# Narrow exotic tetraquark mesons in large-$N_c$ QCD

## TL;DR

This paper analyzes the properties of tetraquark mesons in large-$N_c$ QCD, establishing criteria for their detection and showing they are narrower than ordinary mesons, with specific coupling behaviors for flavor-exotic states.

## Contribution

It formulates rigorous diagram criteria for tetraquark analysis and demonstrates their narrow widths and coupling patterns in large-$N_c$ QCD.

## Key findings

- Tetraquarks have widths of order 1/N_c^2, narrower than ordinary mesons.
- Flavor-exotic tetraquarks require two narrow states, each coupling to a specific meson-meson channel.
- Consistency conditions imply specific coupling behaviors for flavor-exotic states.

## Abstract

Discussing four-point Green functions of bilinear quark currents in large-$N_c$ QCD, we formulate rigorous criteria for selecting diagrams appropriate for the analysis of potential tetraquark poles. We find that both flavor-exotic and cryptoexotic (i.e., flavor-nonexotic) tetraquarks, if such poles exist, have a width of order $O(1/N_c^2)$, so they are parametrically narrower compared to the ordinary $\bar qq$ mesons, which have a width of order $O(1/N_c)$. Moreover, for flavor-exotic states, the consistency of the large-$N_c$ behavior of "direct" and "recombination" Green functions requires two narrow flavor-exotic states, each coupling dominantly to one specific meson-meson channel.