Study of exotic hadrons inS-wave scatterings induced by chiral interaction in the flavor symmetric limit

Abstract

We study $s$-wave bound states of a hadron and a light pseudoscalar meson induced by the Weinberg-Tomozawa (WT) interaction in the flavor SU(3) symmetric limit. The WT interaction is a driving force to generate quasibound states dynamically in the chiral unitary approaches. The strength and sign of the WT interaction are determined only by the group theoretical structure of the target hadrons, and we present a general expression of the strengths for the flavor SU(3) case. We show that, for the channels which are more exotic than the target, the interaction is repulsive in most cases, and the strength of the attractive interaction is universal for any possible target states. We demonstrate that the attractive coupling is not strong enough to generate an exotic state from the physically known masses of target hadrons. In addition, we also find a nontrivial ${N}_{c}$ dependence of the coupling strengths. We show that the channels which are attractive at ${N}_{c}=3$ change into repulsive ones for large ${N}_{c}$, and, therefore, no attractive interaction exists in exotic channels in the large-${N}_{c}$ limit.