  Discussing four-point Green functions of bilinear quark currents in
large-$N_c$ QCD, we formulate rigorous criteria for selecting diagrams
appropriate for the analysis of potential tetraquark poles. We find that both
flavor-exotic and cryptoexotic (i.e., flavor-nonexotic) tetraquarks, if such
poles exist, have a width of order $O(1/N_c^2)$, so they are parametrically
narrower compared to the ordinary $\bar qq$ mesons, which have a width of order
$O(1/N_c)$. Moreover, for flavor-exotic states, the consistency of the
large-$N_c$ behavior of "direct" and "recombination" Green functions requires
two narrow flavor-exotic states, each coupling dominantly to one specific
meson-meson channel.

High Energy Physics - Phenomenology