A new perspective on the ${\mathrm{\Delta }}_{5\mathrm{/}{2}^{+}}(2000)$ puzzle

We argue that ${\mathrm{\Delta }}_{5\mathrm{/}{2}^{+}}(2000)(\ast \ast ),$ cataloged as a resonance in the Particle Data Book Review (PDG), should be interpreted instead as two distinctive resonances, ${\mathrm{\Delta }}_{5\mathrm{/}{2}^{+}}(\sim 1740)$ and ${\mathrm{\Delta }}_{5\mathrm{/}{2}^{+}}(\sim 2200)$. Our argument is based on a solution of the $\pi \mathrm{\Delta }\rho$ problem in a Fixed Center Approximation (FCA) to the Fadeev equations. ${\mathrm{\Delta }}_{5\mathrm{/}{2}^{+}}(\sim 1740)$ can then be interpreted as a $\pi -(\mathrm{\Delta }\rho {)}_{N(1675)}$ bound state. As a corollary ${\mathrm{\Delta }}_{1\mathrm{/}{2}^{+}}(1750)(\ast )$ can be understood as a $\pi N_{1\mathrm{/}{2}^{-}}(1650)$ bound state.