In ultrarelativistic heavy-ion collisions, the Fourier decomposition of the relative azimuthal angle, Δϕ, distribution of particle pairs yields a large cos(3Δϕ) component, extending out to large rapidity separations Δη>1. This component captures a significant portion of the ridge and shoulder structures in the Δϕdistribution, which have been observed after contributions from elliptic flow are subtracted. An average finite triangularity due to event-by-event fluctuations in the initial matter distribution, followed by collective flow, naturally produces a cos(3Δϕ) correlation. Using ideal and viscous hydrodynamics, and transport theory, we study the physics of triangular (v_3) flow in comparison to elliptic (v_2), quadrangular (v_4) and pentagonal (v_5) flow. We make quantitative predictions for v_3 at RHIC and LHC as a function of centrality and transverse momentum. Our results for the centrality dependence of v_3 show a quantitative agreement with data extracted from previous correlation measurements by the STAR collaboration. This study supports previous results on the importance of triangular flow in the understanding of ridge and shoulder structures. Triangular flow is found to be a sensitive probe of initial geometry fluctuations and viscosity.
We present results for the elliptic and triangular flow coefficients in Au+Au collisions at root-s=200 AGeV using event-by-event (3+1)D viscous hydrodynamic simulations. We study the effect of initial state fluctuations and finite viscosities on the flow coefficients v_2 and v_3 as functions of transverse momentum and pseudo-rapidity. Fluctuations are essential to reproduce the measured centrality dependence of elliptic flow. We argue that simultaneous measurements of v_2 and v_3 can determine eta/s more precisely.
Viscous hydrodynamics gives a satisfactory description of the transverse momentum spectra, of the elliptic and triangular flow, and of the femtoscopic correlations for particles produced in relativistic heavy-ion collisions. On general grounds, a similar collective behavior has been predicted for proton-lead (p-Pb) collisions at the LHC. We present results of the hydrodynamics calculation of the elliptic and triangular flow in p-Pb. We discuss the mass dependence of flow coefficients and of the average transverse momentum for identified particles.
The first calculation of triangular flow $v_3$ in Au+Au collisions at $\sqrt{s_{\rm NN}}=200A$ GeV from an event-by-event (3+1)-d transport+hydrodynamics hybrid approach is presented. As a response to the initial triangularity $ε_3$ of the collision zone, $v_3$ is computed in a similar way to the standard event-plane analysis for elliptic flow $v_2$. It is found that the triangular flow exhibits weak centrality dependence and is roughly equal to elliptic flow in most central collisions. We also explore the transverse momentum and rapidity dependence of $v_2$ and $v_3$ for charged particles as …
It is shown that a simultaneous comparison of both elliptic and triangular flow from (2+1)-dimensional viscous fluid dynamics with recent measurements in Pb+Pb collisions at the Large Hadron Collider (LHC) favors a small specific shear viscosity (eta/s)_QGP approximately equal to 1/(4pi) for the quark-gluon plasma. Using this viscosity value, the relative magnitude of the elliptic and triangular flow is well described with Monte-Carlo Glauber (MC-Glauber) initial conditions while Monte-Carlo Kharzeev-Levin-Nardi (MC-KLN) initial conditions require twice as large viscosity to reproduce the elli…
Based on the Nakajima-Zubarev type nonequilibrium density operator, we derive microscopic formulae of the transport coefficients in the second order hydrodynamics.
We calculate the triangular flow parameter $v_3$ of thermal photons from an event-by-event ideal hydrodynamic model for $0--40\%$ central collisions of Pb nuclei at $\sqrt{s_{NN}}$=2.76 TeV at LHC. $v_3$ determined with respect to the participant plane (PP) is found to be non-zero, positive and its $p_T$ dependence is qualitatively similar to the elliptic flow parameter $v_2$(PP) of thermal photons in the range $1 \le p_T \le 6$ GeV/$c$. In the range $p_T \, \le $ 3 GeV/$c$, $v_3$(PP) is found to be about $50--75\%$ of $v_2$(PP) and for $p_T \, >$ 3 GeV/$c$ the two anisotropy parameters become…
We study the collision energy dependence of elliptic flow v_2 and triangular flow v_3 in Au+Au collisions within the energy range sqrt(s_{NN}) = 5-200 GeV, utilizing a transport + hydrodynamics hybrid model. The transport part is described by the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) approach, combined with an intermediate (3+1)-dimensional ideal hydrodynamical evolution phase using a chiral model equation of state. We find the decrease of v_2 produced by hydrodynamics at lower collision energies partially compensated by the transport dynamics. This does not apply to v_3, which …
In a hydrodynamic model, with fluctuating initial conditions, the correlation between triangular flow and initial spatial triangularity is studied. The triangular flow, even in ideal fluid, is only weakly correlated with the initial triangularity. The correlation is largely reduced in viscous fluid. Elliptic flow on the other hand appears to be strongly correlated with initial eccentricity. Weak correlation between triangular flow and initial triangularity indicate that a part of triangular flow is unrelated to initial triangularity. Triangularity acquired during the fluid evolution also contr…
We present a new direct simulation Monte-Carlo method for solving the relativistic Boltzmann equation. We solve numerically the 2-dimensional Boltzmann equation using this new algorithm. We find that elliptic flow from this transport calculation smoothly converges towards the value from ideal hydrodynamics as the number of collisions per particle increases, as expected on general theoretical grounds, but in contrast with previous transport calculations.
In heavy ion collisions, event-by-event fluctuations in participating nucleon positions can lead to triangular flow. With fluctuating initial conditions, flow coefficients will also fluctuate. In a hydrodynamic model, we study the fluctuations in elliptic and triangular flow, due to fluctuating initial conditions. Both elliptic and triangular flow fluctuates strongly, triangular flow more strongly than the elliptic flow. Strong fluctuations greatly reduce the sensitivity of elliptic and triangular flow to viscosity.
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 study elliptic and triangular flow in the collisions of deuteron-gold nuclei at $\sqrt{s_{\rm NN}} = 200$ GeV at RHIC and of proton-lead nuclei at $\sqrt{s_{\rm NN}} = 5.02$ TeV at the LHC, utilizing (3+1)-dimensional ideal hydrodynamics for the dynamic evolution of the fireball and a Glauber-based Monte-Carlo energy deposition model for simulating the fluctuating initial conditions. Sizable values of elliptic and triangular flow are obtained for both colliding systems, and the results are consistent with PHENIX, ALICE, ATLAS and CMS measurements. For these studied centralities, we find tha…
Direct photon spectra from uranium-uranium collisions at FAIR energies (E(lab) = 35 AGeV) are calculated within the hadronic Ultra-relativistic Quantum Molecular Dynamics transport model. In this microscopic model, one can optionally include a macroscopic intermediate hydrodynamic phase. The hot and dense stage of the collision is then modeled by a hydrodynamical calculation. Photon emission from transport-hydro hybrid calculations is examined for purely hadronic matter and matter that has a cross-over phase transition and a critical end point to deconfined and chirally restored matter at high…
We calculate, for the first time, $J/ψ$ triangular flow in high energy nuclear collisions. The charmonium motion in medium is controlled by a transport equation with loss and gain terms, and the evolution of the hot medium is governed by a single-shot hydrodynamic equation with a triangularly deformed initial condition. In comparison with the elliptic flow $v_2$, the triangular flow $v_3$ comes almost completely from the charmonium regeneration in the quark gluon plasma and therefore is more sensitive to the medium properties.
We present basic equations of nonequilibrium thermo field dynamics of dense quantum systems. A formulation of nonequilibrium thermo field dynamics has been performed using the nonequilibrium statistical operator method by D.N.Zubarev. Generalized transfer and hydrodynamic equations of a consistent description of kinetics and hydrodynamics have been obtained in thermo field representation. To demonstrate how obtained results do work at the description of kinetics and hydrodynamics of a dense nuclear matter we consider quantum system with strongly coupled states.
Chiral anomaly implies the existence of non-dissipative transport phenomena, such as the chiral magnetic effect. At second order in the derivative expansion, novel quantum transport phenomena emerge. In this paper, we focus on the anomalous transport driven by a combination of shear, vorticity and magnetic field. We find that the corresponding transport phenomena -- shear-induced chiral magnetic and chiral vortical effects (siCME and siCVE) -- induce characteristic charge correlations among the hadrons produced in heavy ion collisions. We propose the charge asymmetry of triangular flow as a si…
In heavy ion collisions, event-by-event fluctuations in participating nucleon positions can lead to triangular flow. Generally, one uses Monte-Carlo Glauber model to obtain the participating nucleon positions. To use in a hydrodynamic model, the positions needs to be smoothened. We study the effect of smoothening of Glauber Monte-Carlo initial conditions on elliptic and triangular flow. It is shown that integrated as well as differential elliptic and triangular flow remain largely unaltered, irrespective of functional form of the smoothening function, or the smoothening parameter
Direct photon emission in heavy-ion collisions is calculated within the relativistic microscopic transport model UrQMD. We compare the results from the pure transport calculation to a hybrid-model calculation, where the high-density part of the evolution is replaced by an ideal 3-dimensional fluiddynamic calculation. The effects of viscosity, present in the transport model but neglected in ideal fluid-dynamics, are examined. We study the contribution of different production channels and non-thermal collisions to the spectrum of direct photons. Detailed comparison to the measurements by the WA~…
We investigate whether hydrodynamic attractors are present in simulations of the quark-gluon plasma formed in heavy-ion collisions. We argue that Lagrangian schemes to solve the relativistic viscous fluid equations can be particularly useful to characterize the properties of attractors in heavy ion collisions. Preliminary results are shown in Israel-Stewart theory to support such a claim. We also discuss how to perform the slow-roll expansion in Israel-Stewart theory undergoing a general flow, which naturally leads to the definition of a resummed shear viscosity coefficient that depends on the…
We studied the relation between the initial geometry anisotropy and the anisotropic flow in a multiphase transport model (AMPT) for both Au+Au and Cu+Cu collisions at $\sqrt{s_{NN}}$ = 200 GeV. It is found that unlike the elliptic flow $v_2$, little centrality dependence of the triangular flow $v_3$ is observed. After removing the initial geometry effect, $v_3/ε_3$ increases with the transverse particle density, which is similar to $v_2/ε_2$. The transverse momentum ($p_T$) dependence of $v_3$ from identified particles is qualitatively similar to the $p_T$ dependence of $v_2$.
We compare 2->2 covariant transport theory and causal Israel-Stewart hydrodynamics in 2+1D longitudinally boost invariant geometry with RHIC-like initial conditions and a conformal e = 3p equation of state. The pressure evolution in the center of the collision zone and the final differential elliptic flow v2(pT) from the two theories agree remarkably well for a small shear viscosity to entropy density ratio eta/s ~ 1/(4 pi), and also for a large cross section sigma ~ 50 mb. A key to this agreement is keeping ALL terms in the Israel-Stewart equations of motion. Our results indicate promising pr…
The triangular flow in ultrarelativistic $^3$He-Au collisions at RHIC energies is enhanced due to the triangular arrangement of the nucleon configurations in $^3$He. We study the fireball eccentricities in the Glauber Monte Carlo model and find that since the configurations of the projectile $^3$He are elongated triangles, the created fireball has a large ellipticity and a smaller triangularity. The dependence of the triangularity on centrality is weak, so it cannot be extracted from the centrality dependence of the triangular flow $v_3$, as it is dominated by the centrality dependence of the …
While the existence of a strongly interacting state of matter, known as 'quark-gluon plasma' (QGP), has been established in heavy ion collision experiments in the past decade, the task remains to map out the transition from the hadronic matter to the QGP. This is done by measuring the dependence of key observables (such as particle suppression and elliptic flow) on the collision energy of the heavy ions. This procedure, known as 'beam energy scan', has been most recently performed at the Relativistic Heavy Ion Collider (RHIC). Utilizing a Boltzmann+hydrodynamics hybrid model, we study the coll…
We have obtained a new set of parameters in a multiphase transport (AMPT) model that are able to describe both the charged particle multiplicity density and elliptic flow measured in Au+Au collisions at center of mass energy $\sqrt{s_{NN}}=200$ GeV at the Relativistic Heavy Ion Collider (RHIC), although they still give somewhat softer transverse momentum spectra. We then use the model to predict the triangular flow due to fluctuations in the initial collision geometry and study its effect relative to those from other harmonic components of anisotropic flows on the di-hadron azimuthal correlati…
Event-by-event hydrodynamics is applied to Cu-Au collisions at 200GeV. Predictions for charged particle distributions in pseudorapidity, transverse momentum spectra, femtoscopy radii are given. The triangular and elliptic flow coefficients are calculated. The directed flow at central rapidity in the reaction plane in asymmetric collisions is nonzero, fluctuations of the initial profile lead to a further increase of the directed flow when measured in the event plane.
Flow signatures in experimental data from relativistic ion collisions are usually interpreted as a fingerprint of the presence of a hydrodynamic phase during the evolution of these systems. In this work, flow signatures arising from event-by-event viscous hydrodynamics are compared to those arising from event-by-event non-interacting particle dynamics (free-streaming), both followed by a late-stage hadronic cascade, in d+Au, 3He+Au at sqrt(s)=200 GeV and p+Pb collisions at sqrt(s)=5 TeV, respectively. For comparison, also Pb+Pb collisions at sqrt(s)=2.76 TeV are simulated. It is found that non…
Experimental data from the Relativistic Heavy Ion Collider (RHIC) suggests that the quark gluon plasma behaves almost like an ideal fluid. Due to its short lifetime, many QGP properties can only be inferred indirectly through a comparison of the final state measurements with transport model calculations. Among the current phenomena of interest are the interdependencies between two collective flow phenomena, elliptic and triangular flow. The former is mostly related to the initial geometry and collective expansion of the system whereas the latter is sensitive to the fluctuations of the initial …
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 carry out a combined analysis of elliptic and triangular flow data using viscous relativistic hydrodynamics. We show that these data allow to put tight constraints on models of the early dynamics of a nucleus-nucleus collision. Specifically, the rms values of the initial ellipticity $\varepsilon_2$ and the initial triangularity $\varepsilon_3$ are constrained to lie within a narrow band for each centrality. We use these constraints as a filter for existing Monte-Carlo models of initial state, and provide a simple test that can be performed on any candidate model to determine its compatibili…
We investigate coefficients in the Israel-Stewart's causal hydrodynamics and discuss the way to calculate them with a microscopic theory. Based on the hadro-molecular simulation based on an event generator URASiMA, we evaluate the coefficients for a hot and dense hadronic fluid.
We derive a set of nontrivial relations between second-order transport coefficients which follow from the second law of thermodynamics upon considering a regime close to uniform rotation of the fluid. We demonstrate that extension of hydrodynamics by spin variable is equivalent to modifying conventional hydrodynamics by a set of second-order terms satisfying the relations we derived. We point out that a novel contribution to the heat current orthogonal to vorticity and temperature gradient reminiscent of the thermal Hall effect is constrained by the second law.
Elliptic flow has been one of the key observables for establishing the finding of the quark-gluon plasma (QGP) at the highest energies of Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). As a sign of collectively behaving matter, one would expect the elliptic flow to decrease at lower beam energies, where the QGP is not produced. However, in the recent RHIC beam energy scan, it has been found that the inclusive charged hadron elliptic flow changes relatively little in magnitude in the energies between 7.7 and 39 GeV per nucleon-nucleon collision. We study the collisi…
The Green-Kubo-Nakano formula should be modified in relativistic hydrodynamics because of the problem of acausality and the breaking of sum rules. In this work, we propose a formula to calculate the transport coefficients of causal hydrodynamics based on the projection operator method. As concrete examples, we derive the expressions for the diffusion coefficient, the shear viscosity coefficient, and corresponding relaxation times.
Many strongly coupled fluids are known to share similar hydrodynamic transport properties. In this work we argue that this similarity could extend beyond hydrodynamics to transient dynamics through the presence of non-hydrodynamic modes. We review non-hydrodynamic modes in kinetic theory and gauge/gravity duality and discuss their signatures in trapped Fermi gases close to unitarity. Reanalyzing previously published experimental data, we find hints of non-hydrodynamic modes in cold Fermi gases in two and three dimensions.
Collective flow and femtoscopy in ultrarelativistic 3He-Au collisions are investigated within the 3+1-dimensional (3+1D) viscous event-by-event hydrodynamics. We evaluate elliptic and triangular flow coefficients as functions of the transverse momentum. We find the typical long-range ridge structures in the two-particle correlations in the relative azimuth and pseudorapidity, in the pseudorapidity directions of both Au and 3He. We also make predictions for the pionic interferometric radii, which decrease with the transverse momentum of the pion pair. All features found hint on collectivity of …
We carry out simulations using a multiphase transport (AMPT) model to describe the observed flow signatures in $\sqrt{s_{NN}}=2.76$ TeV Pb-Pb collisions. Especially, we calculate the flow fluctuations of $v_2$ in terms of cumulant ratios and the standardized skewness. Based on event-by-event AMPT simulations, we study the linear and cubic response relation between $v_2$ and $\varepsilon_2$. We found that the observed response relation is compatible to what has been noticed in hydrodynamic modelings, with similar dependence on shear viscosity. Besides, this response relation is not sensitive to…
We present a combined analysis of elliptic and triangular flow data from LHC and RHIC using viscous relativistic hydrodynamics. Elliptic flow $v_2$ in hydrodynamics is proportional to the participant eccentricity $\varepsilon_2$ and triangular flow is proportional to the participant triangularity $\varepsilon_3$, which means $v_n=C_n\varepsilon_n$, where $C_n$ is the linear response coefficient in harmonic n. Experimental data for $v_2$ and $v_3$ combined with hydrodynamic calculations of $C_n$ thus provide us with the rms values of initial anisotropies $\varepsilon_2$ and $\varepsilon_3$. By …
The microscopic transport model UrQMD and a micro+macro hybrid model are used to calculate direct photon spectra from U+U-collisions at Elab = 35 AGeV as will be measured by the CBM-collaboration at FAIR. In the hybrid model, the intermediate high-density part of the nuclear interaction is described with ideal 3+1-dimensional hydrodynamics. Different equations of state of the matter created in the heavy-ion collisions are investigated and the resulting spectra of direct photons are predicted. The emission patterns of direct photons in space and time are discussed.
In this paper we investigate how the energy and momentum deposited by partonic dijets in the quark-gluon plasma may affect the direct, elliptic and triangular flow of low (and intermediate) $p_T$ hadrons in central Au+Au collisions at RHIC. The dijets are modeled as external sources in the energy-momentum conservation equations for hydrodynamics, which are solved on an event-by-event basis within the ideal fluid approximation. We focus our investigation at mid-rapidity and solve the hydrodynamic equations imposing boost invariance. Differential anisotropic flow coefficients for $p_T \gtrsim 1$…
Recent measurements have established the sensitivity of ultracentral heavy-ion collisions to the deformation parameters of non-spherical nuclei. In the case of ${}^{ 129}$Xe collisions, a quadrupole deformation of the nuclear profile led to an enhancement of elliptic flow in the most central collisions. In ${}^{ 208}$Pb collisions a discrepancy exists in similar centralities, where either elliptic flow is over-predicted or triangular flow is under-predicted by hydrodynamic models; this is known as the $v_2$-to-$v_3$ puzzle in ultracentral collisions. Motivated by low-energy nuclear structure c…
A new formula to calculate the transport coefficients of the causal dissipative hydrodynamics is derived by using the projection operator method (Mori-Zwanzig formalism) in [T. Koide, Phys. Rev. E75, 060103(R) (2007)]. This is an extension of the Green-Kubo-Nakano (GKN) formula to the case of non-Newtonian fluids, which is the essential factor to preserve the relativistic causality in relativistic dissipative hydrodynamics. This formula is the generalization of the GKN formula in the sense that it can reproduce the GKN formula in a certain limit. In this work, we extend the previous work so as…
In this contribution we study the effects of three transport coefficients of dissipative hydrodynamics on thermal dilepton anisotropic flow observables. The first two transport coefficients investigated influence the overall size and growth rate of shear viscous pressure, while the last transport coefficient governs the magnitude of net baryon number diffusion in relativistic dissipative fluid dynamics. All calculations are done using state-of-the-art 3+1D hydrodynamical simulations. We show that thermal dileptons are sensitive probes of the transport coefficients of dissipative hydrodynamics.
In this paper we obtain holographic formulas for the transport coefficients $κ$ and $τ_π$ present in the second-order derivative expansion of relativistic hydrodynamics in curved spacetime associated with a non-conformal strongly coupled plasma described holographically by an Einstein+Scalar action in the bulk. We compute these coefficients as functions of the temperature in a bottom-up non-conformal model that is tuned to reproduce lattice QCD thermodynamics at zero baryon chemical potential. We directly compute, besides the speed of sound, 6 other transport coefficients that appear at second…
The longitudinal long-range correlations of the triangular flow event plane angles are calculated in a Boltzmann + hydrodynamics hybrid approach. The potential to disentangle different energy deposition scenarios is explored by utilizing two different transport approaches for the early non-equilibrium evolution. In the hadronic transport approach the particle production in high energy heavy ion reactions is mainly governed by string excitation and fragmentation processes which are absent in the parton cascade approach. We find that in both approaches the initial state shows a strong longitudin…
In the limit of short mean free path, relativistic kinetic theory gives rise to hydrodynamics through a systematically improvable gradient expansion. In the present work, a systematically improvable expansion in the opposite limit of large mean free path is considered, describing the dynamics of particles which are almost, but not quite, non-interacting. This non-hydrodynamic "eremitic" expansion does not break down for large gradients, and may be useful in situations where a hydrodynamic treatment is not applicable. As applications, azimuthal anisotropies at high transverse momentum in Pb+Pb …
We present a coupled Boltzmann and hydrodynamics approach to relativistic heavy ion reactions. This hybrid approach is based on the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) transport approach with an intermediate hydrodynamical evolution for the hot and dense stage of the collision. Event-by-event fluctuations are directly taken into account via the non-equilibrium initial conditions generated by the initial collisions and string fragmentations in the microscopic UrQMD model. After a (3+1)-dimensional ideal hydrodynamic evolution, the hydrodynamical fields are mapped to hadrons vi…
We analyze the evolution of hydrodynamic fluctuations for QCD matter below $T_c$ in the chiral limit, where the pions (the Goldstone modes) must be treated as additional non-abelian superfluid degrees of freedom, reflecting the broken $SU_L(2) \times SU_R(2)$ symmetry of the theory. In the presence of a finite pion mass $m_π$, the hydrodynamic theory is ordinary hydrodynamics at long distances, and superfluid-like at short distances. The presence of the superfluid degrees of freedom then gives specific contributions to the bulk viscosity, the shear viscosity, and diffusion coefficients of the …
We construct the general hydrodynamic description of (3+1)-dimensional chiral charged (quantum) fluids subject to a strong external magnetic field with effective field theory methods. We determine the constitutive equations for the energy-momentum tensor and the axial charge current, in part from a generating functional. Furthermore, we derive the Kubo formulas which relate two-point functions of the energy-momentum tensor and charge current to 27 transport coefficients: 8 independent thermodynamic, 4 independent non-dissipative hydrodynamic, and 10 independent dissipative hydrodynamic transpo…
