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

Abstract

We investigate the electromagnetic structure of the ground-state $Ω_{ccc}^{++}$ and $Ω_{bbb}^{-}$ 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 $Ω_{bbb}^{-}$. For $Ω_{ccc}^{++}$, 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 $μ_{Ω_{ccc}^{++}}=1.26\,μ_N$ and $μ_{Ω_{bbb}^{-}}=-0.207\,μ_N$. 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.