Viscous corrections to anisotropic flow and transverse momentum spectra from transport theory

Abstract

Viscous hydrodynamics is commonly used to model the evolution of the matter created in an ultra-relativistic heavy-ion collision. It provides a good description of transverse momentum spectra and anisotropic flow. These observables, however, cannot be consistently derived using viscous hydrodynamics alone, because they depend on the microscopic interactions at freeze-out. We derive the ideal hydrodynamic limit and the first-order viscous correction to anisotropic flow ($v_2$, $v_3$ and $v_4$) and momentum spectrum using a transport calculation. The linear response coefficient to the initial anisotropy, $v_n(p_T)/{\epsilon }_n$, depends little on $n$ in the ideal hydrodynamic limit. The viscous correction to the spectrum depends not only on the differential cross section, but also on the initial momentum distribution. This dependence is not captured by standard second-order viscous hydrodynamics. The viscous correction to anisotropic flow increases with $p_T$, but this increase is slower than usually assumed in viscous hydrodynamic calculations. In particular, it is too slow to explain the observed maximum of $v_n$ at $p_T\sim 3$ GeV/c.

arXiv commentminor revision

References in corpus (49)

• Glauber Modeling in High Energy Nuclear Collisions
• Collective flow and viscosity in relativistic heavy-ion collisions
• Full result for the QCD equation of state with 2+1 flavors
• Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?
• Elliptic flow of charged particles in Pb-Pb collisions at 2.76 TeV
• Conformal Relativistic Viscous Hydrodynamics: Applications to RHIC results at sqrt(s_NN) = 200 GeV
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Hydrodynamic Modeling of Heavy-Ion Collisions
• Elliptic Flow of Identified Hadrons in Au+Au Collisions at sqrt(s_NN) = 200 GeV
• The Effect of Shear Viscosity on Spectra, Elliptic Flow, and HBT Radii
• Higher harmonic anisotropic flow measurements of charged particles in Pb-Pb collisions at 2.76 TeV
• Thermalization of gluons in ultrarelativistic heavy ion collisions by including three-body interactions in a parton cascade
• Triangularity and Dipole Asymmetry in Heavy Ion Collisions
• Measurements of Higher-Order Flow Harmonics in Au+Au Collisions at sqrt(s_NN) = 200 GeV
• Triangular flow in hydrodynamics and transport theory
• Saturation of Elliptic Flow and the Transport Opacity of the Gluon Plasma at RHIC
• Early thermalization at RHIC
• Mapping the hydrodynamic response to the initial geometry in heavy-ion collisions
• Observable implications of geometrical and dynamical aspects of freeze-out in heavy ion collisions
• Highly-anisotropic and strongly-dissipative hydrodynamics for early stages of relativistic heavy-ion collisions
• Event-by-event distributions of azimuthal asymmetries in ultrarelativistic heavy-ion collisions
• Non linearities in the harmonic spectrum of heavy ion collisions with ideal and viscous hydrodynamics
• Bulk and shear viscosities of matter created in relativistic heavy-ion collisions
• Relativistic hydrodynamics for heavy-ion collisions
• Radiative energy loss and v2 spectra for viscous hydrodynamics
• Bose--Einstein Condensation and Thermalization of the Quark Gluon Plasma
• Conformal hydrodynamics in Minkowski and de Sitter spacetimes
• Bulk Viscosity Effects in Event-by-Event Relativistic Hydrodynamics
• Momentum spectra, anisotropic flow, and ideal fluids
• Shear Viscosity of a strongly interacting system: Green-Kubo vs. Chapman-Enskog and Relaxation Time Approximation
• Determining initial-state fluctuations from flow measurements in heavy-ion collisions
• Effects of Bulk Viscosity at Freezeout
• Elliptic flow from a parton cascade
• Scalings of Elliptic Flow for a Fluid at Finite Shear Viscosity
• The Fate of the Initial State Fluctuations in Heavy Ion Collisions. II The Fluctuations and Sounds
• Coupling hydrodynamics to nonequilibrium degrees of freedom in strongly interacting quark-gluon plasma
• Constraining models of initial conditions with elliptic and triangular flow data
• Elliptic Flow from Non-equilibrium Initial Condition with a Saturation Scale
• Relativistic viscous hydrodynamics for heavy-ion collisions: A comparison between the Chapman-Enskog and Grad methods
• Elliptic flow in transport theory and hydrodynamics
• Constraining the viscous freeze-out distribution function with data obtained at the BNL Relativistic Heavy Ion Collider (RHIC)
• Anisotropies in momentum space at finite Shear Viscosity in ultrarelativistic heavy-ion collisions
• Second order viscous corrections to the harmonic spectrum in heavy ion collisions
• Azimuthal Anisotropy Distributions in High-Energy Collisions
• Elliptic Flow and Shear Viscosity within a Transport Approach from RHIC to LHC Energy
• Shear viscosity and chemical equilibration of the QGP
• Hydrodynamical evolution of dissipative QGP fluid
• Flow harmonics within an analytically solvable viscous hydrodynamic model
• Properties of the Boltzmann equation in the classical approximation

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• Causal Relativistic Hydrodynamics of Conformal Fermi-Dirac Gases
• Far-from-equilibrium attractors with Full Relativistic Boltzmann approach in 3+1 D: moments of distribution function and anisotropic flows $v_n$
• Second order relativistic viscous hydrodynamics within an effective description of hot QCD medium
• Event shape Engineering analysis of D meson in ultrarelativistic heavy ion collisions