Total cross section of the process $e^+ + e^- \to \Sigma^+ + \bar{\Sigma}^-$ including the $D$-meson loop and three-gluon contributions

In the present paper, we investigate the production of a baryon pair in $e^+e^-$ annihilation to study the structure of baryons. To study the basic structure of the Standard Model, it is also necessary to consider the baryon-antibaryon pair production at the electron-positron linear collider. The production of a baryon pair in electron-positron annihilation provides a powerful tool at higher center-of-mass energies. In this work, we present phenomenological results for $\Sigma^+ \bar {\Sigma}^-$ production in $e^+e^-$ collision at the BESIII Collider. We investigate a hyperon pair produced in the reaction $e^+e^- \to \Sigma^+ \bar{\Sigma}^-$. Two different contributions are considered: the $D$ meson loop and the three-gluon charmonium annihilation loop. Taking into account the contributions of the $D$-meson loop and three-gluon loops and the interference of all diagrams, we calculate the total cross section of the process $e^+e^- \to \Sigma^+ \bar{\Sigma}^-$. With respect to a purely electromagnetic mechanism, large relative phases are generated for these contributions. We obtain as a byproduct a fit of the electromagnetic form factor of the $\Sigma$ hyperon for a large momentum transferred region. In this process, in addition to $\psi(3770)$ charmonium, we also take into account the contributions of other charmonium (-like) states, $\psi(4040)$, \,\,$\psi(4160)$, \,\,$Y(4230)$,\,\,$Y(4360)$,\,\,$\psi(4415)$, and $Y(4660)$. The obtained results are in good agreement with experimental data.