Heavy quark correlations and the effective volume for quarkonia production

Using the Boltzmann transport approach, we study the effective volume of a correlated heavy quark pair in a partonic medium based on their collision rate. We find that the effective volume is finite and depends sensitively on the momentum of the heavy quark and the temperature of the medium. Generally, it increases linearly with time $t$ at the very beginning and the increase then becomes slower due to multiple scattering, and finally it increases linearly with respect to $t^{3/2}$. We further find that the colliding heavy quark pair has an effective temperature similar to that of the medium even though their initial transverse momentum spectra are far from thermal equilibrium.