Bound State versus Collective Coordinate Approaches in Chiral Soliton Models and the Width of the $\Theta^+$ Pentaquark

Abstract

We thoroughly compare the bound state and rigid rotator approaches to three--flavored chiral solitons. We establish that these two approaches yield identical results for the baryon spectrum and kaon--nucleon $S$--matrix in the limit that the number of colors ($N_C$) tends to infinity. After proper subtraction of the background phase shift the bound state approach indeed exhibits a clear resonance behavior in the strangeness $S=+1$ channel. We present a first dynamical calculation of the widths of the $\Theta^+$ and $\Theta^*$ pentaquarks for finite $N_C$ in a chiral soliton model.