Shear-Viscosity to Entropy-Density Ratio of a Relativistic Hadron Gas

Abstract

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 AntideSitter 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 relativistic hydrodynamics, which requires small values of η/s throughout the entire evolution of the reaction in order to successfully describe the collective flow observables at RHIC. We show that the inclusion of non-unit fugacities will reduce η/s in the hadronic phase, yet not sufficiently to be compatible with viscous hydrodynamics. We therefore conclude that the origin of the low viscosity matter at RHIC must be in the partonic phase of the reaction.Ultrarelativistic heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) are thought to have produced a Quark Gluon Plasma (QGP) with the characteristics of a near ideal fluid [1,2,3,4]. One of the most important current challenges in QGP research is to quantify the transport coefficients of this novel state of matter. Recently, attention in the field has been primarily focused on the shear viscosity to entropy density ratio η/s. Certain supersymmetric gauge theories with gravity duals [5] suggest a lower bound of η min = s/4π for this quantity, often referred to as the KSS bound [6]. Relativistic viscous hydrodynamic calculations require very low values of η/s in order to reproduce the RHIC elliptic flow (v 2 ) data [7,8,9]. However, current calculations assume a fixed value of η/s throughout the entire evolution of the system and neglect its temperature dependence. The exact value of η/s in these calculations is only known within a factor of ≈ 3, due to systematic uncertainties related to the choice of equation of state and initial conditions used [9,10]. A viscous hydrodynamical analysis [9] finds that η/s should lie within a range of 0.08-0.24 depending upon the choice of initial conditions and equation of state. This finding is supported by calculations of η/s for pure gluonic QCD, which yield values close to the KSS bound, and indirect estimates of η/s from calculations of the diffusion of heavy quarks, elliptic flow measurements, and transverse momentum correlations that arrive at roughly comparable values [11,12,13,14,15].Note that the shear viscosity of matter in a relativistic heavy ion collision is a time-dependent quantity. While the partonic phase of such a collision is expected to have a very low value of η/s, after hadronization occurs η/s is expected to rapidly increase. In order to quantitatively constrain the viscosity of the deconfined phase of a relativistic heavy ion collision, a separate calculation of the hadronic viscosity is necessary. Several i...

Shear and bulk viscosities of the gluon plasma in a quasiparticle description

“…In fact, the observed possible rapid increase of η/s with decreasing T close to T c as well as the behavior with T in the confined phase [118][119][120] call for refinements in viscous hydrodynamic simulations [133][134][135]. The smallness of ζ /s over a wide range of T , in contrast, could suggest that the impact of bulk viscous effects is less important.…”

Event-by-EventHydrodynamics+JetEnergy Loss: A Solution to theRAA⊗vNoronha-Hostler1, Betz2, Noronha3 et al. 2016Phys. Rev. Lett.11361573View full textAdd to dashboardCite

“…Information about four transport coe cients is required: the temperature-dependent shear and bulk viscosities, ⌘ and ⇣, and their respective relaxation time coe cients, ⌧ ⇡ and ⌧ ⇧ (other 2nd order transport coe cients [71] are not yet taken into account). For simplicity, e↵ects from the temperature dependence of ⌘/s in the hadronic [72][73][74] or in the QGP phase [75] are neglected here and, thus, we set ⌘/s to be a constant. Also, in this first study bulk viscosity [61,62,76] is set to zero.…”

Nonlinear waves in second order conformal hydrodynamics

“…In contrast, at low temperatures and nonzero baryon chemical potentials in the hadron gas phase, viscous effects may be considerably more pronounced [4][5][6][7][8]. Numerical studies of the hydrodynamical evolution of the QuarkGluon Plasma (QGP) show that viscosity produces some visible but not very large effects on global observables [9].…”