Are there narrow flavor-exotic tetraquarks in large-$N_c$ QCD?

International audienceA salient feature shared by all tetraquark candidates observed in experiment is the absence of flavor-exotic states of the type a¯bc¯d, with four different quark flavors. This phenomenon may be understood from the properties of large-Nc QCD. On the one hand, previous work shows that consistency conditions for flavor-exotic Green functions, potentially containing these tetraquark poles, require the existence of two tetraquarks TA and TB: Each of them should decay dominantly via a single two-meson channel, TA→Ma¯bMc¯d and TB→Ma¯dMc¯b, with suppressed rates TA→Ma¯dMc¯b and TB→Ma¯bMc¯d. On the other hand, we have at hand only one diquark-antidiquark flavor structure (a¯c¯)(bd) that might produce a compact tetraquark bound state. Taking into account that the diquark-antidiquark structure is the only viable candidate for a compact tetraquark state, one concludes that it is impossible to obtain two different narrow tetraquarks decaying dominantly into distinct two-meson channels. This contradiction suggests that large-Nc QCD does not support the existence of narrow flavor-exotic tetraquarks. This argument does not rule out the possible existence of broad molecular-type flavor-exotic states or of molecular-type bound states lying very close to the two-meson thresholds