Plausible explanation for theΔ5/2+(2000)puzzle

From a Faddeev calculation for the $\ensuremath{\pi}$-$(\ensuremath{\Delta}\ensuremath{\rho}){}_{{N}_{5/{2}^{\ensuremath{-}}}(1675)}$ 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, ${\ensuremath{\Delta}}_{5/{2}^{+}}(1905)(****)$ and ${\ensuremath{\Delta}}_{5/{2}^{+}}(2000)(**),$ are cataloged in the Particle Data Book Review. Our results give theoretical support to data analyses extracting two distinctive resonances, ${\ensuremath{\Delta}}_{5/{2}^{+}}(~$1740) and ${\ensuremath{\Delta}}_{5/{2}^{+}}(~$2200), from which the mass of ${\ensuremath{\Delta}}_{5/{2}^{+}}(2000)(**)$ is estimated. We propose that these two resonances should be cataloged instead of ${\ensuremath{\Delta}}_{5/{2}^{+}}(2000).$ 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, ${\ensuremath{\Delta}}_{1/{2}^{+}}(1750)(*)$ is naturally interpreted as a $\ensuremath{\pi}{N}_{1/{2}^{\ensuremath{-}}}(1650)$ bound state.