Plausible explanation of the $\Delta_{5/2^{+}}(2000)$ puzzle

From a Faddeev calculation for the $\pi-(\Delta\rho)_{N_{5/2^{-}}(1675)}$ system we show the plausible existence of three dynamically generated $I(J^{P})=3/2 (5/2^{+})$ baryon states below 2.3 GeV whereas only two resonances, $\Delta_{5/2^{+}}(1905)(\ast\ast\ast\ast)$ and $\Delta_{5/2^{+}}(2000)(\ast\ast),$ are cataloged in the Particle Data Book Review. Our results give theoretical support to data analyses extracting two distinctive resonances, $\Delta_{5/2^{+}}(\sim1740)$ and $\Delta_{5/2^{+}}(\sim2200),$ from which the mass of $\Delta_{5/2^{+}}(2000)(\ast\ast)$ is estimated. We propose that these two resonances should be cataloged instead of $\Delta_{5/2^{+}}(2000).$ This proposal gets further support from the possible assignment of the other baryon states found in the approach in the $I=1/2,3/2$ with $J^{P}=1/2^{+},3/2^{+},5/2^+$ sectors to known baryonic resonances. In particular, $\Delta_{1/2^{+}}(1750)(\ast)$ is naturally interpreted as a $\pi N_{1/2^{-}}(1650)$ bound state.