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

Abstract

A salient feature shared by all tetraquark candidates observed in experiment is the absence of flavor-exotic states of the type $\bar{a}b\bar{c}d$, with four different quark flavors. This phenomenon may be understood from the properties of large-$N_c$ QCD: On the one hand, consistency conditions for flavor-exotic Green functions, potentially containing these tetraquark poles, require the existence of two tetraquarks $T_A$ and $T_B$: each of them should decay dominantly via a single two-meson channel, $T_A\to M_{\bar{a}b}{M}_{\bar{c}d}$ and $T_B\to M_{\bar{a}d}{M}_{\bar{c}b}$, with suppressed rates $T_A\to M_{\bar{a}d}{M}_{\bar{c}b}$ and $T_B\to M_{\bar{a}b}{M}_{\bar{c}d}$. On the other hand, we have at hand only one diquark-antidiquark flavor structure $(\bar{a}\bar{c})(bd)$ 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 have two different narrow tetraquarks decaying dominantly into different two-meson channels. This contradiction suggests that large-$N_c$ 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.

Comments: 8 pages