Exotic states and their properties from large-$N_{\rm c}$ QCD

TL;DR

This paper uses large-$N_c$ QCD to derive rigorous conditions for the existence and properties of exotic tetraquark states, revealing their coupling patterns and decay behaviors.

Contribution

It establishes new theoretical constraints on tetraquark states within large-$N_c$ QCD, including their distinguishability and mixing with ordinary mesons.

Findings

Genuinely flavour-exotic tetraquarks require two distinguishable states.

Cryptoexotic tetraquarks may exist as a single state with meson mixing.

Decay widths of tetraquarks decrease as 1/N_c^2 for large N_c.

Abstract

The analysis of two-ordinary-meson scattering amplitudes in the limit of a large number $N_{\rm c}$ of the colour degrees of freedom of quantum chromodynamics, with suitably decreasing strong coupling and all quarks transforming according to the gauge group's fundamental representation, enables us to establish a set of rigorous consistency conditions for the emergence of a tetraquark (i.e., a bound state of two quarks and two antiquarks) as a pole in these amplitudes. For genuinely flavour-exotic tetraquarks, these constraints require the existence of two tetraquark states distinguishable by their preferred couplings to two ordinary mesons, whereas, for cryptoexotic tetraquarks, our constraints may be satisfied by a single tetraquark state, which then, however, may mix with ordinary mesons. For elucidation of the tetraquark features, the consideration of the subleading contributions proves to be mandatory: for both variants of tetraquarks, their decay widths fall off like $1/N_{\rm c}^2$ for large $N_{\rm c}.$