Azimuthal Anisotropy: Ridges, Recombination and Breaking of Quark Number   Scaling
  Azimuthal anisotropy is studied by taking into account the ridges created by semi-hard scattering, which is sensitive to the initial spatial configuration in non-central heavy-ion collisions. No rapid thermalization is required. Although hydrodynamics is not used in this study, the validity of hydrodynamical expansion is not excluded at later time after equilibration is achieved. Phenomenological properties of the bulk and ridge behaviors are used as inputs to determine the elliptic flow of pion and proton at low p_T. At intermediate p_T the recombination of shower partons with thermal partons becomes more important. The phi dependence arises from the variation of the in-medium path length of the hard parton that generates the shower. The p_T dependence of v_2 is therefore very different at intermediate p_T compared to that at low p_T. Quark number scaling of v_2 is shown to be only approximately valid at low p_T, but is broken at intermediate p_T, even though recombination is the mechanism of hadronization in all p_T regions considered. 
Charles B. Chiu, Rudolph C. Hwa and C. B. Yang