Strongly interacting low-viscosity matter created in relativistic nuclear collisions

Early-Times Yang-Mills Dynamics and the Characterization of Strongly Interacting Matter with Statistical Learning

In ultrarelativistic heavy-ion collisions, a plasma of deconfined quarks and gluons is formed within 1  fm/c of the nuclei's impact. The complex dynamics of the collision before ≈1  fm/c is often described with parametric models, which affect the predictivity of calculations. In this work, we perform a systematic analysis of LHC measurements from Pb-Pb collisions, by combining an ab initio model of the early stage of the collisions with a hydrodynamic model of the plasma. We obtain state-of-the-art constraints on the shear and bulk viscosity of quark-gluon plasma. We mitigate the additional cost of the ab initio initial conditions by combining Bayesian model averaging with transfer learning, allowing us to account for important theoretical uncertainties in the hydrodynamics-to-hadron transition. We show that, despite the apparent strong constraints on the shear viscosity, metrics that balance the model's predictivity with its degree of agreement with data do not prefer a temperature-dependent specific shear viscosity over a constant value. We validate the model by comparing with discriminating observables not used in the calibration, finding excellent agreement.

Total and Partial Shear Viscosity in Heavy-Ion Collisions at Energies of BES, FAIR and NICA

We calculated the shear viscosity of hot and dense nuclear matter produced in a symmetric system of central gold–gold collisions at energies of BES RHIC, FAIR and NICA. For calculations of the collisions, the transport model UrQMD was employed. The shear viscosity was obtained within the Green–Kubo formalism. The hadron resonance gas model was used to determine temperature and chemical potentials of baryon charge and strangeness out of microscopic model calculations. In contrast to our previous works, we determined the partial viscosity of the main hadron species, such as nucleons, pions, kaons and Lambdas, via the nucleon–nucleon, pion–pion and so forth, correlators. A decrease in the beam energy from Elab=40 to 10 AGeV leads a to rise in baryon shear viscosity accompanied by a drop in the shear viscosity of mesons. The ratio of total shear viscosity to entropy density also decreases.

Local conservation laws in ultracold Fermi systems with time-dependent interaction potential

In the context of an ultracold Fermi gas, we derive conservation laws for mass, energy and momentum based on a generalized nonlocal Boltzmann equation with gradient corrections in the collision integral. The corrections are expressed in terms of effective collision duration, particle displacement and changes of total momentum and energy. Their origin is in the in-medium T matrix. Using variations of the optical theorem, we show that in the collision integral the particle-hole symmetry can be recast into a form of collision symmetry amenable to semiclassical simulation. Pauli-blocked collisions are distinguished from Bose-stimulated nondissipative ones; the latter are not present in the absence of gradient corrections. Consolidating with the microscopic theory, we extract local conservation laws for a general time-dependent interaction potential, and demonstrate how both types of collisions affect densities and flows of conserving quantities. Comparison is made with the approach of Nozières and Schmitt-Rink in the limit of thermal equilibrium. Under approximations used for normal-state ultracold Fermi gases interacting via Feshbach resonances we demonstrate the effect of the collision delay on the shear viscosity.

Constraining QCD transport coefficients in hadron colliders

We review the phenomenology of relativistic nuclear collisions in the light of ultra-high energy cosmic ray physics. A novel phase of quantum chromodynamics called quark-gluon plasma is expected to appear in nuclear collisions at high energies. The produced hot matter is found to be well-described as a relativistic fluid with small viscosity. We show that the transport coefficient can be quantitatively extracted by comparing theoretical estimations of viscous hydrodynamic models to experimental data.

Moving Forward to Constrain the Shear Viscosity of QCD Matter

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 the RHIC, we find evidence for a small η/s≈0.04 in the QCD crossover 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 constrain the initial state fluctuations in three dimensions and the temperature dependent transport properties of QCD matter.

Measurement of the centrality dependence of the charged-particle pseudorapidity distribution in proton-lead collisions at [Formula: see text] TeV with the ATLAS detector

The centrality dependence of the mean charged-particle multiplicity as a function of pseudorapidity is measured in approximately 1 [Formula: see text]b[Formula: see text] of proton-lead collisions at a nucleon-nucleon centre-of-mass energy of [Formula: see text] [Formula: see text] using the ATLAS detector at the Large Hadron Collider. Charged particles with absolute pseudorapidity less than 2.7 are reconstructed using the ATLAS pixel detector. The [Formula: see text] collision centrality is characterised by the total transverse energy measured in the Pb-going direction of the forward calorimeter. The charged-particle pseudorapidity distributions are found to vary strongly with centrality, with an increasing asymmetry between the proton-going and Pb-going directions as the collisions become more central. Three different estimations of the number of nucleons participating in the [Formula: see text] collision have been carried out using the Glauber model as well as two Glauber-Gribov inspired extensions to the Glauber model. Charged-particle multiplicities per participant pair are found to vary differently for these three models, highlighting the importance of including colour fluctuations in nucleon-nucleon collisions in the modelling of the initial state of [Formula: see text] collisions.

Transport coefficients in Yang-Mills theory and QCD

We calculate the shear-viscosity-over-entropy-density ratio η/s in Yang-Mills theory from the Kubo formula using an exact diagrammatic representation in terms of full propagators and vertices using gluon spectral functions as external input. We provide an analytic fit formula for the temperature dependence of η/s over the whole temperature range from a glueball resonance gas at low temperatures, to a high-temperature regime consistent with perturbative results. Subsequently, we provide a first estimate for η/s in QCD.

Indications for a critical end point in the phase diagram for hot and dense nuclear matter

Excitation functions for the Gaussian emission source radii difference (R_{out}^{2}-R_{side}^{2}) obtained from two-pion interferometry measurements in Au+Au (sqrt[s_{NN}]=7.7-200  GeV) and Pb+Pb (sqrt[s_{NN}]=2.76  TeV) collisions are studied for a broad range of collision centralities. The observed nonmonotonic excitation functions validate the finite-size scaling patterns expected for the deconfinement phase transition and the critical end point (CEP), in the temperature versus baryon chemical potential (T,μ_{B}) plane of the nuclear matter phase diagram. A finite-size scaling (FSS) analysis of these data suggests a second order phase transition with the estimates T^{cep}∼165  MeV and μ_{B}^{cep}∼95  MeV for the location of the critical end point. The critical exponents (ν≈0.66 and γ≈1.2) extracted via the same FSS analysis place this CEP in the 3D Ising model universality class.

Electrical conductivity of hot QCD matter

We study the electric conductivity of hot QCD matter at various temperatures T within the off-shell parton-hadron-string dynamics transport approach for interacting partonic, hadronic or mixed systems in a finite box with periodic boundary conditions. The response of the strongly interacting system in equilibrium to an external electric field defines the electric conductivity σ(0). We find a sizable temperature dependence of the ratio σ(0)/T well in line with calculations in a relaxation time approach for T(c)<T<2.5T(c). The ratio drops in the hadronic phase with T, shows a minimum close to T(c), and becomes approximately constant (~0.3) above ~5T(c). Our findings imply that the QCD matter even at T ≈ T(c) is a much better electric conductor than Cu or Ag (at room temperature).

Influence of shear viscosity of quark-gluon plasma on elliptic flow in ultrarelativistic heavy-ion collisions

We investigate the influence of a temperature-dependent shear viscosity over entropy density ratio η/s on the transverse momentum spectra and elliptic flow of hadrons in ultrarelativistic heavy-ion collisions. We find that the elliptic flow in √S(NN)=200  GeV Au+Au collisions at RHIC is dominated by the viscosity in the hadronic phase and in the phase transition region, but largely insensitive to the viscosity of the quark-gluon plasma (QGP). At the highest LHC energy, the elliptic flow becomes sensitive to the QGP viscosity and insensitive to the hadronic viscosity.

200 A GeV Au + Au collisions serve a nearly perfect quark-gluon liquid

A new robust method to extract the specific shear viscosity (η/s)(QGP) of a quark-gluon plasma (QGP) at temperatures T(c) < T ≲ 2T(c) from the centrality dependence of the eccentricity-scaled elliptic flow v2/ε measured in ultrarelativistic heavy-ion collisions is presented. Coupling viscous fluid dynamics for the QGP with a microscopic transport model for hadronic freeze-out we find for 200 A GeV Au + Au collisions that v2/ε is a universal function of multiplicity density (1/S)(dN(ch)/dy) that depends only on the viscosity but not on the model used for computing the initial fireball eccentricity ε. Comparing with measurements we find 1<4π(η/s)(QGP) < 2.5 where the uncertainty range is dominated by model uncertainties for the values of ε used to normalize the measured v2.

Transport coefficients of hadronic matter near Tc

A hadron resonance gas model including all known particles and resonances with masses m < 2 GeV and an exponentially rising density of Hagedorn states for m > 2 GeV is used to obtain an upper bound on the shear viscosity to entropy density ratio, eta/s approximately 1/(4pi), of hadronic matter near Tc. We found a large trace anomaly and small speed of sound near Tc, which agree well with recent lattice calculations. We comment on the bulk viscosity to entropy density ratio close to Tc.

Shear viscosity coefficient and relaxation time of causal dissipative hydrodynamics in QCD

The shear viscosity coefficient and the corresponding relaxation time for causal dissipative hydrodynamics are calculated based on the microscopic formula proposed in T. Koide and T. Kodama [Phys. Rev. E 78, 051107 (2008)10.1103/PhysRevE.78.051107]. Here, the exact formula is transformed into a more compact form and applied to evaluate these transport coefficients in the chiral perturbation theory and perturbative QCD. It is shown that in the leading order calculation, the causal shear viscosity coefficient eta reduces to that of the ordinary Green-Kubo-Nakano formula, and the relaxation time tau(pi) is related to eta and pressure P by a simple relationship, tau(pi)=eta/P.

Exposing the noncollectivity in elliptic flow

We show that backward-forward elliptic anisotropy correlation provides an experimentally accessible observable which distinguishes between collective and noncollective contributions to the observed elliptic anisotropy v_{2} in relativistic heavy ion collisions. The measurement of this observable will reveal the momentum scale at which collective expansion seizes and where the elliptic anisotropy is dominated by (semi)hard processes.

Angular dependence of jet quenching indicates its strong enhancement near the QCD phase transition

We study dependence of jet quenching on matter density, using "tomography" of the fireball provided by RHIC data on azimuthal anisotropy v_{2} of high p_{t} hadron yield at different centralities. Slicing the fireball into shells with constant (entropy) density, we derive a "layer-wise geometrical limit" v_{2};{max} which is indeed above the data v_{2} < v_{2};{max}. Interestingly, the limit is reached only if quenching is dominated by shells with the entropy density exactly in the near-T_{c} region. We show two models that simultaneously describe the high p_{t} v_{2} and R_{A-A} data and conclude that such a description can be achieved only if the jet quenching is few times stronger in the near-T_{c} region relative to QGP at T > T_{c}. One possible reason for such enhancement may be recent indications that the near-T_{c} region is a magnetic plasma of relatively light color-magnetic monopoles.

Towards a unified understanding of jet quenching and elliptic flow within a perturbative QCD parton transport

The gluonic contribution to the nuclear modification factor R_{AA} is investigated for central Au + Au collisions at sqrt[s] = 200 AGeV employing a perturbative QCD-based parton cascade including radiative processes. A flat quenching pattern is found up to transverse momenta of 30 GeV, which is slightly smaller compared with results from the Gyulassy-Levai-Vitev formalism. We demonstrate that the present microscopic transport description provides a challenging means of investigating both jet quenching and a strong buildup of elliptic flow in terms of the same standard perturbative QCD interactions.

Shear-viscosity to entropy-density ratio of a relativistic hadron gas

Ultrarelativistic heavy-ion collisions at the Brookhaven National Laboratory 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 eta/s, near the lower bound predicted for that quantity by anti-de Sitter space/conformal field theory methods. As the produced matter expands and cools, it evolves through a phase described by a hadron gas with rapidly increasing eta/s. We calculate eta/s as a function of temperature in this phase both in and out of chemical equilibrium and find that its value poses a challenge for viscous relativistic hydrodynamics, which requires small values of eta/s in order to successfully describe the collective flow observables at the RHIC. We therefore conclude that the origin of the low viscosity matter at the RHIC must be in the partonic phase of the reaction.

Perturbative QCD calculations of elliptic flow and shear viscosity in Au+Au collisions at sqrt[s_{NN}]=200 GeV

The elliptic flow v_{2} and the ratio of the shear viscosity over the entropy density, eta/s, of gluon matter are calculated from the perturbative QCD (pQCD) based parton cascade Boltzmann approach of multiparton scatterings. For Au+Au collisions at sqrt[s]=200A GeV the gluon plasma generates large v_{2} values measured at the BNL Relativistic Heavy Ion Collider. Standard pQCD yields eta/s approximately 0.08-0.15 as small as the lower bound found from the anti-de Sitter/conformal field theory conjecture.

Heavy quark diffusion in perturbative QCD at next-to-leading order

We compute the momentum diffusion coefficient of a heavy quark in a hot QCD plasma, to next-to-leading order in the weak-coupling expansion. Corrections arise at [see formula]; physically they represent interference between overlapping scatterings, as well as soft, electric scale (p approximately gT) gauge field physics, which we treat using the hard thermal loop effective theory. In 3-color, 3-flavor QCD, the momentum diffusion constant of a fundamental representation heavy quark at next-to-leading order is kappa = 16pi/3alpha(s)(2)T(3)(ln1/g(s)+0.07428+1.9026 g(s)). The convergence of the perturbative expansion is poor.

Microscopic formula for transport coefficients of causal hydrodynamics

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 Rapid Communication, 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.

Has the QCD critical point been signaled by observations at the BNL relativistic heavy ion collider?

The shear viscosity to entropy ratio (eta/s) is estimated for the hot and dense QCD matter created in Au+Au collisions at BNL Relativistic Heavy Ion Collider (square root[s_{NN}]=200 GeV). A very low value is found; eta/s approximately 0.1, which is close to the conjectured lower bound (1/4pi). It is argued that such a low value is indicative of thermodynamic trajectories for the decaying matter which lie close to the QCD critical end point.