Do $c\bar c n\bar n$ bound states exist?

TL;DR

This study investigates whether bound states of the four-quark system $car c nar n$ exist using a constituent quark model and hyperspherical harmonic formalism, finding no bound states for low-lying configurations.

Contribution

The paper provides a systematic analysis of $car c nar n$ states with various potentials, ruling out their existence as compact tetraquarks in simple quark models.

Findings

No four-quark bound states found for low-lying $J^{PC}$ states.

The X(3872) is unlikely to be a compact tetraquark in simple models.

Additional correlations may be needed to explain such states.

Abstract

The four--quark system $c\bar c n\bar n$ is studied in the framework of the constituent quark model. Using different types of quark-quark potentials, we solve the four--body Schr\"odinger 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.