A Poincaré-covariant $\mathrm{quark}+\mathrm{diquark}$ Faddeev equation is used to develop insights into the structure of the four lightest $(I,J^P=\frac{3}{2},{\frac{3}{2}}^{\pm })$ baryon multiplets. While these systems can contain isovector-axialvector and isovector-vector diquarks, one may neglect the latter and still arrive at a reliable description. The $(\frac{3}{2},{\frac{3}{2}}^{+})$ states are the simpler systems, with features that bear some resemblance to quark model pictures, e.g., their most prominent rest-frame orbital angular momentum component is $\mathsf{S}$-wave and the $\mathrm{\Delta }(1600){\frac{3}{2}}^{+}$ may reasonably be viewed as a radial excitation of the $\mathrm{\Delta }(1232){\frac{3}{2}}^{+}$. The $(\frac{3}{2},{\frac{3}{2}}^{-})$ states are more complex: the $\mathrm{\Delta }(1940){\frac{3}{2}}^{-}$ expresses little of the character of a radial excitation of the $\mathrm{\Delta }(1700){\frac{3}{2}}^{-}$; and while the rest-frame wave function of the latter is predominantly $\mathsf{P}$-wave, the leading piece in the $\mathrm{\Delta }(1940){\frac{3}{2}}^{-}$ wave function is $\mathsf{S}$-wave, in conflict with quark model expectations. Experiments that can test these predictions, such as large momentum transfer resonance electroexcitation, may shed light on the nature of emergent hadron mass.

• Received 24 March 2022
• Accepted 7 June 2022

DOI:https://doi.org/10.1103/PhysRevD.105.114047

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Published by the American Physical Society