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Viscous Flow in Heavy-Ion Collisions from RHIC to LHC

We present a systematic hydrodynamic study of the evolution of hadron spectra and their azimuthal anisotropy from the lowest collision energy studied at the Relativistic Heavy Ion Collider (RHIC), sqrt(s) = 7.7 A GeV, to the highest energy reachable at the Large Hadron Collider (LHC), sqrt(s) = 5500 A GeV. The energy dependence of the flow observables are quantitatively studied for both the Monte-Carlo Glauber and Monte-Carlo Kharzeev-Levin-Nardi (MC-KLN) models. For MC-Glauber model initial conditions with η/s = 0.08, the differential charged hadron elliptic flow v_2^{ch}(p_T, sqrt(s)) is found to exhibit a very broad maximum in the region 39 < sqrt(s) < 2760 A GeV. For MC-KLN initial conditions with η/s = 0.2, a similar "saturation" is not observed up to LHC energies. We emphasize that this "saturation" of elliptic flow arises from the interplay between radial flow and elliptic flow which shifts with sqrt(s) depending on the fluid's viscosity. By generalizing the definition of spatial eccentricity to isothermal hyper-surface, we also calculate ε_x on the kinetic freeze-out surface at different collision energies.