Exotic Hadrons in $s$-Wave Chiral Dynamics

We study $s$-wave scattering of a hadron and a Nambu-Goldstone boson induced by the model-independent low energy interaction in the flavor SU(3) symmetric limit. Establishing the general structure of the interaction based on group theoretical arguments, we find that the interaction in the exotic channels are in most cases repulsive, and that for possible attractive channels the coupling strengths are weak and uniquely given independent of channel. Solving the scattering problem, we show that the attraction in the exotic channels is not strong enough to generate a bound state.

Figure 1

Critical coupling strength $C_{\mathrm{crit}}$ for the averaged mass over the pseudoscalar octet mesons, $m=368\mathrm{MeV}$ (solid line). The dashed line denotes the universal attractive coupling strength in exotic channels $C_{\mathrm{exotic}}=1$.