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For the study of the structure of baryons it is necessary the investigate theproduction of a baryon pair in $e^+e^-$ annihilation. The baryon-antibaryonpair production at the electron-positron linear collider makes it possible toinvestigate in detail the basic structure of the Standard Model. The creationof baryon-antibaryon pairs in electron-positron annihilation provides anincreasingly powerful tool at higher center-of-mass energies. We presentphenomenological results for $\Sigma^0 \bar {\Sigma}^0$ production in $e^+e^-$interaction at the BESIII and BABAR Colliders. In the present work, weinvestigate 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 alldiagrams to the Born approximation. For these contributions large relativephases are generated with respect to the pure electromagnetic mechanism. Forthe large momentum transferred region we obtain as a by product a fit of theelectromagnetic form factor of the $\Sigma$ hyperon. The obtained results arein satisfactory agreement with experimental data.

Calculation of the total cross section of the process $e^+ + e^- \to  \Sigma^0 + \bar{\Sigma}^0$ in the vicinity of charmonium $\psi (3770)$  including the $D$-meson loop and three gluon contributions