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

Abstract

A Poincaré-covariant quark+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. Whilst 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, \emph{e.g}., their most prominent rest-frame orbital angular momentum component is $\mathsf{S}$-wave and the $\Delta (1600){\frac{3}{2}}^{+}$ may reasonably be viewed as a radial excitation of the $\Delta (1232){\frac{3}{2}}^{+}$. The $(\frac{3}{2},{\frac{3}{2}}^{-})$ states are more complex: the $\Delta (1940){\frac{3}{2}}^{-}$ expresses little of the character of a radial excitation of the $\Delta (1700){\frac{3}{2}}^{-}$; and whilst the rest-frame wave function of the latter is predominantly $\mathsf{P}$-wave, the leading piece in the $\Delta (1940){\frac{3}{2}}^{-}$ 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.

Comments: 13 pages, 8 figures, 8 tables