On the existence of exotic and non-exotic multiquark meson states

TL;DR

This paper introduces an exact hyperspherical harmonics method to analyze four-quark meson states, exploring their stability and potential exotic nature without relying on simplifying assumptions.

Contribution

It presents a novel exact approach for four-quark systems that avoids common approximations like diquark assumptions.

Findings

Potential stability of $QQ\bar n \bar n$ states.

Instability of $Q\bar Qn \bar n$ states suggests complex quark correlations.

Method applicable to various quark-quark potentials.

Abstract

To obtain an exact solution of a four-body system containing two quarks and two antiquarks interacting through two-body terms is a cumbersome task that has been tackled with more or less success during the last decades. We present an exact method for the study of four-quark systems based on the hyperspherical harmonics formalism that allows us to solve it without resorting to further approximations, like for instance the existence of diquark components. We apply it to systems containing two heavy and two light quarks using different quark-quark potentials. While $QQ\bar n \bar n$ states may be stable in nature, the stability of $Q\bar Qn \bar n$ states would imply the existence of quark correlations not taken into account by simple quark dynamical models.