Are there compact heavy four-quark bound states?

We present an exact method to study four-quark systems based on the hyperspherical harmonics formalism. We apply it to several physical systems of interest containing two heavy and two light quarks using different quark-quark potentials. Our conclusions mark the boundaries for the possible existence of compact, non-molecular, four-quark bound states. While $QQ\bar{n}\bar{n}$ states may be stable in nature, the stability of $Q\bar{Q}n\bar{n}$ states would imply the existence of quark correlations not taken into account by simple quark dynamical models