Flow harmonics from self-consistent particlization of a viscous fluid

Abstract

The quantitative extraction of quark-gluon plasma (QGP) properties from heavy-ion data, such as its specific shear viscosity η/s, typically requires comparison to viscous hydrodynamic or "hybrid" hydrodynamics+transport simulations. In either case, one has to convert the fluid to hadrons, yet without additional theory input the conversion is ambiguous for dissipative fluids. Here, shear viscous phase-space corrections calculated using linearized transport theory are applied in CooperFrye freezeout to quantify the effects on anisotropic flow coefficients vn(pT ) at both RHIC and LHC energies. Expanding upon our previous flow harmonics studies [1,2], we calculate pion and proton v2(pT ), v4(pT ), and v6(pT ), but here we incorporate a hadron gas that is chemically frozen below a temperature of 175 MeV and use hypersurfaces from realistic viscous hydrodynamic simulations. For additive quark model cross sections and relative phase-space corrections with p 3/2 momentum dependence rather than the quadratic Grad form, we find at moderately high transverse momentum noticeably higher v4(pT ) and v6(pT ) for protons than for pions. In addition, the value of η/s deduced from elliptic flow data differs by nearly 50% from the value extracted using the naive "democratic Grad" form of freeze-out distributions. To facilitate the use of the self-consistent viscous corrections calculated here in hydrodynamic and hybrid calculations, we also present convenient parameterizations of the corrections for the various hadron species (cf. Table I).

Self-consistent conversion of a viscous fluid to particles

“…where E LR ≡ (pu) is the energy of the particle in the LR frame. The prefactor in (10) has a quadratic momentum dependence at high momenta. Here A, B, and C are dimensionless constants that only depend on the particle mass to temperature ratio z ≡ m/T , and are constrained by the conditions that the bulk δf contributes neither to the local energy density, nor to the local particle density:…”

“…as long as χ satisfies the constraints (32). Bulk viscosity results from the Grad ansatz (10) are discussed in Sec. III B.…”

“…This section lists the thermal integrals that appear while matching the Grad correction (10) to a given bulk pressure. For a local local equilibrium distribution…”

“…The approach has been demonstrated in [1] for shear viscous corrections, where it was found that self-consistent corrections have a weaker momentum dependence than the typically assumed quadratic terms. This difference affects identified particle harmonic flow (v n ) and the extraction of shear viscosity as well [10] from data. The self-consistent results for shear were also validated [11] in a comparison of several shear δf models against actual near-local-equilibrium evolution from covariant transport.…”

Suppression of elliptic flow without viscosity

“…In particular, for shear corrections, the most popular quadratic in momentum (Grad) distortion of phase space densities is not supported by kinetic theory calculations [3,4]. This translates into appreciable systematic uncertainties in the extraction of transport coefficients from data [5].…”