Sean Gavin, George Moschelli
Correlation studies exhibit a ridge-like feature in rapidity and azimuthal angle, with and without a jet trigger. We ask whether the feature in untriggered correlations can be a consequence of transverse flow and viscous diffusion.
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Hydrodynamic behavior and the associated discussions of viscosity at RHIC has inspired a r enaissance in modeling viscous hydrodynamics. An explanation of Israel-Stewart hydrodynamics is presented here, with an emphasis on the tangible benefits compared to Navier Stokes.
We show from covariant transport theory that, for a massless ideal gas equation of state, even a small shear viscosity to entropy density ratio $η\approx s/(4 π)$ generates significant 15-30% dissipative corrections to elliptic flow for conditions expected in mid-peripheral (b = 8 fm) Au+Au collisions at $\sqrt{s_{NN}} \sim 200$ GeV at RHIC.
We study the effects of bulk viscosity on p_T spectra and elliptic flow in heavy ion collisions at RHIC. We argue that direct effect of the bulk viscosity on the evolution of the velocity field is small, but corrections to the freezeout distributions can be significant. These effects are dominated by chemical non-equilibration in the hadronic phase. We show that a non-zero bulk viscosity in the range $ζ/s \lsim 0.05$ improves the description of spectra and flow at RHIC.
A variety of physical phenomena can lead to viscous effects. In this talk we review several sources of shear and bulk viscosity with an emphasis on the bulk viscosity associated with chiral restoration. We show that in the limit of a second order phase transition, the viscosity peaks in a singularity at the critical point.
A variety of physical phenomena can lead to viscous effects. Several sources of shear and bulk viscosity are reviewed with an emphasis on the bulk viscosity associated with chiral restoration and with chemical non-equilibrium. We show that in a mean-field treatment of the limiting case of a second order phase transition, the bulk viscosity peaks in a singularity at the critical point.
We consider the longitudinal hydrodynamic evolution of the fireball created in a relativistic heavy-ion collision. Nonzero shear viscosity reduces the colling rate of the system and hinders the acceleration of the longitudinal flow. As a consequence, the initial energy density needed to reproduce the experimental data at RHIC energies is significantly reduced. At LHC energies, we expect that shear viscosity helps to conserve a Bjorken plateau in the rapidity distributions during the expansion.
We describe ultra-relativistic heavy ion collisions at RHIC and the LHC 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.
We report recent progress on causal viscous hydrodynamics for relativistic heavy ion collisions. For fixed specific shear viscosity eta/s, uncertainties in the elliptic flow arising from initial conditions, equation of state, bulk viscosity and numerical viscosity, and the treatment of the highly viscous hadronic stage and freeze-out procedure are analysed. A comparison of current viscous hydrodynamic results with experimental data yields a robust upper limit eta/s < 5/(4pi).
We investigate the consequences of long range rapidity correlations in the Glasma. Particles produced locally in the transverse plane are correlated by approximately boost invariant flux tubes of longitudinal color electric and magnetic fields that are formed when two sheets of Colored Glass Condensate pass through one another, each acquiring a modified color charge density in the collision. We argue that such long range rapidity correlations persist during the evolution of the Quark Gluon Plasma formed later in the collision. When combined with transverse flow, these correlations reproduce ma…
We obtain prompt di-photon cross-section in proton-nucleus collisions in Hamiltonian light-cone approach within a hybrid approximation, treating the projectile proton in the parton model and the target nucleus in the Color-Glass-Condensate approach. We study in details the di-photon correlations in quark-nucleus and proton-nucleus collisions at RHIC and the LHC. We show that the single fragmentation di-photon produces the away side correlations peak, and the double fragmentation component of prompt di-photon is responsible for the near-side peak, and the long-range in rapidity near-side azimut…
In this article, we briefly review the recent progress related to extracting the quark-gluon plasma (QGP) specific shear viscosity from the flow data measured at Relativistic Heavy-Ion Collider (RHIC) and the Large Hadron Collider (LHC).
We argue that "ridge" in 2-particle correlation function associated with hard trigger at RHIC heavy ion collisions is naturally explained by an interrelation of jet quenching and hydrodynamical transverse flow. The excess particles forming the ridge are produced by QCD bremsstrahlung along the beam (and thus have wide rapidity distribution) and then boosted by transverse flow. Nontrivial correlation between directions of the jet and the radial flow is provided by jet quenching: our straightforward and basically parameter-independent calculation reproduces the angular shape, width and other pro…
The interplay between shear and bulk viscosities on the flow harmonics, $v_n$'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 den…
Relativistic viscous hydrodynamic fits to RHIC data on the centrality dependence of multiplicity, transverse and elliptic flow for sqrt{s}=200 GeV Au+Au collisions are presented. For Glauber-type initial conditions, while data on integrated v_2 is consistent with a ratio of viscosity over entropy density up to eta/s=0.16, data on minimum bias v_2 seems to favor a much smaller viscosity over entropy ratio, below the bound from the AdS/CFT conjecture. Some caveats on this result are discussed.
Within a covariant parton cascade, we discuss the impact of both finite shear viscosity $η$ and freeze-out dynamics on the elliptic flow generated at RHIC. We find that the enhancement of $η/s$ in the cross-over region of the QGP phase transition cannot be neglected in order to extract the information from the QGP phase. We also point out that the elliptic flow $v_2(p_T)$ for a fluid at $η/s \sim 0.1-0.2$ is consistent with the one needed by quark number scaling drawing a nice consistency between the nearly perfect fluid property of QGP and the coalescence process.
We study real photons produced in heavy ion collisions at RHIC, and we calculate their spectrum and its azimuthal momentum anisotropy. The photons from a variety of sources are included, and the interplay and the time-evolution of those sources are modelled in a full 3D hydrodynamic simulation. We quantify the v_2 of thermal photons produced in ideal and viscous fluids, and the consequences of using different initial conditions are explored.
The origin of the trigger-angle dependence of the ridge structure in two-hadron long-range correlations, as observed at RHIC, is discussed as due to an interplay between the elliptic flow caused by the initial state global geometry and flow produced by fluctuations.
Hadron correlations in jets, ridges and opposite dijets at all $p_T$ above 2 GeV/c are discussed. Since abundant data are available from RHIC at intermediate $p_T$, a reliable hadronization scheme at that $p_T$ range is necessary in order to relate the semihard partonic processes to the observables. The recombination model is therefore first reviewed for that purpose. Final-state interaction is shown to be important for the Cronin effect, large B/M ratio and forward production. The effect of semihard partons on the medium is then discussed with particular emphasis on the formation of ridge wit…
The specific shear viscosity (eta/s)_QGP of quark-gluon plasma (QGP) can be extracted from elliptic flow data in heavy-ion collisions by comparing them with the dynamical model VISHNU which couples a viscous fluid dynamic description of the QGP with a microscopic kinetic description of the late hadronic rescattering and freeze-out stage. A robust method for fixing (eta/s)_QGP from the collision centrality dependence of the eccentricity-scaled charged hadron elliptic flow is presented. The systematic uncertainties associated with this extraction method are discussed, with specific attention to …
Experiments at the Relativistic Heavy Ion Collider (RHIC) suggest that the state of matter produced in the experiments has a low shear-viscosity to entropy-density ratio. We ask here the question what is this ratio in usual finite nuclei at low temperature. We use the experimental and theoretical results for the widths of giant vibrational states in nuclei in order to calculate the above ratio. We find that the values of this ratio are not very different from the ones found in the RHIC experiments.
Elliptic flow measurements at RHIC suggest that quark gluon plasma flows with very little viscosity compared to weak coupling expectations, challenging theorists to explain why this fluid is so nearly ``perfect''. It is therefore vital to find quantitative experimental information on the viscosity of the plasma. We propose that measurements of transverse momentum fluctuations can be used to determine the shear viscosity. We use current data to estimate the viscosity-to-entropy ratio in the range from 0.08 to 0.3, and discuss how future measurements can reduce this uncertainty.
Recent data from heavy ion collisions at RHIC show unexpectedly large near-angle correlations that broaden longitudinally with centrality. The amplitude of this ridge-like correlation rises rapidly with centrality, reaches a maximum, and then falls in the most central collisions. In this talk we explain how this behavior can be easily understood in a picture where final momentum-space correlations are driven by initial coordinate space density fluctuations. We propose $v_n^2/ε_{n,part}^{2}$ as a useful way to study these effects and explain what it tells us about the collision dynamics.
We show that the key features of the CMS result on the ridge correlation seen for high multiplicity events in sqrt(s)=7TeV proton-proton collisions at the LHC can be understood in the Color Glass Condensate framework of high energy QCD. The same formalism underlies the explanation of the ridge events seen in A+A collisions at RHIC, albeit it is likely that flow effects may enhance the magnitude of the signal in the latter.
Two-dimensional angular correlation data from the STAR experiment at RHIC and from the LHC experiments provide critical information about dynamical processes in relativistic heavy-ion collisions. The principal correlation structures of interest are a broad jet-related peak at small relative azimuth ($ϕ$) extending to large relative pseudorapidity ($η$), the dijet ridge at large relative azimuth, and an independent double ridge on $ϕ$ represented by a quadrupole function. The broad peak at small relative azimuth has been attributed, in large part, to initial-state fluctuations and hydrodynamic …
Using ideal and viscous hydrodynamics, the ratio of azimuthal moments v4/(v2)^2 is calculated for pions, protons, and kaons in sqrt{s}=200 A*GeV Au+Au collisions. For any value of viscosity here is little dependence on particle species. Ideal hydrodynamics and data show a flat curve as a function of pt. Adding viscosity in the standard way destroys this flatness. However, it can be restored by replacing the standard quadratic ansatz for delta f (the viscous correction to the distribution function at freeze-out) with a weaker momentum dependence.
Recent data from heavy ion collisions at RHIC show unexpectedly large near-angle correlations that broaden longitudinally with increasing centrality. The amplitude of this ridge-like correlation rises rapidly, reaches a maximum, and then falls in the most central collisions. In this letter we explain how this behavior can be explained as initial-state coordinate-space anisotropies converted into final-state momentum-space correlations. We propose $v_n^2/ε_{n,\mathrm{part}}^{2}$ as a useful way to study length scales and provide a prediction for the ridge in Pb+Pb collisions at $\sqrt{s_{\mathr…
In the (Delta phi)-(Delta eta) correlation associated with a near-side jet observed by the STAR Collaboration in heavy-ion collisions at RHIC [Ref. 1-6], the ridge structure can be explained by the momentum kick model in which the ridge particles are identified as medium partons which suffer a collision with the jet and acquire a momentum kick along the jet direction. If this is indeed the correct mechanism, the ridge structure associated with the near-side jet may be used to probe the parton momentum distribution at the moment of the jet-parton collision, leading to the result that at that in…
This work reports on investigations of the effects on the evolution of viscous hydrodynamics and on the flow coefficients of thermal dileptons, originating from a temperature-dependent specific shear viscosity $η/s (T)$ at temperatures beyond 180 MeV formed at the Relativistic Heavy-Ion Collider (RHIC). We show that the elliptic flow of thermal dileptons can resolve the magnitude of $η/s$ at the high temperatures, where partonic degrees of freedom become relevant, whereas discriminating between different specific functional forms will likely not be possible at RHIC using this observable.
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…
Recent hexadecapole (v4) and elliptic (v2) flow measurements are used to constrain estimates for the degree of local equilibrium, mean free path $λ$, and the viscosity to entropy density ratio (eta/s) of the plasma produced in Au+Au collisions at RootS = 200 GeV. The eccentricity-scaled flow coefficients v2/e2 and v4/e4 indicate that the plasma achieves a degree of local equilibrium within 5 - 10% of the value expected for a fluid with eta/s equal to the conjectured lower bound of 1/4pi. Estimates for $λ$ and eta/s as a function of collision centrality and particle transverse momentum pT, poin…
Ultrarelativistic heavy-ion collisions at the Relativistic Heavy-Ion Collider (RHIC) are thought to have produced a state of matter called the Quark-Gluon-Plasma, characterized by a very small shear viscosity to entropy density ratio $η/s$, near the lower bound predicted for that quantity by Anti-deSitter space/Conformal Field Theory (AdS/CFT) methods. As the produced matter expands and cools, it evolves through a phase described by a hadron gas with rapidly increasing $η/s$. We calculate $η/s$ as a function of temperature in this phase and find that its value poses a challenge for viscous rel…
We show how the measurement of appropriately constructed particle-energy/momentum correlations allows access to the bulk viscosity of strongly interacting hadron matter in heavy ion collisions. This measurement can be performed by the LHC and RHIC experiments in events with high-particle multiplicity, following up on existing estimates of the shear viscosity based on elliptic flow.
Predictions for flow harmonic distributions and flow factorization ratios at RHIC
针对RHIC能区难以区分初始条件与粘滞系数影响的问题，研究对比NeXus和TRENTO两种初始条件模型，发现RHIC能区因子化破缺比率的模型差异远大于LHC，可作为约束初始条件的有效可观测量。
We investigate the effects of a temperature-dependent shear viscosity over entropy density ratio eta/s on the flow anisotropy coefficients v_2 and v_4 in ultrarelativistic heavy-ion collisions at RHIC and LHC. We find that v_4 is more sensitive to the viscosity at low temperatures than v_2. At RHIC v_2 is mostly affected by the viscosity around the phase transition, but the larger the collision energy, the more the quark-gluon plasma viscosity affects v_2.
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 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…
Starting from IP-Glasma initial conditions, we investigate the effects of bulk pressure on thermal dilepton production at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) energies. Though results of the thermal dilepton $v_2$ under the influence of both bulk and shear viscosity is presented for top RHIC energy, more emphasis is put on LHC energy where such a calculation is computed for the first time. The effects of the bulk pressure on thermal dilepton $v_2$ at the LHC are explored through bulk-induced modifications on the dilepton yield.
We compute v4/(v2)^2 in ideal and viscous hydrodynamics. We investigate its sensitivity to details of the hydrodynamic model and compare the results to experimental data from RHIC. Whereas v2 has a significant sensitivity only to initial eccentricity and viscosity while being insensitive to freeze out temperature, we find that v4/(v2)^2 is quite insensitive to initial eccentricity. On the other hand, it can still be sensitive to shear viscosity in addition to freeze out temperature, although viscous effects do not universally increase v4/(v2)^2 as originally predicted. Consistent with data, we…
We speculate that the quark matter produced at RHIC, behaves like a perfect fluid may be considered as Landau chromo-diamagnetic material in presence of color magnetic field. We have shown that in such a system the viscosity coefficient can be small enough and in the extreme case of ultra-strong color magnetic field strength, it behaves like a super fluid.
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)_…
We present a 3-D hydro + cascade model in which viscosity and a realistic freezeout process for the hadronic phase are taken into account. We compare our results to experimental data and discuss the finite state interaction effects on physical observables.
In this work, we have extracted the initial tempearture from the transverse momentum spectra of charged particles in $Au+Au$ collisions using STAR data at RHIC energies from $\sqrt{s_{NN}}$ = 7.7 to 200 GeV. The initial energy density ($\varepsilon$), shear viscosity to entropy density ratio ($η/s$), trace anomaly ($Δ$), the squared speed of sound ($C_s^2$), entropy density, and bulk viscosity to entropy density ratio ($ζ/s$) are obtained and compared with the lattice QCD calculations for (2+1) flavor. The initial temperatures obtained are compared with various hadronization and chemical freez…
It is by now well known that the relativistic heavy-ion collisions at RHIC, BNL have produced a strongly interacting fluid with remarkable properties, among them the lowest ever observed ratio of the coefficient of shear viscosity to entropy density. Arguments based on ideas from the String Theory, in particular the AdS/CFT correspondence, led to the conjecture --- now known to be violated --- that there is an absolute lower limit $1/4 π$ on the value of this ratio. Causal viscous hydrodynamics calculations together with the RHIC data have put an upper limit on this ratio, a small multiple of …
Recently, transport coefficients viz. shear viscosity, electrical conductivity etc. of strongly interacting matter produced in heavy-ion collisions have drawn considerable interest. We study the normalised electrical conductivity ($σ_{\rm el}$/T) of hot QCD matter as a function of temperature (T) using the Color String Percolation Model (CSPM). We also study the temperature dependence of shear viscosity and its ratio with electrical conductivity for the QCD matter. We compare CSPM estimations with various existing results and lattice Quantum Chromodynamics (lQCD) predictions with (2+1) dynamic…
We study the influence of a temperature-dependent shear viscosity over entropy density ratio $η/s$, different shear relaxation times $τ_π$, as well as different initial conditions on the transverse momentum spectra of charged hadrons and identified particles. We investigate the azimuthal flow asymmetries as a function of both collision energy and centrality. The elliptic flow coefficient turns out to be dominated by the hadronic viscosity at RHIC energies. Only at higher collision energies the impact of the viscosity in the QGP phase is visible in the flow asymmetries. Nevertheless, the shear …
We review the models suggested, to date, as an explanation for the so called "ridge" phenomenon, an elongation in rapidity of 2-particle correlations seen at RHIC and LHC energies. We argue that these models can be divided into two phenomenologically distinct classes: "Hotspot+flow" driven correlations, where initial state correlations created by structures local in configuration space are collimated by transverse flow, and models where the azimuthal correlation is created through local partonic interactions in a high gluon density initial state. We further argue that the key to distinguish th…
In this paper we consider the suppression of bottomonium states in ultrarelativistic heavy ion collisions. We compute the suppression as a function of centrality, rapidity, and transverse momentum for the states Upsilon(1s), Upsilon(2s), Upsilon(3s), chi_b1, and chi_b2. Using this information, we then compute the inclusive Upsilon(1s) suppression as a function of centrality, rapidity, and transverse momentum including feed down effects. Calculations are performed for both RHIC sqrt(s_NN)=200 GeV Au-Au collisions and LHC sqrt(s_NN)=2.76 TeV Pb-Pb collisions. From the comparison of our theoretic…
Search for the conjectured QCD critical point is one of the major scientific goals for the Beam Energy Scan program at RHIC. The growth of the correlation length is a universal feature for systems near criticality, and bulk viscosity exhibits the strongest dependence on the correlation length. We investigate its effects using a relativistic hydrodynamic model to find that rapidity distributions of charged particles and net baryon number are visibly modified if the fireball passes through the vicinity of the QCD critical point on the phase diagram. We also discuss how critical modification of d…
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 η/s of QCD matter. Comparing results from hydrodynamic calculations with experimental data from RHIC, we find evidence for a small η/s $\approx$ 0.04 in the QCD cross-over region and a strong temperature dependence in the hadronic phase. A temperature independent η/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 c…
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