  For the study of the structure of baryons it is necessary to investigate the
production of a baryon pair in $e^+e^-$ annihilation. The baryon-antibaryon
pair production at the electron-positron linear collider makes it possible to
investigate in detail the basic structure of the Standard Model. The creation
of baryon-antibaryon pairs in electron-positron annihilation provides an
increasingly powerful tool at higher c.m. energies. We present phenomenological
results for $\Sigma^0 \bar {\Sigma}^0$ production in $e^+e^-$ interaction at
the BESIII and BABAR Colliders. In the present work, we investigate a hyperon
pair produced in the reaction $e^+e^- \to \Sigma^0 \bar{\Sigma}^0$. We
calculate the total cross section of the process $e^+e^- \to \Sigma^0 \bar
{\Sigma}^0$ taking into account the contributions of the $D$-meson loop and
three gluon loops as well as the interference of all diagrams to the Born
approximation. For these contributions large relative phases are generated with
respect to the pure electromagnetic mechanism. For the large momentum
transferred region we obtain as a byproduct a fit of the electromagnetic form
factor of the $\Sigma$ hyperon.
