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

TL;DR

This paper uses the hidden gauge formalism to interpret certain baryon resonances as bound states of $ ho$ and $ riangle$, providing a novel explanation for their structure and resolving previous quark model puzzles.

Contribution

It demonstrates that the $ ho riangle$ interaction can generate specific resonances, offering a new perspective on their composition and addressing longstanding theoretical challenges.

Findings

$ riangle_{5/2^{-}}(1930)$ is a $ ho riangle$ bound state

Some resonances contain significant $ ho riangle$ components

Degenerate $J^{P}=1/2^{-},3/2^{-},5/2^{-}$ $N^{*}$ states are predicted

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 $J^{P}=1/2^{-},3/2^{-},5/2^{-}$ $N^{*}$ states but their assignment to experimental resonances is more uncertain.