Composition of low-lying $\mathbf{J=\tfrac{3}{2}^\pm \,\Delta}$-baryons

A Poincar\'e-covariant quark+diquark Faddeev equation is used to develop insights into the structure of the four lightest $(I,J^P=\tfrac{3}{2},\tfrac{3}{2}^\pm)$ baryon multiplets. Whilst these systems can contain isovector-axialvector and isovector-vector diquarks, one may neglect the latter and still arrive at a reliable description. The $(\tfrac{3}{2},\tfrac{3}{2}^+)$ states are the simpler systems, with features that bear some resemblance to quark model pictures, \emph{e.g}., their most prominent rest-frame orbital angular momentum component is $\mathsf S$-wave and the $\Delta(1600)\tfrac{3}{2}^+$ may reasonably be viewed as a radial excitation of the $\Delta(1232)\tfrac{3}{2}^+$. The $(\tfrac{3}{2},\tfrac{3}{2}^-)$ states are more complex: the $\Delta(1940)\tfrac{3}{2}^-$ expresses little of the character of a radial excitation of the $\Delta(1700)\tfrac{3}{2}^-$; and whilst the rest-frame wave function of the latter is predominantly $\mathsf P$-wave, the leading piece in the $\Delta(1940)\tfrac{3}{2}^-$ 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.