allowing us to account for important theoretical uncertainties in the hydrodynamics-to-hadron transition. We show that, despite the apparent strong constraints on the shear viscosity, metrics that balance the model’s predictivity with its degree of agreement with data do not prefer a temperature-dependent specific shear viscosity over a constant value. We validate the model by comparing with discriminating observables not used in the calibration, finding excellent agreement.
In this paper, we consider a theory defined by an energy-momentum tensor depending on a set of general fields, including the space-time metric. We prove that if the theory is causal, bounded and transforms appropriately under diffeomorphism, it will depend only on the local values of the independent fields and their covariant derivatives up to a finite order. The implications are that the energy-momentum tensor of a causal relativistic fluid can only depend on covariant derivatives only up to a finite order.
We calculate all transport coefficients of second-order transient hydrodynamics in two effective kinetic theory models: a hadron-resonance gas and a quasiparticle model with thermal masses tuned to reproduce quantum chromodynamics thermodynamics. We compare the corresponding results with calculations for an ultrarelativistic single-component gas, that are widely employed in hydrodynamic simulations of heavy ion collisions. We find that both of these effective models display a qualitatively different normalized bulk viscosity, when compared to the calculation for the single-component gas. Indeed, ζ/[τΠ(ϵ0+P0)]≃16.91(1/3−cs2)2, for the hadron-resonance gas model, and ζ/[τΠ(ϵ0+P0)]≃5(1/3−cs2) for the quasiparticle model. Differences are also observed for many second-order transport coefficients, specially those related to the bulk viscous pressure. The transport coefficients derived are shown to be consistent with fundamental linear stability and causality conditions.
This work presents the first Bayesian inference study of the (3+1)D dynamics of relativistic heavy-ion collisions and quark-gluon plasma viscosities using an event-by-event (3+1)D hydrodynamics+hadronic transport theoretical framework and data from the Relativistic Heavy Ion Collider Beam energy scan program. Robust constraints on initial state nuclear stopping and the baryon chemical potential-dependent shear viscosity of the produced quantum chromodynamic (QCD) matter are obtained. The specific bulk viscosity of the QCD matter is found to exhibit a preferred maximum around sNN=19.6 GeV. This result allows for the alternative interpretation of a reduction (and/or increase) of the speed of sound relative to that of the employed lattice-QCD based equation of state for net baryon chemical potential μB∼0.2(0.4) GeV.
Owing to large pressure gradients at early times, standard hydrodynamic model simulations of relativistic heavy-ion collisions do not become reliable until O(1) fm/c after the collision. To address this one often introduces a prehydrodynamic stage that models the early evolution microscopically, typically as a conformal, weakly interacting gas. In such an approach the transition from the prehydrodynamic to the hydrodynamic stage is discontinuous, introducing considerable theoretical model ambiguity. Alternatively, fluids with large anisotropic pressure gradients can be handled macroscopically using the recently developed viscous anisotropic hydrodynamics (VAH). In high-energy heavy-ion collisions VAH is applicable already at very early times, and at later times transitions smoothly into conventional second-order viscous hydrodynamics. We present a Bayesian calibration of the VAH model with experimental data for Pb-Pb collisions at the LHC at sNN=2.76 TeV. We find that the VAH model has the unique capability of constraining the specific viscosities of the quark-gluon plasma at higher temperatures than other previously used models.
This article summarizes our present knowledge about nuclear matter at the highest energy densities and its formation in relativistic heavy ion collisions. We review what is known about the structure and properties of the quark-gluon plasma and survey the observables that are used to glean information about it from experimental data.
Due to their weak final state interactions, the ϕ meson and Ω baryon provide unique probes of the properties of the quark-gluon plasma (QGP) formed in relativistic heavy-ion collisions. Using the quark recombination model with the quark phase-space information parametrized in a viscous blast wave, we study the transverse-momentum spectra and elliptic flows of ϕ and Ω in Au+Au collisions at sNN=200 GeV and Pb+Pb collisions at sNN=2.76 TeV. The viscous blast wave includes nonequilibrium deformations of thermal distributions due to shear and bulk stresses and thus carries information on the specific shear viscosity η/s and the specific bulk viscosity ζ/s of the QGP. We perform a model-to-data comparison with Bayesian inference and simultaneously obtain η/s=(2.08−1.09+1.10)/4π and ζ/s=0.06−0.04+0.04 at 90% C.L. for the baryon-free QGP at crossover temperature of about 160 MeV. Our work provides a unique approach to simultaneously determine the η/s and ζ/s of the QGP at hadronization.
Out-of-equilibrium reactions between different particle species are the main processes contributing to bulk viscosity in neutron stars. In this work, we numerically compare three different approaches to the modeling of bulk viscosity: the multicomponent fluid with reacting particle species and two bulk stress formalism based on the Müller-Israel-Stewart theory, namely the Hiscock-Lindblom and the Maxwell-Cattaneo models, whose flux-conservative formulation in radial gauge-polar slicing coordinates and spherical symmetry is derived in a companion paper. To our knowledge, this is the first time that a neutron star is simulated with the complete Hiscock-Lindblom model of bulk viscosity. We find that the Hiscock-Lindblom and Maxwell-Cattaneo models are good approximations of the multicomponent fluid for small perturbations and when the nonequilibrium equation of state of the fluid depends on only one independent particle fraction. For more than one independent particle fraction and for large perturbations, the bulk stress approximation is still valid but less accurate. In addition, we include the energy loss due to the luminosity of the reactions in the bulk stress formulation. We find that the energy loss due to bulk viscosity has a larger effect on the dynamics than the bulk stress or the variation in particle composition per se. The new one-dimensional, general-relativistic hydrodynamic code developed for this work, hydro-bulk-1D, is publicly available.
Binary neutron-star mergers and heavy-ion collisions are related through the properties of the hot and dense nuclear matter formed during these extreme events. In particular, low-energy heavy-ion collisions offer exciting prospects to recreate such extreme conditions in the laboratory. However, it remains unexplored to what degree those collisions can actually reproduce hot and dense matter formed in binary neutron star mergers. As a way to understand similarities and differences between these systems, we discuss their geometry and perform a direct numerical comparison of the thermodynamic conditions probed in both collisions. To enable a direct comparison, we employ a finite-temperature equation of state able to describe the entire high-energy phase diagram of quantum chromodynamics. Putting side by side the evolution of both systems, we find that laboratory heavy-ion collisions at the energy range of Elab=0.4–0.6A MeV probe (thermodynamic) states of matter that are very similar to those created in binary neutron-star mergers. These results can inform future low-energy heavy-ion collisions probing this regime.
We present (3+1)-dimensional [(3+1)D] dynamical simulations of asymmetric nuclear collisions at the BNL Relativistic Heavy Ion Collider (RHIC). Employing a dynamical initial state model coupled to (3+1)D viscous relativistic hydrodynamics, we explore the rapidity dependence of anisotropic flow in the RHIC small system scan at 200 GeV center-of-mass energy. We calibrate parameters to describe central He3+Au collisions and make extrapolations to d+Au and p+Au collisions. Our calculations demonstrate that approximately 50% of the v3(pT) difference between the measurements by the STAR and PHENIX Collaborations can be explained by the use of reference flow vectors from different rapidity regions. This emphasizes the importance of longitudinal flow decorrelation for anisotropic flow measurements in asymmetric nuclear collisions, and the need for (3+1)D simulations. We also present results for the beam energy dependence of particle spectra and anisotropic flow in d+Au collisions.
In this paper, we study and predict flow observables in 2.76 and 5.02 A TeV Pb + Pb collisions, using the iEBE-VISHNU hybrid model with TRENTo and AMPT initial conditions and with different forms of the QGP transport coefficients. With properly chosen and tuned parameter sets, our model calculations can nicely describe various flow observables in 2.76 A TeV Pb + Pb collisions, as well as the measured flow harmonics of all charged hadrons in 5.02 A TeV Pb + Pb collisions. We also predict other flow observables, including of identified particles, event-by-event distributions, event-plane correlations, (normalized) symmetric cumulants, non-linear response coefficients and -dependent factorization ratios, in 5.02 A TeV Pb + Pb collisions. We find many of these observables to remain approximately the same values as the ones in 2.76 A TeV Pb + Pb collisions. Our theoretical studies and predictions could shed light to the experimental investigations in the near future.
The elliptic, triangular, quadrangular and pentagonal anisotropic flow coefficients for π±, K± and in Pb-Pb collisions at TeV were measured with the ALICE detector at the Large Hadron Collider. The results were obtained with the Scalar Product method, correlating the identified hadrons with reference particles from a different pseudorapidity region. Effects not related to the common event symmetry planes (non-flow) were estimated using correlations in pp collisions and were subtracted from the measurement. The obtained flow coefficients exhibit a clear mass ordering for transverse momentum (pT) values below ≈ 3 GeV/c. In the intermediate pT region (3 < pT< 6 GeV/c), particles group at an approximate level according to the number of constituent quarks, suggesting that coalescence might be the relevant particle production mechanism in this region. The results for pT< 3 GeV/c are described fairly well by a hydrodynamical model (iEBE-VISHNU) that uses initial conditions generated by A Multi-Phase Transport model (AMPT) and describes the expansion of the fireball using a value of 0.08 for the ratio of shear viscosity to entropy density (η/s), coupled to a hadronic cascade model (UrQMD). Finally, expectations from AMPT alone fail to quantitatively describe the measurements for all harmonics throughout the measured transverse momentum region. However, the comparison to the AMPT model highlights the importance of the late hadronic rescattering stage to the development of the observed mass ordering at low values of pT and of coalescence as a particle production mechanism for the particle type grouping at intermediate values of pT for all harmonics.
We demonstrate that measurements of rapidity differential anisotropic flow in
heavy ion collisions can constrain the temperature dependence of the shear
viscosity to entropy density ratio {\eta}/s of QCD matter. Comparing results
from hydrodynamic calculations with experimental data from RHIC, we find
evidence for a small {\eta}/s 0.04 in the QCD cross-over region and a
strong temperature dependence in the hadronic phase. A temperature independent
{\eta}/s is disfavored by the data. We further show that measurements of the
event-by-event flow as a function of rapidity can be used to independently
constrain the initial state fluctuations in three dimensions and the
temperature dependent transport properties of QCD matter.
In this work it is shown that the use of a hydrodynamical model of heavy ion
collisions which incorporates recent developments, together with updated photon
emission rates greatly improves agreement with both ALICE and PHENIX
measurements of direct photons, supporting the idea that thermal photons are
the dominant source of direct photon momentum anisotropy. The event-by-event
hydrodynamical model uses IP-Glasma initial states and includes, for the first
time, both shear and bulk viscosities, along with second order couplings
between the two viscosities. The effect of both shear and bulk viscosities on
the photon rates is studied, and those transport coefficients are shown to have
measurable consequences on the photon momentum anisotropy.
We present high precision measurements of elliptic flow near midrapidity
() for multi-strange hadrons and meson as a function of
centrality and transverse momentum in Au+Au collisions at center of mass energy
200 GeV. We observe that the transverse momentum dependence of
and is similar to that of and p, respectively,
which may indicate that the heavier strange quark flows as strongly as the
lighter up and down quarks. This observation constitutes a clear piece of
evidence for the development of partonic collectivity in heavy-ion collisions
at the top RHIC energy. Number of constituent quark scaling is found to hold
within statistical uncertainty for both 0-30 and 30-80 collision
centrality. There is an indication of the breakdown of previously observed mass
ordering between and proton at low transverse momentum in the
0-30 centrality range, possibly indicating late hadronic interactions
affecting the proton .
The production of and baryons and their anti-particles in Pb–Pb collisions at has been measured using the ALICE detector. The transverse momentum spectra at mid-rapidity ( ) for charged Ξ and Ω hyperons have been studied in the range and , respectively, and in several centrality intervals (from the most central 0–10% to the most peripheral 60–80% collisions). These spectra have been compared with the predictions of recent hydrodynamic models. In particular, the Kraków and EPOS models give a satisfactory description of the data, with the latter covering a wider range. Mid-rapidity yields, integrated over , have been determined. The hyperon-to-pion ratios are similar to those at RHIC: they rise smoothly with centrality up to and saturate thereafter. The enhancements (yields per participant nucleon relative to those in pp collisions) increase both with the strangeness content of the baryon and with centrality, but are less pronounced than at lower energies.
The ALICE measurement of KS0 and Λ production at midrapidity in Pb-Pb collisions at √sNN=2.76 TeV is presented. The transverse momentum (pT) spectra are shown for several collision centrality intervals and in the pT range from 0.4 GeV/c (0.6 GeV/c for Λ) to 12 GeV/c. The pT dependence of the Λ/KS0 ratios exhibits maxima in the vicinity of 3 GeV/c, and the positions of the maxima shift towards higher pT with increasing collision centrality. The magnitude of these maxima increases by almost a factor of three between most peripheral and most central Pb-Pb collisions. This baryon excess at intermediate pT is not observed in pp interactions at √s=0.9 TeV and at √s=7 TeV. Qualitatively, the baryon enhancement in heavy-ion collisions is expected from radial flow. However, the measured pT spectra above 2 GeV/c progressively decouple from hydrodynamical-model calculations. For higher values of pT, models that incorporate the influence of the medium on the fragmentation and hadronization processes describe qualitatively the p T dependence of the Λ/KS0 ratio.
We study the effects of hadronic rescattering on hadron distributions in
high-energy nuclear collisions by using an integrated dynamical approach. This
approach is based on a hybrid model combining (3+1)-dimensional ideal
hydrodynamics for the quark gluon plasma (QGP), and a transport model for the
hadron resonance gas. Since the hadron distributions are the result of the
entire expansion history of the system, understanding the QGP properties
requires investigating how rescattering during the hadronic stage affects the
final distributions of hadrons. We include multi-strange hadrons in our study,
and quantify the effects of hadronic rescattering on their mean transverse
momenta and elliptic flow. We find that multi-strange hadrons scatter less
during the hadronic stage than non-strange particles, and thus their
distributions reflect the properties of the system in an earlier stage than the
distributions of non-strange particles.
Using the VISHNU hybrid model, we calculate the multiplicity, spectra, and
elliptic flow of , and in 2.76 A TeV Pb+Pb collisions.
Comparisons between our calculations and the ALICE measurements show that the
model generally describes the soft hadron data of these strange and
multi-strange hadrons at several centrality bins. Mass ordering of elliptic
flow among , K, p, , and has also been studied and
discussed. With a nice description of the particle yields, we explore chemical
and thermal freeze-out of various hadrons species at the LHC within the
framework of the VISHNU hybrid model.
We investigate the consequences of a nonzero bulk viscosity coefficient on
the transverse momentum spectra, azimuthal momentum anisotropy, and
multiplicity of charged hadrons produced in heavy ion collisions at LHC
energies. The agreement between a realistic 3D hybrid simulation and the
experimentally measured data considerably improves with the addition of a bulk
viscosity coefficient for strongly interacting matter. This paves the way for
an eventual quantitative determination of several QCD transport coefficients
from the experimental heavy ion and hadron-nucleus collision programs.
New PHENIX measurements of the anisotropic flow coefficients ,
, and for identified particles
(, , and ) obtained relative to the event planes
in Au+Au collisions at = 200 GeV are presented as
functions of collision centrality and particle transverse momenta . The
coefficients show characteristic patterns consistent with hydrodynamical
expansion of the matter produced in the collisions. For each harmonic n, a
modified valence quark number scaling plotting versus
is observed to yield a single curve for all the measured
particle species for a broad range of transverse kinetic energies .
A simultaneous blast wave model fit to the observed particle spectra and
coefficients identifies spatial eccentricities at freeze-out,
which are much smaller than the initial-state geometric values.
The interplay between shear and bulk viscosities on the flow harmonics,
's, at RHIC is investigated using the newly developed relativistic 2+1
hydrodynamical code v-USPhydro that includes bulk and shear viscosity effects
both in the hydrodynamic evolution and also at freeze-out. While shear
viscosity is known to attenuate the flow harmonics, we find that the inclusion
of bulk viscosity decreases the shear viscosity-induced suppression of the flow
harmonics bringing them closer to their values in ideal hydrodynamical
calculations. Depending on the value of the bulk viscosity to entropy density
ratio, , in the quark-gluon plasma, the bulk viscosity-driven
suppression of shear viscosity effects on the flow harmonics may require a
re-evaluation of the previous estimates of the shear viscosity to entropy
density ratio, , of the quark-gluon plasma previously extracted by
comparing hydrodynamic calculations to heavy ion data.
We compute the transport coefficients that appear in the fluid-dynamical
equations for the bulk viscous pressure and shear-stress tensor using the
14-moment approximation in the limit of small, but finite, masses. In this
limit, we are able to express all these coefficients in terms of known
thermodynamic quantities, such as the thermodynamic pressure, energy density,
and the velocity of sound. We explicitly demonstrate that the ratio of bulk
viscosity to bulk relaxation time behaves very differently, as a function of
temperature, than the ratio of shear viscosity to shear relaxation time. We
further explicitly compute, for the first time, the transport coefficients that
couple the bulk viscous pressure to the shear-stress tensor and vice versa. The
coefficient that couples bulk viscous pressure to shear-stress tensor is found
to be orders of magnitude larger than the bulk viscosity itself, suggesting
that bulk viscous pressure production owes more to this coupling than to the
expansion rate of the system.
In this paper measurements are presented of π±, K±, p, and p¯ production at midrapidity (|y|<0.5), in Pb-Pb collisions at sNN=2.76 TeV as a function of centrality. The measurement covers the transverse-momentum (pT) range from 100, 200, and 300 MeV/c up to 3, 3, and 4.6 GeV/c for π, K, and p, respectively. The measured pT distributions and yields are compared to expectations based on hydrodynamic, thermal and recombination models. The spectral shapes of central collisions show a stronger radial flow than measured at lower energies, which can be described in hydrodynamic models. In peripheral collisions, the pT distributions are not well reproduced by hydrodynamic models. Ratios of integrated particle yields are found to be nearly independent of centrality. The yield of protons normalized to pions is a factor ∼1.5 lower than the expectation from thermal models.
Using the VISHNU hybrid model that couples viscous hydrodynamics to a
microscopic hadronic transport model, we calculate the multiplicity, p_T
spectra and elliptic flow for pions, kaons, and protons in 2.76 A TeV Pb+Pb
collisions, and compare the results of our calculation to data taken by the
ALICE collaboration. Using the same inputs, we predict the p_T spectra and
elliptic flow for phi mesons and explore its flow development in the strong and
weak coupling limits through hydrodynamic calculations with different
decoupling temperatures. In addition we study the influence of baryon and
anti-baryon annihilation processes on common observables and demonstrate that
by including annihilation processes below a switching temperature of 165 MeV,
VISHNU provides a good description of the multiplicity and p_T spectra for
pions, kaons and protons measured by PHENIX and ALICE at both RHIC and the LHC.
Measurements are presented by the CMS Collaboration at the Large Hadron
Collider (LHC) of the higher-order harmonic coefficients that describe the
azimuthal anisotropy of charged particles emitted in sqrt(s[NN]) = 2.76 TeV
PbPb collisions. Expressed in terms of the Fourier components of the azimuthal
distribution, the n = 3-6 harmonic coefficients are presented for charged
particles as a function of their transverse momentum (0.3<pt<8.0GeV), collision
centrality (0-70%), and pseudorapidity (abs(eta) < 2.0). The data are analyzed
using the event plane, multi-particle cumulant, and Lee-Yang zeros methods,
which provide different sensitivities to initial state fluctuations. Taken
together with earlier LHC measurements of elliptic flow (n=2), the results on
higher-order harmonic coefficients develop a more complete picture of the
collective motion in high-energy heavy-ion collisions and shed light on the
properties of the produced medium.
We propose to modify the saturation model of Golec-Biernat and Wüsthoff by including Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution. We find considerable improvement for the total deep inelastic cross section, in particular in the large Q2 region. The successful description of deep inelastic scattering diffraction is preserved.
We predict the elliptic flow parameter v in U+U collisions at (s{sub NN})=200 GeV and in Pb+Pb collisions at (s{sub 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 is described by a hadron cascade model.
The anisotropy of the azimuthal distributions of charged particles produced in sNN=2.76 TeV PbPb collisions is studied with the CMS experiment at the LHC. The elliptic anisotropy parameter, v2, defined as the second coefficient in a Fourier expansion of the particle invariant yields, is extracted using the event-plane method, two- and four-particle cumulants, and Lee-Yang zeros. The anisotropy is presented as a function of transverse momentum (pT), pseudorapidity (η) over a broad kinematic range, 0.3<pT<20 GeV/c, |η|<2.4, and in 12 classes of collision centrality from 0 to 80%. The results are compared to those obtained at lower center-of-mass energies, and various scaling behaviors are examined. When scaled by the geometric eccentricity of the collision zone, the elliptic anisotropy is found to obey a universal scaling with the transverse particle density for different collision systems and center-of-mass energies.
Bulk viscosity effects on the collective flow harmonics in heavy ion
collisions are investigated, on an event by event basis, using a newly
developed 2+1 Lagrangian hydrodynamic code named v-USPhydro which implements
the Smoothed Particle Hydrodynamics (SPH) algorithm for viscous hydrodynamics.
A new formula for the bulk viscous corrections present in the distribution
function at freeze-out is derived starting from the Boltzmann equation for
multi-hadron species. Bulk viscosity is shown to enhance the collective flow
Fourier coefficients from to when GeV
even when the bulk viscosity to entropy density ratio, , is
significantly smaller than .
We find that the single-particle distribution EdN/d3p for an expanding relativistic gas described by a distribution function obeying the Boltzmann transport equation is not of the form of an integral over collective motions of a velocity weight function times a "Lorentz-transformed" rest-frame distribution function. This casts doubt on the algorithms of Milekhin and Hagedorn for determining the single-particle distribution function in their models of particle production. For the hydrodynamic model, the correct algorithm is presented.
Identified charged-particle spectra of π±, K±, p, and p̅ at midrapidity (|y|<0.1) measured by the dE/dx method in the STAR (solenoidal tracker at the BNL Relativistic Heavy Ion Collider) time projection chamber are reported for pp and d+Au collisions at √sNN=200 GeV and for Au+Au collisions at 62.4, 130, and 200 GeV. Average transverse momenta, total particle production, particle yield ratios, strangeness, and baryon production rates are investigated as a function of the collision system and centrality. The transverse momentum spectra are found to be flatter for heavy particles than for light particles in all collision systems; the effect is more prominent for more central collisions. The extracted average transverse momentum of each particle species follows a trend determined by the total charged-particle multiplicity density. The Bjorken energy density estimate is at least several GeV/fm3 for a formation time less than 1 fm/c. A significantly larger net-baryon density and a stronger increase of the net-baryon density with centrality are found in Au+Au collisions at 62.4 GeV than at the two higher energies. Antibaryon production relative to total particle multiplicity is found to be constant over centrality, but increases with the collision energy. Strangeness production relative to total particle multiplicity is similar at the three measured RHIC energies. Relative strangeness production increases quickly with centrality in peripheral Au+Au collisions, to a value about 50% above the pp value, and remains rather constant in more central collisions. Bulk freeze-out properties are extracted from thermal equilibrium model and hydrodynamics-motivated blast-wave model fits to the data. Resonance decays are found to have little effect on the extracted kinetic freeze-out parameters because of the transverse momentum range of our measurements. The extracted chemical freeze-out temperature is constant, independent of collision system or centrality; its value is close to the predicted phase-transition temperature, suggesting that chemical freeze-out happens in the vicinity of hadronization and the chemical freeze-out temperature is universal despite the vastly different initial conditions in the collision systems. The extracted kinetic freeze-out temperature, while similar to the chemical freeze-out temperature in pp, d+Au, and peripheral Au+Au collisions, drops significantly with centrality in Au+Au collisions, whereas the extracted transverse radial flow velocity increases rapidly with centrality. There appears to be a prolonged period of particle elastic scatterings from chemical to kinetic freeze-out in central Au+Au collisions. The bulk properties extracted at chemical and kinetic freeze-out are observed to evolve smoothly over the measured energy range, collision systems, and collision centralities.
The results from the STAR Collaboration on directed flow (v1), elliptic flow (v2), and the fourth harmonic (v4) in the anisotropic azimuthal distribution of particles from Au+Au collisions at √sNN=200 GeV are summarized and compared with results from other experiments and theoretical models. Results for identified particles are presented and fit with a blast-wave model. Different anisotropic flow analysis methods are compared and nonflow effects are extracted from the data. For v2, scaling with the number of constituent quarks and parton coalescence are discussed. For v4, scaling with v22 and quark coalescence are discussed.
We present STAR results on the elliptic flow v2 of charged hadrons, strange and multistrange particles from √sNN=200 GeV Au+Au collisions at the BNL Relativistic Heavy Ion Collider (RHIC). The detailed study of the centrality dependence of v2 over a broad transverse momentum range is presented. Comparisons of different analysis methods are made in order to estimate systematic uncertainties. To discuss the nonflow effect, we have performed the first analysis of v2 with the Lee-Yang zero method for KS0 and Λ. In the relatively low pT region, pT⩽2 GeV/c, a scaling with mT-m is observed for identified hadrons in each centrality bin studied. However, we do not observe v2(pT) scaled by the participant eccentricity to be independent of centrality. At higher pT,2⩽pT⩽6 GeV/c,v2 scales with quark number for all hadrons studied. For the multistrange hadron Ω, which does not suffer appreciable hadronic interactions, the values of v2 are consistent with both mT-m scaling at low pT and number-of-quark scaling at intermediate pT. As a function of collision centrality, an increase of pT-integrated v2 scaled by the participant eccentricity has been observed, indicating a stronger collective flow in more central Au+Au collisions.
The centrality dependence of transverse momentum distributions and yields for π±,K±,p, and p̅ in Au+Au collisions at √sNN=200 GeV at midrapidity are measured by the PHENIX experiment at the Relativistic Heavy Ion Collider. We observe a clear particle mass dependence of the shapes of transverse momentum spectra in central collisions below ∼2 GeV∕c in pT. Both mean transverse momenta and particle yields per participant pair increase from peripheral to midcentral and saturate at the most central collisions for all particle species. We also measure particle ratios of π−∕π+, K−∕K+, p̅ ∕p, K∕π, p∕π, and p̅ ∕π as a function of pT and collision centrality. The ratios of equal mass particle yields are independent of pT and centrality within the experimental uncertainties. In central collisions at intermediate transverse momenta ∼1.5–4.5 GeV∕c, proton and antiproton yields constitute a significant fraction of the charged hadron production and show a scaling behavior different from that of pions.
We review progress in the hydrodynamic description of heavy-ion collisions, focusing on recent developments in modeling the fluctuating initial state and event-by-event viscous hydrodynamic simulations. We discuss how hydrodynamics can be used to extract information on fundamental properties of quantum chromodynamics from experimental data, and review successes and challenges of the hydrodynamic framework.
We report measurements of the third harmonic coefficient of the azimuthal
anisotropy, v_3, known as triangular flow. The analysis is for charged
particles in Au+Au collisions at sqrtsNN = 200 GeV, based on data from the STAR
experiment at the Relativistic Heavy Ion Collider. Two-particle correlations as
a function of their pseudorapidity separation are fit with narrow and wide
Gaussians. Measurements of triangular flow are extracted from the wide
Gaussian, from two-particle cumulants with a pseudorapidity gap, and also from
event plane analysis methods with a large pseudorapidity gap between the
particles and the event plane. These results are reported as a function of
transverse momentum and centrality. A large dependence on the pseudorapidity
gap is found. Results are compared with other experiments and model
calculations.
Extensive experimental data from high-energy nucleus-nucleus collisions were recorded using the PHENIX detector at the Relativistic Heavy Ion Collider (RHIC). The comprehensive set of measurements from the first three years of RHIC operation includes charged particle multiplicities, transverse energy, yield ratios and spectra of identified hadrons in a wide range of transverse momenta (pT), elliptic flow, two-particle correlations, nonstatistical fluctuations, and suppression of particle production at high pT. The results are examined with an emphasis on implications for the formation of a new state of dense matter. We find that the state of matter created at RHIC cannot be described in terms of ordinary color neutral hadrons.
We extract the bulk viscosity of hot quark–gluon matter in the presence of light quarks from the recent lattice data on the QCD equation of state. For that purpose we extend the sum rule analysis by including the contribution of light quarks. We also discuss the universal properties of bulk viscosity in the vicinity of a second-order phase transition, as it might occur in the chiral limit of QCD at fixed strange quark mass and most likely does occur in two-flavor QCD. We point out that a chiral transition in the O(4) universality class at zero baryon density as well as the transition at the chiral critical point which belongs to the Z(2) universality class both lead to the critical behavior of bulk viscosity. In particular, the latter universality class implies the divergence of the bulk viscosity, which may be used as a signature of the critical point. We discuss the physical picture behind the dramatic increase of bulk viscosity seen in our analysis, and devise possible experimental tests of related phenomena.
Predictions and comparisons of hadronic flow observables for Pb+Pb collisions at 2.76 A TeV and 5.02 A TeV are presented using a hydrodynamics + hadronic cascade hybrid approach. Initial conditions are generated via a new formulation of the IP-Glasma model and then evolved using relativistic viscous hydrodynamics and finally fed into transport cascade in the hadronic phase. The results of this work show excellent agreement with the recent charged hadron anisotropic flow measurements from the ALICE collaboration of Pb+Pb collisions at 5.02 A TeV. Event-by-event distributions of charged hadron v n , flow event-plane correlations, and flow factorization breaking ratios are compared with existing measurements at 2.76 A TeV, and are predicted at 5.02 A TeV. Further predictions of identified hadron observables (for both light and multi-strange hadrons), such as p T -spectra and anisotropic flow coefficients, are presented.
We quantitatively estimate properties of the quark-gluon plasma created in ultra-relativistic heavy-ion collisions utilizing Bayesian statistics and a multi-parameter model-to-data comparison. The study is performed using a recently developed parametric initial condition model, TRENTO, which interpolates among a general class of particle production schemes, and a modern hybrid model which couples viscous hydrodynamics to a hadronic cascade. We calibrate the model to multiplicity, transverse momentum, and flow data and report constraints on the parametrized initial conditions and the temperature-dependent transport coefficients of the quark-gluon plasma. We show that initial entropy deposition is consistent with a saturation-based picture, extract a relation between the minimum value and slope of the temperature-dependent specific shear viscosity, and find a clear signal for a nonzero bulk viscosity.
Using iEBE-VISHNU hybrid model with the AMPT initial conditions, we study the higher order flow harmonics of identified hadrons in 2.76 A TeV Pb+Pb collisions. Comparison with the recent ALICE measurements at 20-30\% centrality shows that our calculations nicely describe the data below 2 GeV, especially for the , and mass-orderings among pions, kaons and protons. We also extended the calculations to other centrality bins, which presents similar mass-ordering patterns for these flow harmonics as the ones observed at 20-30\% centrality. In the later part of this article, we explore the development of mass ordering/splitting during the hadronic evolution through the comparison runs from iEBE-VISHNU hybrid model and pure hydrodynamics with different decoupling temperatures.
We review several facets of the hydrodynamic description of the relativistic
heavy ion collisions, starting from the historical motivation to the present
understandings of the observed collective aspects of experimental data,
especially those of the most recent RHIC and LHC results. In this report, we
particularly focus on the conceptual questions and the physical foundations of
the validity of the hydrodynamic approach itself. We also discuss recent
efforts to clarify some of the points in this direction, such as the various
forms of derivations of relativistic hydrodynamics together with the
limitations intrinsic to the traditional approaches, variational approaches,
known analytic solutions for special cases, and several new theoretical
developments. Throughout this review, we stress the role of course-graining
procedure in the hydrodynamic description and discuss its relation with the
physical observables through the analysis of a hydrodynamic mapping of a
microscopic transport model. Several questions to be answered to clarify the
physics of collective phenomena in the relativistic heavy ion collisions are
pointed out.
The role of baryon-antibaryon annihilation during the hadronic stage of a relativistic heavy ion collision is explored by simulating the chemical evolution of a hadron gas. Beginning with a chemically equilibrated gas at an initial temperature of 170 MeV, the chemical composition of a representative hydrodynamic cell is followed throughout the hadronic stage. The cell's volume changes with time according to a parametrization that mimics a three-dimensional hydrodynamic expansion. The chemical evolution includes both annihilation and regeneration of baryons, consistent with detailed balance. During the hadronic stage, the number of baryons drops by approximately 40% for the case in which there is no net baryonic charge. When the calculations are performed without the baryon regenerating processes, e.g., 5\pi\rightarrow, the loss of baryons was found to be closer to 50%. After accounting for annihilation, yields are consistent with measurements from the ALICE Collaboration at the Large Hadron Collider (LHC). Baryon annihilation is shown to alter the extracted chemical breakup temperature by significantly changing the p/\pi ratio. Assuming that annihilation cross sections are independent of the strangeness and isospin of the annihilating baryon and antibaryon, the loss of strange baryons from annihilation is found to be similar.
We study the onset of bubble formation (cavitation) in the quark-gluon plasma
as a result of the reduction of the effective pressure from bulk-viscous
corrections. By calculating velocity gradients in typical models for
quark-gluon plasma evolution in heavy-ion collisions, we obtain results for the
critical bulk viscosity above which cavitation occurs. Since present
experimental data for heavy-ion collisions seems inconsistent with the presence
of bubbles above the phase transition temperature of QCD, our results may be
interpreted as an upper limit of the bulk viscosity in nature. Our results
indicate that bubble formation is consistent with the expectation of
hadronisation in low-temperature QCD.
The elliptic flow coefficient () of identified particles in Pb--Pb
collisions at TeV was measured with the ALICE
detector at the LHC. The results were obtained with the Scalar Product method,
a two-particle correlation technique, using a pseudo-rapidity gap of
between the identified hadron under study and the
reference particles. The is reported for , ,
, p+, ,
+, + and
+ in several collision centralities. In the low
transverse momentum () region, GeV/c,
exhibits a particle mass dependence consistent with
elliptic flow accompanied by the transverse radial expansion of the system with
a common velocity field. The experimental data for and
are described fairly well by hydrodynamical calculations coupled to a hadronic
cascade model (VISHNU) for central collisions. However, the same calculations
fail to reproduce the for p+,
, + and
+. For transverse momentum values larger than about 3
GeV/c, particles tend to group according to their type, i.e. mesons and
baryons. However, the experimental data at the LHC exhibit deviations from the
number of constituent quark (NCQ) scaling at the level of 20 for
GeV/c.
Comparison of hydrodynamic and "hybrid" hydrodynamics+transport calculations
to heavy-ion data inevitably requires the conversion of the fluid to particles.
For dissipative fluids the conversion is ambiguous without additional theory
input complementing hydrodynamics. We obtain self-consistent shear viscous
phase space corrections from linearized Boltzmann transport theory for a gas of
hadrons. These corrections depend on the particle species, and incorporating
them in Cooper-Frye freezeout affects identified particle observables. For
example, with additive quark model cross sections,proton elliptic flow is
larger than pion elliptic flow at moderately high in Au+Au collisions
at RHIC. This is in contrast to Cooper-Frye freezeout with the commonly used
"democratic Grad" ansatz that assumes no species dependence. Various analytic
and numerical results are also presented for massless and massive two-component
mixtures to aid the interpretation. Self-consistent viscous corrections for
each species are tabulated in Appendix F for convenient inclusion in pure
hydrodynamic and hybrid calculations.
The first calculation of triangular flow vâ in Au+Au collisions at â(s{sub NN})=200A GeV from an event-by-event (3+1)d transport+hydrodynamics hybrid approach is presented. As a response to the initial triangularity εâ of the collision zone, vâ is computed in a similar way to the standard event-plane analysis for elliptic flow vâ. 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 vâ and vâ for charged particles as well as identified particles. We conclude that an event-by-event treatment of the ideal hydrodynamic evolution starting with realistic initial conditions generates the main features expected for triangular flow.
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(p{sub T}). However, the momentum dependence of the departure from equilibrium is not known a priori, and it is probably not proportional to p{sub 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{sub T}³². The weaker p{sub T} dependence leads to straighter v(p{sub 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.
We present the scaling properties of λ, ξ, and Ï in midrapidity Au+Au collisions at the Brookhaven National Laboratory Relativistic Heavy Ion Collider at â(s{sub NN})=200 GeV. The yield of multistrange baryons per participant nucleon increases from peripheral to central collisions more rapidly than that of λ, indicating an increase of the strange-quark density of the matter produced. The strange phase-space occupancy factor γ{sub s} approaches unity for the most central collisions. Moreover, the nuclear modification factors of p, λ, and ξ are consistent with each other for 2
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 pT-spectra and pseudorapidity distributions for Au+Au collisions at s=200GeV and present results for the anisotropic flow coefficients v2 and v4 as a function of both pT and pseudorapidity eta. We were able to determine v4 with high numerical precision, finding that it does not strongly depend on the choice of initial condition or equation of state.
We argue that known systematics of hadron cross sections may cause different
particles to freeze out of the fireball produced in heavy-ion collisions at
different times. We find that a simple model with two freezeout points is a
better description of data than that with a single freezeout, while still
remaining predictive. The resulting fits seem to present constraints on the
late stage evolution of the fireball, including the tantalizing possibility
that the QCD chiral transition influences the yields at sqrt(S)=2700 GeV and
the QCD critical point those at sqrt(S)=17.3 GeV.
The event-by-event multiplicity distribution, the energy densities and energy density weighted eccentricity moments εn (up to n=6) at early times in heavy-ion collisions at both the BNL Relativistic Heavy Ion Collider (RHIC) (√s=200 GeV) and the CERN Large Hardron Collider (LHC) (√s=2.76 TeV) are computed in the IP-Glasma model. This framework combines the impact parameter dependent saturation model (IP-Sat) for nucleon parton distributions (constrained by HERA deeply inelastic scattering data) with an event-by-event classical Yang-Mills description of early-time gluon fields in heavy-ion collisions. The model produces multiplicity distributions that are convolutions of negative binomial distributions without further assumptions or parameters. In the limit of large dense systems, the n-particle gluon distribution predicted by the Glasma-flux tube model is demonstrated to be nonperturbatively robust. In the general case, the effect of additional geometrical fluctuations is quantified. The eccentricity moments are compared to the MC-KLN model; a noteworthy feature is that fluctuation dominated odd moments are consistently larger than in the MC-KLN model.
From an analysis of various types of data obtained in relativistic nuclear collisions, the following picture has emerged in thermal and hydrodynamical descriptions: as the fluid expands and cools, particles first undergo a chemical freeze out at Tch.f.∼160–200 MeV, then a thermal freeze out at Tth.f.∼100–140 MeV. In this paper we show how to incorporate these separate freeze outs consistently in a hydrodynamical code via a modified equation of state (general case) or via a modified Cooper-Frye formula (particular case of Tch.f. close to Tth.f. or few particle species undergoing early chemical freeze out). The modified equation of state causes faster cooling and may have sizable impact on the predicted values of observables.
In hybrid models, which combine hydrodynamical and transport approaches to
describe different stages of heavy-ion collisions, conversion of fluid to
individual particles, particlization, is a non-trivial technical problem. We
describe in detail how to find the particlization hypersurface in a 3+1
dimensional model, and how to sample the particle distributions evaluated using
the Cooper-Frye procedure to create an ensemble of particles as an initial
state for the transport stage. We also discuss the role and magnitude of the
negative contributions in the Cooper-Frye procedure.
This paper describes the conclusions that can be drawn from the data taken thus far with the PHOBOS detector at RHIC. In the most central Au + Au collisions at the highest beam energy, evidence is found for the formation of a very high energy density system whose description in terms of simple hadronic degrees of freedom is inappropriate. Furthermore, the constituents of this novel system are found to undergo a significant level of interaction. The properties of particle production at RHIC energies are shown to follow a number of simple scaling behaviors, some of which continue trends found at lower energies or in simpler systems. As a function of centrality, the total number of charged particles scales with the number of participating nucleons. When comparing Au + Au at different centralities, the dependence of the yield on the number of participants at higher pT (∼4 GeV/c) is very similar to that at low transverse momentum. The measured values of charged particle pseudorapidity density and elliptic flow were found to be independent of energy over a broad range of pseudorapidities when effectively viewed in the rest frame of one of the colliding nuclei, a property we describe as “extended longitudinal scaling”. Finally, the centrality and energy dependences of several observables were found to factorize to a surprising degree.
We study the elliptic flow coefficient v2(η,b) in Au + Au collisions at as a function of pseudorapidity η and impact parameter b. Using a hybrid approach which combines early ideal fluid dynamical evolution with late hadronic rescattering, we demonstrate strong dissipative effects from the hadronic rescattering stage on the elliptic flow. With Glauber model initial conditions, hadronic dissipation is shown to be sufficient to fully explain the differences between measured v2 values and ideal hydrodynamic predictions. Initial conditions based on the Color Glass Condensate model generate larger elliptic flow and seem to require additional dissipation during the early quark–gluon plasma stage in order to achieve agreement with experiment.
We compare the trace anomaly, strangeness and baryon number fluctuations calculated in lattice QCD with expectations based on hadron resonance gas model. We find that there is a significant discrepancy between the hadron resonance gas and the lattice data. This discrepancy is largely reduced if the hadron spectrum is modified to take into account the larger values of the quark mass used in lattice calculations as well as the finite lattice spacing errors. We also give a simple parametrization of QCD equation of state, which combines hadron resonance gas at low temperatures with lattice QCD at high temperatures. We compare this parametrization with other parametrizations of the equation of state used in hydrodynamical models and discuss differences in hydrodynamic flow for different equations of state.
We discuss two special limiting forms of QCD matter which may be produced at RHIC. We conclude from the available empirical evidence that an equilibrated, but strongly coupled quark–gluon plasma has been made in such collisions. We also discuss the growing body of evidence that its source is a color glass condensate.