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

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