Do Chiral Soliton Models Predict Pentaquarks?

Abstract

We reconsider the relationship between the bound state and the SU(3) rigid rotator approaches to strangeness in chiral soliton models. 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 $m_K$, there are no $S=+1$ kaon bound states or resonances in the spectrum. This shows that for large $N$ and small $m_K$ the exotic state is an artifact of the rigid rotator approach. An $S=+1$ near-threshold state with the quantum numbers of the $Θ^+$ pentaquark comes into existence only when sufficiently strong SU(3) breaking is introduced into the chiral lagrangian. Therefore, pentaquarks are not generic predictions of the chiral soliton models.