Constraints from the $1/N_{\rm c}$ Expansion on Properties of Exotic Tetraquark Mesons

TL;DR

This paper uses the large-$N_c$ limit in QCD to derive constraints on exotic tetraquark mesons, showing they must come in pairs with narrow decay widths decreasing as $1/N_c^2$, which impacts their observable properties.

Contribution

It provides rigorous selection criteria and self-consistency conditions for the existence and properties of tetraquarks in the large-$N_c$ limit of QCD, especially for flavor-exotic states.

Findings

Flavor-exotic tetraquarks come in at least two variants with distinct large-$N_c$ behaviors.

All tetraquarks are predicted to be narrow states with decay widths decreasing as $1/N_c^2$.

Constraints imply specific patterns in the couplings of tetraquarks to ordinary mesons.

Abstract

Scrutinizing the scattering of ordinary mesons in the limiting case of the number of colour degrees of freedom $N_{\rm c}$ of quantum chromodynamics approaching infinity, we formulate Feynman-diagram selection criteria and from these deduce rigorous self-consistency conditions for the manifestation of a tetraquark, a two-quark-two-antiquark bound state, as a pole in the corresponding amplitudes. Our constraints bear rather far-reaching consequences: In particular, all flavour-exotic tetraquarks, composed of four (anti)quarks of disparate flavour, must come in, at least, two variants differing in (and thus readily identifiable by) the large-$N_{\rm c}$ behaviour of their couplings to two ordinary mesons. Quite generally, irrespective of their flavour composition, all tetraquarks prove to be narrow. Their decay rates behave, for large $N_{\rm c},$ like $1/N_{\rm c}^2$ and thus decrease faster than those of ordinary mesons.