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Hyperon electromagnetic timelike elastic form factors at large $q^2$

We present estimates of the hyperon elastic form factors for the baryon octet and the $Ω^-$ baryon for large four-momentum transfer squared, $q^2$, in the timelike region ($q^2>0$). Experimentally, those form factors can be extracted from the $e^+ e^- \to B \bar B$ and $p \bar p \to B \bar B$ processes, where $B$ stands for a general baryon. Our results are based on calculations of the elastic electromagnetic form factors in the spacelike region ($Q^2 = - q^2 > 0$) within a covariant quark model. To connect the results in the spacelike region to those in the timelike region, we use asymptotic relations between the two regions which are constraints derived from analyticity and unitarity. We calculate the effective form factors $|G(q^2)|$ and compare them with the integrated cross section data $σ_{\rm Born} (q^2)$ from BaBar, BES III, and CLEO. The available data are at the moment restricted to $Λ$, $Σ^0$, $Σ^-$, $Ξ^-$, $Ξ^0$, and $Ω^-$ as well as to $e^+ e^- \to Λ\bar Σ^0 $ and $e^+ e^- \to Σ^0 \bar Λ$ reactions. Our results provide useful reference for future experiments and seem to indicate that the present data are still in the non-perturbative QCD region, while the onset for the asymptotic constraints from analyticity and unitarity happens much before the region of the perturbative QCD falloff of the form factors.