Radiative energy loss andv2spectra for viscous hydrodynamics

Abstract

This work investigates the first correction to the equilibrium phase-space distribution and its effects on spectra and elliptic flow in heavy-ion collisions. We show that the departure from equilibrium on the freeze-out surface is the largest part of the viscous corrections to ${v}_{2}({p}_{T})$. However, the momentum dependence of the departure from equilibrium is not known a priori, and it is probably not proportional to ${p}_{T}^{2}$ as has been assumed in hydrodynamic simulations. At high momentum in weakly coupled plasmas, it is determined by the rate of radiative energy loss and is proportional to ${p}_{T}^{3/2}$. The weaker ${p}_{T}$ dependence leads to straighter ${v}_{2}({p}_{T})$ curves at the same value of viscosity. Furthermore, the departure from equilibrium is generally species dependent. A species-dependent equilibration rate, with baryons equilibrating faster than mesons, can explain ``constituent quark scaling'' without invoking coalescence models.