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

We use the $\rho \mathrm{\Delta }$ interaction in the hidden gauge formalism to dynamically generate $N^{\ast }$ and ${\mathrm{\Delta }}^{\ast }$ resonances. We show, through a comparison of the results from this analysis and from a quark model study with data, that the ${\mathrm{\Delta }}_{5\mathrm{/}{2}^{-}}(1930),$ ${\mathrm{\Delta }}_{3\mathrm{/}{2}^{-}}(1940)$ and ${\mathrm{\Delta }}_{1\mathrm{/}{2}^{-}}(1900)$ resonances can be assigned to $\rho \mathrm{\Delta }$ bound states. More precisely the ${\mathrm{\Delta }}_{5\mathrm{/}{2}^{-}}(1930)$ can be interpreted as a $\rho \mathrm{\Delta }$ bound state whereas the ${\mathrm{\Delta }}_{3\mathrm{/}{2}^{-}}(1940)$ and ${\mathrm{\Delta }}_{1\mathrm{/}{2}^{-}}(1900)$ may contain an important $\rho \mathrm{\Delta }$ 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 $J^P=1\mathrm{/}{2}^{-},3\mathrm{/}{2}^{-},5\mathrm{/}{2}^{-}$ $N^{\ast }$ states but their assignment to experimental resonances is more uncertain.