Electromagnetic form factors of the $\mathbf{\Omega}$ baryon: space-like structure and time-like extrapolation

Abstract

We calculate the elastic electromagnetic multipole form factors of the $\Omega^-$ baryon using a symmetry-preserving vector$\,\otimes\,$vector contact interaction in rainbow--ladder truncation and a Poincar\'e-covariant quark--diquark Faddeev equation. A conserved electromagnetic current yields the electric monopole, magnetic dipole, electric quadrupole, and magnetic octupole form factors. We examine their sensitivity to a phenomenological transverse dressed-quark anomalous magnetic moment (AMM). The magnetic and higher multipoles show the strongest dependence, whereas the AMM contribution is progressively suppressed with increasing momentum transfer. The calculated magnetic moment is larger in magnitude than the experimental value, and a positive AMM contribution increases this discrepancy, exposing a limitation of the present truncation. We also construct a model-dependent time-like extrapolation of the space-like results, motivated by their asymptotic behavior, and use it to evaluate the effective form factor measured in $e^+e^-\to\Omega^-\bar{\Omega}^+$. The extrapolation describes the broad trend at larger energies but does not incorporate resonances, final-state interactions, unitarity cuts, or the complex phase structure required near threshold.