Tetraquark and two-meson states at large $N_{\mathrm{c}}$

TL;DR

This paper analyzes the role of subleading diagrams in large-$N_c$ QCD, demonstrating how two-meson and tetraquark states emerge and constraining tetraquark properties, notably predicting narrow decay widths for compact tetraquarks.

Contribution

It provides a theoretical framework for understanding tetraquark formation and properties from large-$N_c$ QCD, especially through subleading diagram analysis and consistency constraints.

Findings

Two-meson contributions are predictable from leading-order $N_c$-behaviors.

Tetraquarks, if compact, should have narrow decay widths of order $N_c^{-2}$.

Exotic tetraquarks with four different flavors require two types with specific decay channels.

Abstract

Considering four-point correlation functions of color-singlet quark bilinears, we investigate, in the large-$N_{\mathrm{c}}$ limit of QCD, the subleading diagrams that involve, in the $s$-channel of meson-meson scattering amplitudes, two-quark--two-antiquark intermediate states. The latter contribute, together with gluon exchanges, to the formation, at the hadronic level, of two-meson and tetraquark intermediate states. It is shown that the two-meson contributions, which are predictable, in general, from leading-order $N_{\mathrm{c}}$-behaviors, consistently satisfy the constraints resulting from the $1/N_{\mathrm{c}}$ expansion procedure and thus provide a firm basis for the extraction of tetraquark properties from $N_{\mathrm{c}}$-subleading diagrams. We find that, in general, tetraquarks, if they exist in compact form, should have narrow decay widths, of the order of $N_{\mathrm{c}}^{-2}$. For the particular case of exotic tetraquarks, involving four different quark flavors, two different types of tetraquark are needed, each having a preferred decay channel, to satisfy the consistency constraints.