Radial excitations of low--lying baryons and the $Z^+$ penta--quark

Abstract

Within an extended Skyrme soliton model for baryons the interplay between the collective radial motion and the SU(3)--flavor--rotations is investigated. The coupling between these modes is mediated by flavor symmetry breaking. Collective coordinates which describe the corresponding large amplitude fluctuations are introduced and treated canonically. When diagonalizing the resulting Hamiltonian flavor symmetry breaking is fully taken into consideration. As eigenstates not only the low--lying ${1/2}^+$ and ${3/2}^+$ baryons but also their radial excitations are obtained and compared to the empirical data. In particular the relevance of radial excitations for the penta--quark baryon $Z^+$ (Y=2, I=0, $J^π={1/2}^+$) is discussed. In this approach its mass is predicted to be $1.58{\rm GeV}$. Furthermore the widths for various hadronic decays are estimated which, for example, yields $Γ(Z^+\to NK)\sim 100{\rm MeV}$ for the only permissible decay process of the $Z^+$.