Compact Exotic Tetraquark Mesons in Large-$N_c$ QCD

TL;DR

This paper investigates the behavior and properties of tetraquark mesons in large-$N_c$ QCD, proposing criteria to identify potential tetraquark states and analyzing their decay rates and existence conditions.

Contribution

It introduces a systematic method to isolate tetraquark contributions in large-$N_c$ QCD scattering amplitudes and deduces decay rate scaling and existence conditions for different tetraquark categories.

Findings

Tetraquark decay rates are at least of order 1/N_c^2.

Tetraquarks with four or two open quark flavors have specific decay channel preferences.

Existence of certain tetraquark states is implied by internal consistency requirements.

Abstract

We embark on systematic explorations of the behaviour of tetraquark mesons (colour-singlet bound states of two quarks and two antiquarks) in the (idealized) limit of a large number $N_c$ of colour degrees of freedom of quantum chromodynamics. Considering the scattering of two ordinary mesons into two ordinary mesons, we start off with formulating a set of selection criteria that should enable us to unambiguously single out precisely those contributions to all encountered scattering amplitudes that potentially will develop tetraquark poles. Assuming that tetraquark mesons do exist and, if so, emerge in the contributions compatible with our criteria at largest admissible order of $N_c$, we deduce, for the categories of tetraquarks that exhibit either four or only two different open quark flavours, that the decay rates of these tetraquark types are, at least, of order $1/N_c^2$ and that internal consistency requires all the members of the first species to exist pairwise, distinguishable by their favoured two-ordinary-meson decay channels.