Wave functions of (I,JP)=(12,32∓) baryons

Abstract

Using a Poincar\'e-covariant $\mathrm{quark}+\mathrm{diquark}$ Faddeev equation, we provide structural information on the four lightest $(I,{J}^{P})=(\frac{1}{2},{\frac{3}{2}}^{\ensuremath{\mp}})$ baryon multiplets. These systems may contain five distinct types of diquarks; but in order to obtain reliable results, it is sufficient to retain only isoscalar-scalar and isovector-axialvector correlations, with the latter being especially important. Viewed with low resolution, the Faddeev equation description of these states bears some resemblance to the associated quark model pictures; namely, they form a set of states related via orbital angular momentum excitation: the negative parity states are primarily $\mathsf{P}$-wave in character, whereas the positive parity states are $\mathsf{D}$ wave. However, a closer look reveals far greater structural complexity than is typical of quark model descriptions, with $\mathsf{P}$, $\mathsf{D}$, $\mathsf{S}$, $\mathsf{F}$ waves and interferences between them all playing a large role in forming observables. Large momentum transfer resonance electroexcitation measurements can be used to test these predictions and may thereby provide insights into the nature of emergent hadron mass.