The presence of a critical point in the QCD phase diagram can deform the trajectories describing the evolution of the expanding fireball in the QCD phase diagram. The deformation of the hydrodynamic trajectories will change the transverse velocity dependence of the proton-antiproton ratio when the fireball passes in the vicinity of the critical point. An unusual transverse velocity dependence of the anti-proton/proton ratio in a narrow beam energy window would thus signal the presence of the critical point.
Relativistic hydrodynamics for ideal and viscous fluids is discussed as a tool to describe relativistic heavy-ion collisions and to extract transport properties of the quark-gluon plasma from experimentally measured hadron momentum spectra.
We review the basic concepts of perturbative quantum chromodynamics (QCD) and relativistic hydrodynamics, and their applications to hadron production in high energy nuclear collisions. We discuss results from the Relativistic Heavy Ion Collider (RHIC) in light of these theoretical approaches. Perturbative QCD and hydrodynamics together explain a large amount of experimental data gathered during the first decade of RHIC running, although some questions remain open. We focus primarily on practical aspects of the calculations, covering basic topics like perturbation theory, initial state nuclear …
We investigate hadronic particle spectra and flow characteristics of heavy-ion reactions in the FAIR/NICA energy range of $1\ A{\rm GeV} \le E_{\rm lab} \le 10\ A{\rm GeV}$ within a relativistic ideal hydrodynamic one-fluid approach. The particlization is realized by sampling the Cooper-Frye distribution for a grand canonical hadron gas on a hypersurface of constant energy density. Results of the hydrodynamic calculations for different underlying equations of state are presented and compared with experimental data and microscopic transport simulations. The sensitivity of the approach to physic…
We describe fireballs that rehadronize from a perfectly fluid quark matter to a chemically frozen, multi-component hadron gas. In the hydrodynamics of these fireballs, we utilize the lattice QCD equation of state, however, we also apply non-relativistic kinematics for simplicity and clarity. Two new classes of exact, analytic solutions of fireball hydrodynamics are presented: the first class describes triaxially expanding, non-rotating ellipsoidal fireballs, while the second class of exact solutions corresponds to spheroidally symmetric, rotating fireballs. In both classes of solutions, we fin…
We generalize a previously known class of exact analytic solutions of relativistic perfect fluid hydrodynamics for the first time to arbitrary temperature-dependent Equation of State. We investigate special cases of this class of solutions, in particular, we present hydrodynamical solutions with the Equation of State determined from lattice QCD calculations. We discuss the phenomenological relevance of these solutions as well.
We consider the experimental implications of the axial current triangle diagram anomaly in a hydrodynamic description of high density QCD. We propose a signal of an enhanced production of spin-excited hadrons in the direction of the rotation axis in off-central heavy ion collisions.
We show that the centrality and system-size dependence of elliptic flow measured at RHIC are fully described by a simple model based on eccentricity scaling and incomplete thermalization. We argue that the elliptic flow is at least 25% below the (ideal) ``hydrodynamic limit'', even for the most central Au-Au collisions. This lack of perfect equilibration allows for estimates of the effective parton cross section in the Quark-Gluon Plasma and of its viscosity to entropy density ratio. We also show how the initial conditions affect the transport coefficients and thermodynamic quantities extracte…
We compute the longitudinal hydrodynamic flow in ultrarelativistic heavy ion collisions at $\sqrt{s}$ = 5500 GeV by using boost non-invariant initial conditions following from perturbative QCD. The transfer of entropy and energy from the central region to larger rapidities caused by boost non-invariance is determined and the associated decrease in the lifetime of the system is estimated.
Heavy-ion collisions are well described by a dynamical evolution with a long hydrodynamical phase. In this phase the properties of the strongly coupled quark-gluon plasma are reflected in the equation of state (EoS) and the transport coefficients, most prominently by the shear and bulk viscosity over entropy density ratios $η$/s(T) and $ζ$/s(T), respectively. While the EoS is by now known to a high accuracy, the transport coefficients and in particular their temperature and density dependence are not well known from first-principle computations yet, as well as the possible influence they can h…
We compute the hydrodynamic relaxation times $τ_π$ and $τ_j$ for hot QCD at next-to-leading order in the coupling with kinetic theory. We show that certain dimensionless ratios of second-order to first-order transport coefficients obey bounds which apply whenever a kinetic theory description is possible; the computed values lie somewhat above these bounds. Strongly coupled theories with holographic duals strongly violate these bounds, highlighting their distance from a quasiparticle description.
High-energy nuclear collisions produce a nonequilibrium plasma of quarks and gluons which thermalizes and exhibits hydrodynamic flow. There are currently no practical frameworks to connect the early particle production in classical field simulations to the subsequent hydrodynamic evolution. We build such a framework using nonequilibrium Green's functions, calculated in QCD kinetic theory, to propagate the initial energy-momentum tensor to the hydrodynamic phase. We demonstrate that this approach can be easily incorporated into existing hydrodynamic simulations, leading to stronger constraints …
We present the energy density and flux distribution of a heavy quark moving through high temperature QCD plasmas and compare them with those in the strongly coupled N = 4 SYM plasma. The Boltzmann equation is reformulated as a Fokker-Planck equation at the leading log approximation and is solved numerically with nontrivial boundary conditions in momentum space. We use kinetic theory and perform a Fourier transform to calculate the energy and momentum density in position space. The angular distributions exhibit the transition to the ideal hydrodynamics and are analyzed with the first and second…
We compute the initial energy densities produced in ultrarelativistic heavy-ion collisions from NLO perturbative QCD using a saturation conjecture to control soft particle production, and describe the subsequent space-time evolution of the system with hydrodynamics, event by event. The resulting centrality dependence of the low-$p_T$ observables from this pQCD + saturation + hydro ("EKRT") framework are then compared simultaneously to the LHC and RHIC measurements. With such an analysis we can test the initial state calculation, and constrain the temperature dependence of the shear viscosity-t…
We analyze the behavior of (net-)proton number cumulants in central collisions of heavy ions across a broad collision energy range by utilizing hydrodynamic simulations. The calculations incorporate essential non-critical contributions to proton fluctuations such as repulsive baryonic core and exact baryon number conservation. The experimental data are consistent with non-critical physics at collision energies $\sqrt{s_{\rm NN}} \geq 20$ GeV. The data from STAR and HADES Collaborations at lower collision energies indicate an excess of (multi-)proton correlations over the non-critical reference…
Finding the existence and the location of the QCD critical point is one of the main goals of the RHIC beam energy scan program. To make theoretical predictions and corroborate with the experimental data requires modeling the space-time evolution of the matter created in heavy-ion collisions by dynamical models such as the relativistic hydrodynamics with an appropriate Equation of State (EoS). In the present exploratory study, we use a viscous 2+1 dimensional event-by-event (e-by-e) hydrodynamic code at finite baryon densities with two different EoSs (i) Lattice QCD + HRG with a crossover trans…
We introduce an event-by-event pQCD + saturation + hydro ("EKRT") framework for high-energy heavy-ion collisions, where we compute the produced fluctuating QCD-matter energy densities from next-to-leading order (NLO) perturbative QCD (pQCD) using saturation to control soft particle production, and describe the space-time evolution of the QCD matter with viscous hydrodynamics, event by event (EbyE). We compare the computed centrality dependence of hadronic multiplicities, p_T spectra and flow coefficients v_n against LHC and RHIC data. We compare also the computed EbyE probability distributions…
We propose a new strategy for the experimental search of the QCD phase transition in heavy ion collisions: One may tune collision energy around the point where the lifetime of the fireball is expected to be longest. We demonstrate that the hydrodynamic evolution of excited nuclear matter does change dramatically as the initial energy density goes through the "softest point" (where the pressure to energy density ratio reaches its minimum). For our choice of equation of state, this corresponds to epsilon_i approx. = 1.5 GeV/fm^3 and collision energy E_lab/A approx. = 30 GeV (for Au+Au). Various …
We report the continuum limits of the speed of sound, c_s, and the specific heat at constant volume, c_v, in quenched QCD at temperatures of 2Tc and 3Tc. At these temperatures, c_s is within 2-sigma of the ideal gas value, whereas c_v differs significantly from the ideal gas. However, both are compatible with results expected in a theory with conformal symmetry. We investigate effective measures of conformal symmetry in the high temperature phase of QCD.
A hybrid transport approach for the bulk evolution of viscous QCD matter produced in ultra-relativistic heavy-ion collisions is presented. The expansion of the dense deconfined phase of the reaction is modeled with viscous hydrodynamics while the dilute late hadron gas stage is described microscopically by the Boltzmann equation. The advantages of such a hybrid approach lie in the improved capability of handling large dissipative corrections in the late dilute phase of the reaction, including a realistic treatment of the non-equilibrium hadronic chemistry and kinetic freeze-out. By varying the…
We bring the EKRT framework, which combines perturbative QCD (pQCD) minijet production with gluon saturation and hydrodynamics, to next-to-leading order (NLO) in pQCD as rigorously as possible. We chart the model uncertainties, and study the viability and predictive power of the model in the light of the RHIC and LHC measurements in central $A+A$ collisions. In particular, we introduce a new set of measurement functions to define the infrared- and collinear-safe minijet transverse energy, $E_T$, in terms of which we formulate the saturation. We update the framework with the EPS09 NLO nuclear p…
Hydrodynamical calculations have been successful in describing global observables in ultrarelativistic heavy ion collisions, which aim to observe the production of the quark-gluon plasma. On the other hand, recently, a lot of evidence that there exists a critical end point (CEP) in the QCD phase diagram has been accumulating. Nevertheless, so far, no equation of state with the CEP has been employed in hydrodynamical calculations. In this paper, we construct the equation of state with the CEP on the basis of the universality hypothesis and show that the CEP acts as an attractor of isentropic tr…
We solve the relativistic Navier-Stokes equations with homogeneous boost-invariant boundary conditions, and perform a stability analysis of the solution. We show that, if the bulk viscosity has a peak around $T_c$ as inferred from QCD-based arguments, the background solution "freezes" at $T_c$ to a nearly constant temperature state. This state is however highly unstable with respect to certain inhomogeneous modes. Calculations show that these modes have enough time to blow up and tear the system into droplets. We conjecture that this is how freeze-out occurs in the QGP created in heavy ion col…
In this proceeding, we briefly describe the viscous hydrodynamics + hadron cascade hybrid model VISHNU for relativistic heavy ion collisions and report the current status on extracting the QGP viscosity from elliptic flow data.
Near the critical point in the QCD phase diagram, hydrodynamics breaks down at a momentum where the frequency of the fastest hydrodynamic mode becomes comparable with the decay rate of the slowest non-hydrodynamic mode. Hydro+ was developed as a framework which extends the range of validity of hydrodynamics beyond that momentum value. This was achieved through coupling the hydrodynamic modes to the slowest non-hydrodynamic mode. In this work, analyzing the spectrum of linear perturbations in Hydro+, we find that a slow mode falls out of equilibrium if its momentum is greater than a characteris…
A hydrodynamic + cascade model of relativistic heavy ion collisions is presented and compared to available hadronic data from the SPS to RHIC. The model consistently reproduces the radial and elliptic flow data for different particles, collision energies, and impact parameters. Three ingredients are essential to the success: (a) a reasonable EOS exhibiting the hard and soft features of the QCD phase transition, (b) thermal hadronization at the phase boundary, and (c) subsequent hadronic rescattering. Some features of the RHIC data are readily explained: (i) the observed elliptic flow and its d…
We compute the spectral densities of $T^{μν}$ and $J^μ$ in high temperature QCD plasmas at small frequency and momentum,\, $ω,k \sim g^4 T$. The leading log Boltzmann equation is reformulated as a Fokker Planck equation with non-trivial boundary conditions, and the resulting partial differential equation is solved numerically in momentum space. The spectral densities of the current, shear, sound, and bulk channels exhibit a smooth transition from free streaming quasi-particles to ideal hydrodynamics. This transition is analyzed with conformal and non-conformal second order hydrodynamics, and a…
Multiplicity fluctuations are one of the most crucial observables in the Beam Energy Scan program of the Relativistic Heavy Ion Collider. It is understood that they can be utilized to probe the whereabouts of the critical point on the phase diagram of the QCD matter. However, a significant portion of these fluctuations is, apart from that related to the QCD phase transition, attributed to the other origins, which we refer to as "noncritical" ones. The present study is dedicated to the noncritical aspects of the multiplicity fluctuations in heavy-ion collisions. In particular, we focus on those…
We provide a general framework for the derivation of the hydrodynamical corrections to the QCD electromagnetic emissivities in a viscous fluid. Assuming that the emission times are short in comparison to the fluid evolution time, we show that the leading corrections in the fluid gradients are controlled by the bulk and shear tensors times pertinent response functions involving the energy-momentum tensor. In a hadronic fluid phase, we explicit these contributions using spectral functions. Using the vector dominance approximation, we show that the bulk viscosity correction to the photon rate is …
The chemical freeze-out irregularities found with the most advanced hadron resonance gas model and possible signals of two QCD phase transitions are discussed. We found that the center-of-mass collision energy range of tricritical endpoint of QCD phase diagram is [9; 9.2] GeV which is consistent both with QCD inspired exactly solvable model and with experimental findings.
The evolution of a heavy ion collision passes close to the O(4) critical point of QCD, where fluctuations of the order parameter are expected to be enhanced. Using the appropriate stochastic hydrodynamic equations in mean field near the the pseudo-critical point, we compute how these enhanced fluctuations modify the transport coefficients of QCD. Finally, we estimate the expected critical enhancement of soft pion yields, which provides a plausible explanation for the excess seen in experiment relative to ordinary hydrodynamic computations.
We compute the relaxation rate of the spin density of heavy quarks in a perturbative QCD plasma to leading-log order in the coupling constant $g$. The spin relaxation rate $Γ_s$ in spin hydrodynamics is shown to be $Γ_s\sim g^4\log(1/g)T (T/M)^2$ in the heavy-quark limit $T/M\ll 1$, which is smaller than the relaxation rate of other non-hydrodynamic modes by additional powers of $T/M$. We demonstrate three different methods to evaluate the spin relaxation rate: 1) the Green-Kubo formula in the spin hydrodynamic regime, 2) the spin density correlation function in the strict hydrodynamic limit, …
The second-order hydrodynamic equations for evolution of shear and bulk viscous pressure have been derived within the framework of covariant kinetic theory based on the effective fugacity quasiparticle model. The temperature-dependent fugacity parameter in the equilibrium distribution function leads to a mean field term in the Boltzmann equation which affects the interactions in the hot QCD matter. The viscous corrections to distribution function, up to second-order in gradient expansion, have been obtained by employing a Chapman-Enskog like iterative solution of the effective Boltzmann equati…
Three subjects are considered here: the relativistic hydrodynamics equations for a boost-invariant expanding fluid; the fuzzy bag model for the pressure which recently appeared in QCD phenomenology; and the early space-time evolution of the QCD matter, drawn from model studies, which can also be expected to arise in realistic fluid dynamics relevant to heavy ion collisions at LHC.
We investigate the hydrodynamics of the QCD plasma using dimensionless numbers built from the thermodynamics and transport theory of the plasma and characteristic dimensions of the fireball produced in heavy-ion collisions. We find that by the usual measures, dissipation is strong, and the fireball is on the borderline of equilibrium. As a result, the system is richer in phenomena than ideal hydrodynamics would predict. One general implication is that it may be possible to get a direct view of the QCD plasma phase rather than having to infer its existence indirectly from signals that come from…
Initial conditions for relativistic heavy-ion collisions may be far from equilibrium (i.e. there are large initial contributions from the shear stress tensor and bulk pressure) but it is expected that on very short time scales the dynamics converge to a universal attractor that defines hydrodynamic behavior. Thus far, studies of this nature have only considered an idealized situation at LHC energies (high temperatures $T$ and vanishing baryon chemical potential $μ_B=0$) but, in this work, we investigate for the first time how far-from-equilibrium effects may influence experimentally driven sea…
In jet quenching, a hard QCD parton, before fragmenting into a jet of hadrons, deposits a fraction of its energy in the medium, leading to suppressed production of high-$p_T$ hadrons. Assuming that the deposited energy quickly thermalizes, we simulate the subsequent hydrodynamic evolution of the QGP fluid. Hydrodynamic evolution and subsequent particle emission depend on the jet trajectories. Azimuthal distribution of excess $π^-$ due to quenching jet, averaged over all the trajectories, reasonably well reproduce the di-hadron correlation as measured by the STAR and PHENIX collaboration in cen…
The experimental results on heavy ion collisions at RHIC and LHC indicate that QCD plasma behaves as a nearly perfect fluid described by relativistic hydrodynamics. Hydrodynamics is an effective low-energy Theory Of Everything stating that the response of a system to external perturbations is dictated by conservation laws that are a consequence of the symmetries of the underlying theory. In the case of QCD fluid produced in heavy ion collisions, this theory possesses anomalies, so some of the apparent classical symmetries are broken by quantum effects. Even though the anomalies appear as a res…
Hydrodynamic calculations of ultra-relativistic heavy ion collisions are performed using the iEBE-VISHNU 2+1D code with fluctuating initial conditions and three different parameterizations of the Lattice QCD equations of state: continuum extrapolations for stout and HISQ/tree actions, as well as the s95p-v1 parameterization based upon calculations using the p4 action. All parameterizations are matched to a hadron resonance gas equation of state at T = 155 MeV, at which point the calculations are continued using the UrQMD hadronic cascade. Calculations for $\sqrt{s_{NN}}=200$ GeV Au+Au collisio…
We analyze the evolution of hydrodynamic fluctuations in a heavy ion collision as the system passes close to the QCD critical point. We introduce two small dimensionless parameters $λ$ and $Δ_s$ to characterize the evolution. $λ$ compares the microscopic relaxation time (away from the critical point) to the expansion rate $λ\equiv τ_0/τ_Q$, and $Δ_s$ compares the baryon to entropy ratio, $n/s$, to its critical value, $Δ_s\equiv (n/s - n_c/s_c)/(n_c/s_c)$. We determine how the evolution of critical hydrodynamic fluctuations depends parametrically on $λ$ and $Δ_s$. Finally, we use this parametri…
The existence of hydrodynamic attractors in rapidly expanding relativistic systems has shed light on the success of relativistic hydrodynamics in describing heavy-ion collisions at zero chemical potential. As the search for the QCD critical point continues, it is important to investigate how out of equilibrium effects influence the trajectories on the QCD phase diagram. In this proceedings, we study a Bjorken expanding hydrodynamic system based on DMNR equations of motion with initial out of equilibrium effects and finite chemical potential in a system with a critical point. We find that the i…
We study the thermal dilepton and photon production from relativistic heavy ion collisions in presence of viscosities by employing the recently developed second order dissipative hydrodynamic formulation estimated within a quasiparticle description of thermal QCD (Quantum Chromo-Dynamics) medium. The sensitivity of shear and bulk viscous pressures to the temperature dependence of relaxation time is analyzed within one dimensional boost invariant expansion of quark gluon plasma (QGP).The dissipative corrections to the phase-space distribution functions upto first order in gradients are obtained…
Anisotropic hydrodynamics improves upon standard dissipative fluid dynamics by treating certain large dissipative corrections non-perturbatively. Relativistic heavy-ion collisions feature two such large dissipative effects: (i) Strongly anisotropic expansion generates a large shear stress component which manifests itself in very different longitudinal and transverse pressures, especially at early times. (ii) Critical fluctuations near the quark-hadron phase transition lead to a large bulk viscous pressure on the conversion surface between hydrodynamics and a microscopic hadronic cascade descri…
We report here on a recent lattice study of the QCD transition region at finite temperature and zero chemical potential using domain wall fermions (DWF). We also present a parameterization of the QCD equation of state obtained from lattice QCD that is suitable for use in hydrodynamics studies of heavy ion collisions. Finally, we show preliminary results from a multi-stage hydrodynamics/hadron cascade model of a heavy ion collision, in an attempt to understand how well the experimental data (e.g. particle spectra, elliptic flow, and HBT radii) can constrain the inputs (e.g. initial temperature,…
In this work, we study the lensing effect of the QCD critical point on hydrodynamic trajectories, and its consequences on the net-proton kurtosis $κ_4$. Including critical behavior by means of the BEST Collaboration equation of state (EoS), we first consider a scenario in equilibrium, then compare with hydrodynamic 0+1D simulations with Bjorken expansion, including both shear and bulk viscous terms. We find that, both in and out-of-equilibrium, the size and shape of the critical region directly affect if the signal will survive through the dynamical evolution.
Using a viscous hydrodynamic model coupled to a hadronic cascade code, numerous features of the dynamics and equilibrium properties are explored for their impact on femtoscopic measurements. The equation of state, viscous parameters and initial conditions are investigated. We find that femtoscopy is affected by numerous model features at the 10% level, and that by including features and adjusting unknown parameters, one can explain experimental source size measurements to better than 10%.
We use leading order effective kinetic theory to simulate the pre\nobreakdash-equilibrium evolution of transverse energy and flow perturbations in heavy-ion collisions. We provide a Green function which propagates the initial perturbations of the energy-momentum tensor to a time when hydrodynamics becomes applicable. With this map, the pre-thermal evolution from saturated nuclei to hydrodynamics can be modeled in the framework of weakly coupled QCD.
We apply stochastic hydrodynamics to the study of charge density fluctuations in QCD matter undergoing Bjorken expansion. We find that the charge density correlations are given by a time integral over the history of the system, with the dominant contribution coming from the QCD crossover region where the change of susceptibility per entropy, chi T/s, is most significant. We study the rapidity and azimuthal angle dependence of the resulting charge balance function using a simple analytic model of heavy-ion collision evolution. Our results are in agreement with experimental measurements, indicat…
Baryon fluctuations exceeding Poisson expectations can signal a nearly first order phase transition at RHIC. We show how these fluctuations can be measured, and apply a dissipative-hydrodynamic formulation used in condensed matter physics to simulate their evolution.
