Bose-Einstein condensation of diquark molecules in three-flavor quark matter

We study the phase diagram of strongly interacting matter with three quark flavors at low and intermediate densities and non-zero temperatures in the framework of an NJL-type model with four-point interactions. At large densities, when the interactions are weak due to asymptotic freedom, quarks form loosely bound Cooper pairs. However, when the density decreases, interactions become stronger and quark Cooper pairs transform smoothly into tightly bound diquark molecules. We find that such molecules are stable at low density and temperature and that they dissociate above a temperature $T_{\rm diss}$ of the order of the chiral phase transition temperature $T_c \sim 170$ MeV. We also explore the conditions under which these molecules undergo Bose-Einstein condensation (BEC). We find that BEC is only possible if we increase the attractive interaction in the diquark channel to (probably unrealistically) large values.