Is Θ(1540) a Kaon–Skyrmion Resonance?

We reconsider the relationship between the bound state and the SU(3) rigid rotator approaches to strangeness in the Skyrme model. For non-exotic S = −1 baryons the bound state approach matches for small mK onto the rigid rotator approach, and the bound state mode turns into the rotator zero-mode. However, for small mK , we find no S = +1 kaon bound states or resonances in the spectrum, confirming previous work. This suggests that, at least for large N and small mK , the exotic state may be an artifact of the rigid rotator approach to the Skyrme model. An S = +1 near-threshold state comes into existence only for sufficiently large SU(3) breaking. If such a state exists, then it has the expected quantum numbers of Θ+: I = 0, J = 12 and positive parity. Other exotic states with I = 1, J = 32 + , and I = 1, J = 12 + appear as its SU(2) rotator excitations. As a test of our methods, we also identify a D-wave S = −1 near-threshold resonance that, upon SU(2) collective coordinate quantization, reproduces the mass splittings of the observed states Λ(1520), Σ(1670) and Σ(1775) with good accuracy.