Quarkonium production in heavy ion collisions: coupled Boltzmann transport equations

We develop a set of coupled Boltzmann equations to describe the dynamical evolution of heavy quarks and quarkonia inside the quark-gluon plasma. The quarkonium dissociation and recombination terms are calculated from pNRQCD. Their interplay drives the system to a detailed balance. The heavy quark energy loss term is necessary for the system to reach kinematic thermalization. By coupling the transport equations with initial particles' momenta generated by PYTHIA and hydrodynamic medium evolutions, we can describe the $R_{AA}$ of $\Upsilon$ family at both RHIC and LHC energies. The transverse momentum azimuthal anisotropy of $\Upsilon$(1S) in $2.76$ TeV peripheral Pb-Pb collisions is also studied.