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

Abstract

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, ${\Delta }_{5/2^{+}}(\sim 1740)$ and ${\Delta }_{5/2^{+}}(\sim 2200),$ 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.

13 pages, 7 figures

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