We investigate the effect of hydrodynamic fluctuations on the rapidity decorrelations of anisotropic flow in high-energy nuclear collisions using a (3+1)-dimensional integrated dynamical model. The integrated dynamical model consists of twisted initial conditions, fluctuating hydrodynamics, and hadronic cascades on an event-by-event basis. To understand the rapidity decorrelation, we analyze the factorization ratio in the longitudinal direction. Comparing the factorization ratios between fluctuating hydrodynamics and ordinary viscous hydrodynamics, we find a sizable effect of hydrodynamic fluctuations on rapidity decorrelations. We also propose to calculate the Legendre coefficients of the flow magnitude and the event-plane angle to understand the decorrelation of anisotropic flow in the longitudinal direction.
An "event-shape twist" technique is proposed to study the longitudinal dynamics of harmonic flow, in particular the effects of rapidity fluctuation and event-plane decorrelation. This technique can distinguish between two types of rapidity decorrelation effects: a systematic rotation versus a random fluctuation of flow angles along the rapidity direction. The technique is demonstrated and the magnitude of the two decorrelation effects is predicted using the AMPT model via a single particle analysis and two-particle correlation analysis. An observed decorrelation can be attributed to a systemat…
Within A Multi-Phase Transport model, we investigate decorrelation of event planes over pseudorapidity and its effect on azimuthal anisotropy measurements in relativistic heavy-ion collisions. The decorrelation increases with increasing η gap between particles used to reconstruct the event planes. The third harmonic event planes are found even anticorrelated between forward and backward rapidities, the source of which may root in the opposite orientation of the collision geometry triangularities. The decorrelation may call into question the anisotropic flow measurements with pseudorapidity gap…
We discuss rapidity decorrelation caused by hydrodynamic fluctuations in high-energy nuclear collisions at the LHC energy. We employ an integrated dynamical model which is a combination of the Monte Carlo version of Glauber model with extension to longitudinal direction for initial conditions, full three-dimensional relativistic fluctuating hydrodynamics for the space-time evolution of created matter in the intermediate stage and a hadronic cascade model in the late stage. We switch on and off the hydrodynamic fluctuations in the hydrodynamic stage to understand the effects of hydrodynamic flu…
Rapidity decorrelation in high energy heavy-ion collisions is one of the hot topics in understanding longitudinal dynamics of the quark gluon plasma (QGP). In this study we employ an integrated dynamical model with full three dimensional relativistic hydrodynamics and perform event-by-event numerical simulations of Pb+Pb collisions at the LHC energy. We analyze factorization ratios to understand rapidity decorrelation from hydrodynamic fluctuations and initial longitudinal fluctuations. We show that factorization breaking happens due to both hydrodynamic fluctuations and initial longitudinal f…
The decorrelation of the orientation of the event-plane angles in the initial state of relativistic Pb-Pb and p-Pb collisions, the "torque effect," is studied in a model of entropy deposition in the longitudinal direction involving fluctuations of the longitudinal source profile on large scales. The radiation from a single wounded nucleon is asymmetric in space-time rapidity. It is assumed that the extent in rapidity of the region of deposited entropy is random. Fluctuations in the deposition of entropy from each source increase the event-plane decorrelation: for Pb-Pb collisions they improve …
We perform the first study on asymmetric longitudinal decorrelations of elliptic, triangular and quadrangular flows in proton-nucleus collisions at the LHC and RHIC energies. To measure the longitudinal flow decorrelations for asymmetric collision systems, we propose a new set of rapidity-asymmetric flow decorrelation functions. Our event-by-event hydrodynamic calculations show that the flow decorrelations in proton-going direction are larger than those in nucleus-going direction. We also find that proton-nucleus collisions at RHIC have larger longitudinal flow decorrelation effects than those…
We present the first calculation of longitudinal decorrelation of anisotropic flow at RHIC Beam Energy Scan (BES) energies using event-by-event viscous hydrodynamic model (vHLLE), with two different initial states (GLISSANDO2 and UrQMD) and hadronic cascade. We investigate the origin of the observed decorrelation by checking separately flow angle and flow magnitude decorrelation and by calculating decorrelation in the initial state eccentricity.
We investigate the interplay between hydrodynamic fluctuations and initial longitudinal fluctuations for their effects on the rapidity decorrelation of collective flow in high-energy nuclear collisions. We use a (3+1)-dimensional integrated dynamical model in which we combine initial conditions with longitudinal fluctuations, fluctuating hydrodynamics and hadronic cascades. We analyse the factorisation ratio in the longitudinal direction to study the effect of these fluctuations on the rapidity decorrelation. We find an essential difference between the effects of the hydrodynamic fluctuations …
We discuss the forward-backward correlations of harmonic flow in Pb+Pb collisions at the CERN Large Hadron Collider (LHC), applying standard multibin measures, as well as proposed here new measures. We illustrate the methods with hydrodynamic model simulations based on event-by-event initial conditions from the wounded quark model with asymmetric rapidity emission profiles. Within the model we examine independently the event-plane angle and the flow magnitude decorrelations. We find specific hierarchy between various flow decorrelation measures and confirm certain factorization relations. We f…
Decorrelation of the elliptic flow in rapidity is calculated within a hybrid approach which includes event-by-event viscous fluid dynamics and final state hadronic cascade model. The simulations are performed for Au+Au collisions at center-of-mass collision energies of 27 and 200 GeV per nucleon pair, as well as various colliding systems at 72 GeV per nucleon pair. Initial conditions determined by an extended Monte Carlo Glauber model show better agreement with experimental data than initial conditions from the UrQMD transport model. We show how the observed decorrelation is connected with the…
Harmonic flow in relativistic heavy-ion collisions is observed in a broad range of rapidities, and the flow at different rapidities is correlated. However, fluctuations lead to a small decorrelation of the harmonic flow magnitudes and flow angles at different rapidities. Using a hydrodynamic model with Glauber Monte Carlo initial conditions we show that the flow angle decorrelation strongly depends on the flow magnitude in the event. We propose observables to measure this effect in experiment.
The collective harmonic flow in heavy-ion collisions correlates particles at all transverse momenta to be emitted preferably some directions. The factorization breaking coefficient measures the small decorrelation of the flow harmonics at two different transverse momenta. Using the hydrodynamic model I study in details the decorrelation of the harmonic flow due to the flow angle and the flow magnitude decorrelation at two transverse momenta. The effect can be seen in experiment measuring factorization breaking coefficients for the square of the harmonic flow vector at two transverse momenta. T…
In the RHIC Beam Energy Scan program, gold nuclei are collided with different collision energies in the range from few to 62.4 GeV. The goals of the program are to explore the onset of QGP creation, locate the critical point of QCD and study dense baryon matter. We report on the first application of Monte Carlo Glauber (GLISSANDO2) and T$_{\rm R}$ENTo $p=0$ initial states extended to 3D for event-by-event viscous fluid dynamic (vHLLE) with hadronic cascade modelling of Au+Au collisions at $\sqrt{s_{_{\rm NN}}}=27$ and 62.4 GeV, which is the upper region of RHIC BES energies. The initial states…
We use the string melting version of a multi-phase transport (AMPT) model to study Cu+Au collisions at $\sqrt{s_{NN}}=200$ GeV. The rapidity distributions of identified hadrons show asymmetric dependences on rapidity. In addition, elliptic and triangular flows at mid-rapidity from the AMPT model for pions, kaons, and protons agree reasonably with the experimental data up to $p_{T}\sim1$ GeV$/c$. We then investigate the forward/backward asymmetry of $v_2$ and $v_3$. We find that these anisotropic flows are larger on the Au-going side than the Cu-going side, while the asymmetry tends to go away …
We perform a systematic study on the decorrelation of anisotropic flows along the pseudorapidity in relativistic heavy-ion collisions at the LHC and RHIC energies. The dynamical evolution of the QGP fireball is simulated via the CLVisc (ideal) (3+1)-dimensional hydrodynamics model, with the fully fluctuating initial condition from A-Multi-Phase-Transport (AMPT) model. Detailed analysis is performed on the longitudinal decorrelations of elliptic, triangular and quadrangular flows in terms of flow vectors, flow magnitudes and flow orientations (event planes). It is found that pure flow magnitude…
We study photon production in the early stage of heavy-ion collisions using a multistage model combining IP-Glasma, KøMPøST and relativistic hydrodynamics. We discuss the small momentum anisotropy of these photons, highlighting the role of the photon-hadron event-plane decorrelation. We comment that this singular characteristic of early photons could be used to provide dynamical information on the complex pre-hydrodynamics phase of heavy-ion collisions.
Viscous diffusion can broaden the rapidity dependence of two-particle transverse momentum fluctuations. Surprisingly, measurements at RHIC by the STAR collaboration demonstrate that this broadening is accompanied by the appearance of unanticipated structure in the rapidity distribution of these fluctuations in the most central collisions. Although a first order classical Navier-Stokes theory can roughly explain the rapidity broadening, it cannot explain the additional structure. We propose that the rapidity structure can be explained using the second order causal Israel-Stewart hydrodynamics w…
Studies of fluctuations and correlations of soft hadrons and hard and electromagnetic probes of the dense and strongly interacting medium require event-by-event hydrodynamic simulations of high-energy heavy-ion collisions that are computing intensive. We develop a (3+1)D viscous hydrodynamic model -- CLVisc that is parallelized on Graphics Processing Unit (GPU) using Open Computing Language (OpenCL) with 60 times performance increase for space-time evolution and more than 120 times for the Cooper-Frye particlization relative to that without GPU parallelization. The pseudo-rapidity dependence o…
We show that in proton-lead (p+Pb) collisions at the LHC, the Color Glass Condensate (CGC) and hydrodynamics lead to qualitatively different behavior of the average transverse momentum, <p_T>, with the particles rapidity. In hydrodynamics, the <p_T> decreases as one goes from zero rapidity, y=0, to the proton fragmentation region since the number of particles decreases. In contrast, in the CGC the saturation momentum increases as one goes from y=0 to the proton fragmentation region, and so the <p_T> increases. At the LHC, the difference between the two models may be large enough to be tested e…
We study the longitudinal decorrelations of elliptic, triangular and quadrangular flows in heavy-ion collisions at the LHC and RHIC energies. The event-by-event CLVisc (3+1)-dimensional hydrodynamics model, combined with the fully fluctuating AMPT initial conditions, is utilized to simulate the space-time evolution of the strongly-coupled quark-gluon plasma. Detailed analysis is performed for the longitudinal decorrelations of flow vectors, flow magnitudes and flow orientations. We find strong correlations between final-state longitudinal decorrelations of anisotropic flows and initial-state l…
The initial energy density distribution and fluctuation in the transverse direction lead to anisotropic flows of final hadrons through collective expansion in high-energy heavy-ion collisions. Fluctuations along the longitudinal direction, on the other hand, can result in decorrelation of anisotropic flows in different regions of pseudo rapidity ($η$). Decorrelation of the $2$nd and $3$rd order anisotropic flows with different $η$ gaps for final charged hadrons in high-energy heavy-ion collisions is studied in an event-by-event (3+1)D ideal hydrodynamic model with fully fluctuating initial con…
The charged-particle's final state spectrum is derived from an analytic perturbative solution for the relativistic viscous hydrodynamics. By taking into account the longitudinal acceleration effect in relativistic viscous hydrodynamics, the pseudorapidity spectrum describes well the nucleus-nucleus colliding systems at RHIC and LHC. Based on both the extracted longitudinal acceleration parameters $λ^{*}$ and a phenomenological description of the $λ^{*}$, the charged-particle's pseudorapidity distributions for $\sqrt{s_{NN}}$ = 5.44 TeV Xe+Xe collisions are computed from the final state express…
We analyze non-central heavy-ion collisions at the relativistic energy within a full (3+1) dimensional hydrodynamic model. First, the initial parameters in the hydrodynamic model are chosen so that we reproduce the experimental data of both the rapidity distribution and the slope of transverse mass distribution in central Pb + Pb collisions at 158 $A$ GeV at the CERN SPS. We next study the validity of the ansatz of wounded nucleon scaling for the initial condition of the hydrodynamic model through analysis of the rapidity distribution of negative pions in non-central collisions. Moreover, a si…
Fluctuations in the initial geometry of a nucleus-nucleus collision have been recently shown to result in a new type of directed flow (v_1) that, unlike the usual directed flow, is also present at midrapidity. We compute this new v_1 versus transverse momentum and centrality for Au-Au collisions at RHIC using the hydrodynamic code NeXSPheRIO. We find that the event plane of v_1 is correlated with the angle of the initial dipole of the distribution, as predicted, though with a large dispersion. It is uncorrelated with the reaction plane. Our results are in excellent agreement with results infer…
We show that measurements of the rapidity dependence of transverse momentum correlations can be used to determine the characteristic time $τ_π$ that dictates the rate of isotropization of the stress energy tensor, as well as the shear viscosity $ν= η/sT$. We formulate methods for computing these correlations using second order dissipative hydrodynamics with noise. Current data are consistent with $τ_π/ν\sim 10$ but targeted measurements can improve this precision.
The quark-gluon plasma behaves as a relativistic viscous fluid in high-energy heavy ion collisions. I develop a causal dissipative hydrodynamic model at finite baryon density for RHIC and LHC to estimate the net baryon rapidity distribution. The net baryon number is found to be carried to forward rapidity by the flow, effectively enhancing the transparency of the collisions. This suggests that the energy available for the production of a hot medium could be larger than that naively implied from experimental data. Also the distribution can be sensitive to baryon dissipation as much as to shear …
We modified the gluon saturation model by rescaling the momentum fraction according to saturation momentum and introduced the Cooper-Frye hydrodynamic evolution to systematically study the pseudo-rapidity distributions of final charged hadrons at different energies and different centralities for Au-Au collisions in relativistic heavy-ion collisions at BNL Relativistic Heavy Ion Collider (RHIC). The features of both gluon saturation and hydrodynamic evolution at different energies and different centralities for Au-Au collisions are investigated in this paper.
We analyze correlations between the event-plane angles in different intervals of pseudorapidity within the 3+1-dimensional viscous hydrodynamics with the Glauber-model initial conditions. As predicted earlier, the fluctuations in the particle production mechanism in the earliest stage, together with asymmetry of the emission profiles in pseudorapidity from the forward- and backward going wounded nucleons, lead to the torque effect, namely, decorrelation of the event-plane angles in distant pseudorapidity bins. We use two- or three-bin measures of correlation functions to quantify the effect, w…
We present new, exact, finite solutions of relativistic hydrodynamics for longitudinally expanding fireballs for arbitrary constant value of the speed of sound. These new solutions generalize earlier, longitudinally finite, exact solutions, from an unrealistic to a reasonable equation of state, characterized by a temperature independent (average) value of the speed of sound. Observables like the rapidity density and the pseudorapidity density are evaluated analytically, resulting in simple and easy to fit formulae that can be matched to the high energy proton-proton and heavy ion collision dat…
Fluctuations in the initial transverse energy-density distribution lead to anisotropic flows as observed in central high-energy heavy-ion collisions. Studies of longitudinal fluctuations of the anisotropic flows can shed further light on the initial conditions and dynamical evolution of the hot quark-gluon matter in these collisions. Correlations between anisotropic flows with varying pseudorapidity gaps in Pb+Pb collisions at the CERN Large Hadron Collider are investigated using both an event-by-event (3+1)-D ideal hydrodynamical model with fluctuating initial conditions and the a multiphase …
We review the formulation of Landau hydrodynamics and find that the rapidity distribution of produced particles in the center-of-mass system should be more appropriately modified as dN/dy \exp[\sqrt{y_b^2-y^2}], where y_b=\ln[\sqrt{s_{NN}}/m_p] is the beam nucleon rapidity, instead of Landau's original distribution, dN/dy(Landau) \exp[\sqrt{L^2-y^2}], where L=\ln[\sqrt{s_{NN}}/2m_p]. The modified distribution agrees better with experimental dN/dy data than the original Landau distribution and can be represented well by the Gaussian distribution, dN/dy(Gaussian) \exp[-y^2/2L]. Past successes of…
This study presents generalization of the Landau hydrodynamic solution for multiparticle production applied to non-central relativistic heavy ion collisions. Obtained results shows longitudinal scaling of elliptic flow $v_2$ as a function of rapidity shifted by beam rapidity ($y-y_{beam}$) for different energies ($\sqrt{s_{NN}}=62.4$ GeV and 200 GeV) and for different systems (Au-Au and Cu-Cu). It is argued, that the elliptic flow and its longitudinal scaling is due to the initial transverse energy density distribution and initial longitudinal thickness effect.
Landau hydrodynamics is a plausible description for the evolution of the dense hot matter produced in high-energy heavy-ion collisions. We review the formulation of Landau hydrodynamics to pave the way for its application in high-energy heavy-ion collisions. It is found that Landau's rapidity distribution needs to be modified to provide a better quantitative description. In particular, the rapidity distribution in the center-of-mass system should be more appropriately given as dN/dy \exp{\sqrt{y_b^2-y^2}}, where y_b=\ln{\sqrt{s_NN}/m_p} is the beam nucleon rapidity, instead of Landau's origina…
The pseudo-rapidity dependence of the elliptic flow at various excitation energies measured by the PHOBOS Collaboration in Au+Au collisions at RHIC is one of the surprising results that has not been explained before in terms of hydrodynamical models. Here we show that these data are in agreement with theoretical predictions based on perfect fluid hydrodynamics. We also show that these PHOBOS data satisfy the universal scaling relation predicted by the Buda-Lund hydrodynamical model, based on exact solutions of perfect fluid hydrodynamics.
We study the effects of hydrodynamic fluctuations in non-boost-invariant longitudinal expansion of matter formed in relativistic heavy ion collisions. We formulate the theory of thermal noise within second-order viscous hydrodynamics treating noise as a perturbation on top of the non-boost-invariant flow. We develop a numerical simulation model to treat the (1+1)-dimension hydrodynamic evolution. The code is tested to reproduce the analytic results for the Riemann solver for expansion of matter in vacuum. For viscous hydrodynamic expansion, the initial energy density distribution are obtained …
We highlight some of the interesting properties of a new and finite, exact family of solutions of 1 + 1 dimensional perfect fluid relativistic hydrodynamics. After reviewing the main properties of this family of solutions, we present the formulas that connect it to the measured rapidity and pseudo-rapidity densities and illustrate the results with fits to p+p collisions at 8 TeV and Pb+Pb collisions at $\sqrt{s_{NN}} = 5.02 $ TeV.
The individual studies of the anisotropic flow vector, flow angle and flow magnitude fluctuations with multi-particle correlations provide insight into the initial conditions and properties of the quark-gluon plasma (QGP) created in high-energy heavy-ion collisions. Recent measurements of these fluctuations have been available and the comparison to hydrodynamic models shows unique sensitivities to the initial conditions of the system, but also a puzzling dependence on the specific shear viscosity $η/s$. In this paper, a systematic study with A Multi-Phase Transport (AMPT) model using different…
The Large Hadron Collider (LHC) experiments have revealed that the predictions of the color glass condensate (CGC) tend to underestimate the multiplicity at mid-rapidity. We develop and estimate a full second-order viscous hydrodynamic model for the longitudinal expansion to find that the CGC rapidity distributions are visibly deformed during the hydrodynamic stage due to the interplay between the entropy production and the entropy flux to forward rapidity. The results indicate the importance of viscous hydrodynamic evolution with non-boost invariant flow for understanding the CGC in terms of …
Interpretation of long-range rapidity correlations in terms of the fluctuating rapidity density distribution of the system created in high-energy collisions is proposed. When applied to recent data of the STAR coll., it shows a substantial asymmetric component in the shape of this system in central Au-Au collisions, implying that boost invariance is violated on the event-by-event basis even at central rapidity. This effect may seriously influence the hydrodynamic expansion of the system.
The pseudo-rapidity dependence of the elliptic flow at various excitation energies measured by the PHOBOS Collaboration in Au+Au collisions at RHIC is one of the surprising results that has not been explained before in terms of hydrodynamical models. Here we show that these data are in agreement with theoretical predictions and satisfy the universal scaling relation predicted by the Buda-Lund hydrodynamical model, based on exact solutions of perfect fluid hydrodynamics. We also show a theoretical prediction on the rapidity and transverse momentum scaling of the HBT radii measured in heavy ion …
The rapidity dependence of elliptic, $v_2$, and triangular, $v_3$, flow coefficients in proton-nucleus (p+A) collisions is predicted in hydrodynamics and in a multi-phase transport model (AMPT). We find that $v_n$ ($n=2,3$) on a nucleus side is significantly larger than on a proton side and the ratio between the two, $v_n^{\rm Pb}/v_n^{\rm p}$, weekly depends on the transverse momentum of produced particles.
We find an analytical solution to relativistic viscous hydrodynamics for a 1+1 dimensional Landau flow profile. We consider relativistic Navier-Stokes form of the dissipative hydrodynamic equation, for a non-conformal system with a constant speed of sound, and employ the obtained solution to fit rapidity spectrum of observed pions in $\sqrt{s_{NN}}=$ 200, 17.3, 12.3, 8.76, 7.62, 6.27, 4.29, 3.83, 3.28 and 2.63 GeV collision energies. We find that at the freeze-out hypersurface with improved Landau's freeze-out prescription, the viscous corrections do not affect the rapidity spectra. We demonst…
Two-particle correlations in relative rapidity and azimuth are studied for the p-Pb collisions at the LHC energy of 5.02 TeV in the framework of event-by-event 3+1-dimensional viscous hydrodynamics. It is found that for the highest-multiplicity events the observed ridge structures appear in a natural way, suggesting that collective flow may be an important element in the evolution of the system. We also discuss the role of the charge balancing and the transverse-momentum conservation.
Based on the (3+1)-dimensional hydrodynamic model, the space-time evolution of hot and dense nuclear matter produced in non-central relativistic heavy-ion collisions is discussed. The elliptic flow parameter v_2 is obtained by Fourier analysis of the azimuthal distribution of pions and protons which are emitted from the freeze-out hypersurface. As a function of rapidity, the pion and proton elliptic flow parameters both have a peak at midrapidity.
We present the hybrid hadron string dynamic (HydHSD) model connecting the parton-hadron-string dynamic model (PHSD) and a hydrodynamic model taking into account shear viscosity within the Israel-Stewart approach. The performance of the code is tested on the pion and proton rapidity and transverse mass distributions calculated for Au+Au and Pb+Pb collision at AGS--SPS energies. The influence of the switch time from transport to hydro models, the viscous parameter, and freeze-out time are discussed. Since the applicability of the Israel-Stewart hydrodynamics assumes the perturbative character of…
We present event-by-event viscous hydrodynamic calculations of the anisotropic flow coefficients v_2 to v_5 for heavy-ion collisions at the Relativistic Heavy-Ion Collider (RHIC). We study the dependence of different flow harmonics on shear viscosity and the morphology of the initial state. v_3 and higher flow harmonics exhibit a particularly strong dependence on both the initial granularity and shear viscosity. We argue that a combined analysis of all available flow harmonics will allow to determine eta/s of the quark gluon plasma precisely. Presented results strongly hint at a value (eta/s)_…
Relativistic dissipative hydrodynamic model at finite density is a promising tool for analyzing the dense QCD matter created in the beam energy scan experiments. The hydrodynamic frame can be chosen in the direction of energy flow, which is called the Landau frame, or conserved charge flow, which is called the Eckart frame. In this study, I investigate the stability and causality of full second-order relativistic hydrodynamic equations in the two frames. Then the effects of frame choice on hydrodynamic variables and experimental observables are estimated numerically and are found to be visible…
