Non-ordinary light meson couplings and the $1/N_c$ expansion

TL;DR

This paper analyzes how various light meson couplings behave in the large N_c limit, focusing on ordinary and non-ordinary states like tetraquarks and glueballs, revealing unique coupling properties.

Contribution

It provides a detailed study of the large N_c behavior of light meson couplings, especially highlighting the unique properties of generalized tetraquark states.

Findings

Certain tetraquark states decouple exponentially with N_c from the ππ channel.

Most meson couplings vanish or become weak at large N_c, except for specific tetraquark configurations.

The width of some non-ordinary mesons does not necessarily vanish as N_c increases.

Abstract

We study the large $N_c$ behavior of couplings among light meson states with different compositions in terms of quarks and gluons. We shortly review the most common compositions of mesons, which are of interest for the understanding of low-lying meson resonances, namely, the ordinary quark-antiquark states as well as the non-ordinary, glueball, tetraquark, etc. We dedicate special attention to Jaffe's generalization of the tetraquark with $N_c-1$ $q\bar{q}$ pairs, that is the only type of state we have identified, whose width does not necessarily vanish with $N_c$, while it does decouple exponentially with $N_c$ from the $\pi\pi$ channel, so that is weakly coupled to the meson-meson system.