From hydro to jet quenching, coalescence and hadron cascade: a coupled approach to solving the $R_{AA}\otimes v_2$ puzzle.

Hydrodynamics and jet quenching are responsible for the elliptic flow $v_2$ at low transverse momentum $p_T$ and hadron suppression and $v_2$ at high $p_T$, respectively, in high-energy heavy-ion collisions. A consistent description of the hadron suppression factor $R_{AA}$ and $v_2$, especially at intermediate $p_T$, however, remains a challenge. We solve this long-standing $R_{AA}\otimes v_2$ puzzle by describing hadron production from low to intermediate and high $p_T$ within the coupled linear Boltzmann transport-hydro model that combines concurrent jet transport and medium hydro evolution with quark coalescence in the hadronization and hadron casacde in the final evolution of the system. We illustrate that quark coalescence and hadron cascade are the keys to solving the puzzle. They also lead to a splitting of $v_2$ for pions, kaons and protons in the intermediate $p_T$ region. We demonstrate for the first time that experimental data on $R_{AA}$, $v_2$ and their hadron flavor dependence from low to intermediate and high $p_T$ in high-energy heavy-ion collisions can be understood within this coupled framework.