Space- and time-like electromagnetic form factors of the $\mathbf{\Omega }$ baryon

Abstract

We present predictions for the elastic electromagnetic form factors of the $\Omega$ baryon in both space-like and time-like regions, computed within a confining, symmetry-preserving framework based on a vector$\otimes$vector contact interaction. The calculation is performed in the rainbow-ladder truncation of QCD's Dyson-Schwinger equations, combined with a Poincaré-covariant Faddeev equation for the three-quark bound state. The $\Omega$ baryon, composed solely of strange quarks, provides a particularly clean environment in which to investigate the role of quark mass and SU(3)-flavor symmetry in shaping baryon structure. Within this approach, the electromagnetic current is constructed consistently with the Ward-Takahashi identity, yielding four independent form factors associated with the electric monopole, magnetic dipole, electric quadrupole, and magnetic octupole moments. We compute these form factors over a broad kinematic domain and analyze their behavior in both space-like and time-like regions. The resulting static electromagnetic moments and multipole form factors of the $\Omega$ baryon exhibit a visible sensitivity to the dressed-quark anomalous magnetic moment, particularly in the magnetic and higher-order multipole sectors. The time-like form factors are obtained through asymptotic analytic continuation of the corresponding space-like solutions, allowing the construction of the effective form factor and its comparison with available experimental data and recent phenomenological analyses.

Comments: 13 pages, 8 figures, 2 tables