Tetraquarks in large-$N_c$ QCD

TL;DR

This paper reviews the extension of large-$N_c$ QCD to tetraquark states, analyzing their formation mechanisms, properties, and signatures in Feynman diagrams, providing insights into their theoretical description and experimental relevance.

Contribution

It offers a detailed analysis of tetraquark properties in large-$N_c$ QCD, highlighting formation mechanisms and their signatures in scattering amplitudes, advancing the theoretical understanding of exotic multiquark states.

Findings

Tetraquark formation mainly arises from mesonic cluster interactions.

Two independent tetraquark states can occur in coupled-channel scattering.

Large-$N_c$ analysis clarifies mechanisms behind tetraquark formation.

Abstract

The present work reviews the various aspects of the extension of the large-$N_c$ approach, as had been proposed and developed by 't Hooft, to the case of tetraquark states, which are a category of the general class of exotic states, also called multiquark states, whose internal valence-quark structure does not match with that of ordinary hadrons, and which have received, in recent years, many experimental confirmations. The primary question of describing, or probing, on theoretical grounds, multiquark states is first examined. The signature of such states inside Feynman diagrams in relation with their singularities is highlighted. The main mechanisms of formation of tetraquark states, provided by the diquark model and the molecular scheme, are considered together with their specific implications. The properties of tetraquark states at large $N_c$ are analyzed through the Feynman diagrams that describe two-meson scattering amplitudes. It turns out that, in that limit, the possible formation of tetraquark states is mainly due to the mutual interactions of their internal mesonic clusters. These essentially arise from the quark-rearrangement, or quark-interchange, mechanism. In coupled-channel meson-meson scattering amplitudes, one may expect the occurrence of two independent tetraquark states, each having priviledged couplings with the two mesons of their dominant channel. The question of the energy balance of various schemes in the static limit is also analyzed. The clarification of the mechanisms that are at work in the formation of tetraquarks is the main outcome from the large-$N_c$ approach to this problem.