Is Θ+(1540) a kaon–skyrmion resonance?

Abstract

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 m K onto the rigid rotator approach, and the bound state mode turns into the rotator zero-mode. However, for small m K , 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 m K , 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= 1 2 and positive parity. Other exotic states with (I=1,J P= 3 2 +) , (I=1,J P= 1 2 +) , (I=2,J P= 5 2 +) and (I=2,J P= 3 2 +) 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.