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.

arXiv comment13 pages, 8 figures, 8 tables

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Cited by in corpus (4)

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• Contact interaction analysis of octet baryon axialvector and pseudoscalar form factors
• Polarised parton distribution functions and proton spin
• Space-like Electromagnetic Form Factors of Lambda- and Sigma-Baryons from Quark-Diquark Faddeev Equations