Quarkonium In-Medium Transport Equation Derived from First Principles

We use the open quantum system formalism to study the dynamical in-medium evolution of quarkonium. The system of quarkonium is described by potential non-relativistic QCD while the environment is a weakly coupled quark-gluon plasma in local thermal equilibrium below the melting temperature of the quarkonium. Under the Markovian approximation, it is shown that the Lindblad equation leads to a Boltzmann transport equation if a Wigner transform is applied to the system density matrix. Our derivation illuminates how the microscopic time-reversibility of QCD is consistent with the time-irreversible in-medium evolution of quarkonium states. Static screening, dissociation and recombination of quarkonium are treated in the same theoretical framework. In addition, quarkonium annihilation is included in a similar way, although the effect is negligible for the phenomenology of the current heavy ion collision experiments. The methods used here can be extended to study quarkonium dynamical evolution inside a strongly coupled QGP, a hot medium out of equilibrium or cold nuclear matter, which is important to studying quarkonium production in heavy ion, proton-ion, and electron-ion collisions.