Do c[overline c]n[overline n] bound states exist?

Abstract

The four-quark system c[overline c]n[overline n] is studied in the framework of the constituent quark model. Using different types of quark-quark potentials, we solve the four-body Schrodinger equation by means of the hyperspherical harmonic formalism. Exploring the low laying J(PC) 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.