Wave functions of $(I,J^P) = (\tfrac{1}{2},\tfrac{3}{2}^\mp)$ baryons

TL;DR

This paper uses a Poincaré-covariant quark+diquark Faddeev equation approach to analyze the internal structure of the lightest $(I,J^P)=(1/2,3/2^ ext{±})$ baryons, revealing complex wave compositions beyond simple quark models.

Contribution

It provides a detailed structural analysis of these baryons using a covariant Faddeev approach, highlighting the importance of multiple wave components and diquark correlations.

Findings

Negative parity states are mainly P-wave.

Positive parity states are mainly D-wave.

Complex wave interference significantly influences observables.

Abstract

Using a Poincar\'e-covariant quark+diquark Faddeev equation, we provide structural information on the four lightest $(I,J^P)=(\tfrac{1}{2},\tfrac{3}{2}^\mp)$ 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.