Electromagnetic Structure of ${\Omega }_{ccc}^{++}$ and ${\Omega }_{bbb}^{-}$ baryons from a covariant three-body Faddeev equation

Abstract

We investigate the electromagnetic structure of the ground-state ${\Omega }_{ccc}^{++}$ and ${\Omega }_{bbb}^{-}$ baryons using a Poincaré-covariant three-body Faddeev equation within the rainbow--ladder truncation. We calculate the complete set of elastic spin-$3/2$ multipole form factors, $G_{E0}$, $G_{M1}$, $G_{E2}$, and $G_{M3}$. The leading electric and magnetic form factors become markedly harder from the charm to the bottom sector, revealing the substantially more compact electromagnetic structure of the ${\Omega }_{bbb}^{-}$. For ${\Omega }_{ccc}^{++}$, the electric form factor and charge radius at low momentum transfer agree well with the available lQCD results. From the magnetic-dipole form factor at zero momentum transfer, $G_{M1}(0)$, we obtain the magnetic moments ${\mu }_{{\Omega }_{ccc}^{++}}=1.26{\mu }_N$ and ${\mu }_{{\Omega }_{bbb}^{-}}=-0.207{\mu }_N$. For $G_{E2}$ and $G_{M3}$, the electric-quadrupole structure exhibits a stronger charm-to-bottom evolution than the charge-normalized magnetic-octupole structure. Finally, comparison of the charm and bottom systems shows that both $G_{M1}(0)$ and the relation between the electric and magnetic radii move closer to their leading nonrelativistic heavy-quark expectations as the quark mass increases.