Cross section of the process $e^+ + e^- \to \Xi^0 + \bar{\Xi}^0$ including three-gluon and $D$-meson loop contributions

In this paper, we investigate the production of a $\Xi^0 \bar{\Xi}^0$ using $e^+e^-$ collision data at ten center-of-mass energies between 3.51 and 4.95 GeV collected with the BESIII detector at the BEPCII collider and corresponding to an integrated luminosity of 30 $\rm{fb}^{-1}$ to study the structure of baryons. The data collected by the BESIII detector are useful for the study of XYZ states, and this collaboration continues the exploration of these exotic charmonium-like states. We explore a hyperon pair produced in the electron-positron annihilation reactions. In the present paper we present the phenomenological results of our studies on the production of $\Xi^0 \bar{\Xi}^0$ in $e^+e^-$ annihilation at the BESIII detector at the BEPCII Collider. In the reaction $e^+e^- \to \Xi^0 \bar{\Xi}^0$, we consider two different contributions: one from the $D$ meson loop and the ofther from the three-gluon charmonium annihilation. We compute the total cross section of the process $e^+e^- \to \Xi^0 \bar{\Xi}^0$ including the contributions of the $D$-meson loop and three-gluon loops as well as the interference of all diagrams. As for the purely electromagnetic mechanism, large relative phases are generated for these contributions. For a large momentum transferred region we get as a byproduct a fit of the electromagnetic form factor of the $\Xi^0$ - hyperon. In this paper, in addition to the $\psi(3770)$ charmonium, we also take into account the contributions of other charmonium (-like) states, such as $\psi(4040)$, $\psi(4160)$, $Y(4230)$, $Y(4360)$, $\psi(4415)$, and $Y(4660)$. On the whole our results are in good agreement with the available experimental data.