Do cc̄nn̄ bound states exist?

The four-quark system cc̄nn̄ is studied in the framework of the constituent quark model. Using different types of quark-quark potentials, we solve the four-body Schrödinger equation by means of the hyperspherical harmonic formalism. Exploring the low laying JPC states for different isospin configurations no four-quark bound states have been found. Of particular interest is the possible four-quark structure of the X(3872). We rule out the possibility that this particle is a compact tetraquark system, unless additional correlations, either in the form of diquarks or at the level of the interacting potential, not considered in simple quark models do contribute.