An explanation of the ${\Delta }_{5/2^{-}}(1930)$ as a $\rho \Delta$ bound state

Abstract

We use the $\rho \Delta$ interaction in the hidden gauge formalism to dynamically generate $N^{\ast }$ and ${\Delta }^{\ast }$ resonances. We show, through a comparison of the results from this analysis and from a quark model study with data, that the ${\Delta }_{5/2^{-}}(1930),$ ${\Delta }_{3/2^{-}}(1940)$ and ${\Delta }_{1/2^{-}}(1900)$ resonances can be assigned to $\rho \Delta$ bound states. More precisely the ${\Delta }_{5/2^{-}}(1930)$ can be interpreted as a $\rho \Delta$ bound state whereas the ${\Delta }_{3/2^{-}}(1940)$ and ${\Delta }_{1/2^{-}}(1900)$ may contain an important $\rho \Delta$ component. This interpretation allows for a solution of a long-standing puzzle concerning the description of these resonances in constituent quark models. In addition we also obtain degenerate $J^P=1/2^{-},3/2^{-},5/2^{-}$ $N^{\ast }$ states but their assignment to experimental resonances is more uncertain.

Comments: 19 pags, 8 figs