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

Abstract

Abstract Considering four-point correlation functions of color-singlet quark bilinears, we investigate, in the large- $$N_{\mathrm {c}}$$ N 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 $$N_{\mathrm {c}}$$ N c -behaviors, consistently satisfy the constraints resulting from the $$1/N_{\mathrm {c}}$$ 1 / N c expansion procedure and thus provide a firm basis for the extraction of tetraquark properties from $$N_{\mathrm {c}}$$ N c -subleading diagrams. We find that, in general, tetraquarks, if they exist in compact form, should have narrow decay widths, of the order of $$N_{\mathrm {c}}^{-2}$$ N 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.