Flavour-Exotic Tetraquarks in Large-$N_{\rm c}$ QCD: Do They Exist?

TL;DR

This paper investigates the theoretical possibility of flavour-exotic tetraquark mesons within large-$N_c$ QCD, concluding that such states likely do not exist due to incompatible constraints from different theoretical limits.

Contribution

It provides a theoretical analysis showing the incompatibility of forming compact flavour-exotic tetraquarks in large-$N_c$ QCD, challenging their presumed existence.

Findings

Compact flavour-exotic tetraquarks are unlikely to exist.

Two conflicting theoretical constraints prevent their formation.

The analysis suggests nonexistence of such states in QCD.

Abstract

Flavour-exotic tetraquark mesons, by definition bound states of two quarks and two antiquarks of four mutually different quark flavours, are, for given Lorentz features, subject to two incompatible constraints: On the one hand, within quantum chromodynamics a formation of compact tetraquark states is most easily envisaged by merging two colour-antisymmetric two-quark clusters, a diquark and an antidiquark. This path, however, leads to merely a single tetraquark state of chosen Lorentz characteristics. On the other hand, in the limit of the number of colour degrees of freedom growing beyond bounds, internal consistency at leading order calls for the presence of (at least) two of such tetraquark states of identical quark-flavour composition. The failure of attempts to reconcile these two contradictory insights suggests the nonexistence of compact flavour-exotic tetraquark mesons.