In order to confirm the existence of the dibaryon state observed at WASA@COSY, we estimate the cross section for production of the possible dibaryon and anti-dibaryon pair in the energy region of the upcoming experiments at anda. Based on some qualitative properties of extracted from the analyses in the non-relativistic quark model, the production cross section for this spin-3 particle pair are calculated with the help of a phenomenological effective relativistic and covariant Lagrangian approach.
Although $d^*(2380)$ was first observed by WASA@COSY, its existence has yet to be further confirmed in different types of processes at other facilities. In this work, the possible production of the single dibaryon state $d^*(2380)$ in the process of $p\bar{p}\to d^*(2380)\bar{p}\bar{n}$ at future experiment of $\bar{\rm{P}}$anda is estimated. Following the method used in our previous study (Chinese Physics C {\bf 46}, 023105) a phenomenological Lagrangian approach is employed to study the single $\ds$ production. Based on the conclusions obtained by the non-relativistic constituent quark model, the cross section of the $p\bar{p}\to d^*(2380)\bar{p}\bar{n}$ reaction via the $\Delta\bar{\Delta}$ intermediate state is estimated, which is in the order of $nb$. It is shown that the dominant contribution comes from the diagram with the $\bar{\Delta}\bar{\Delta}\to \bar{p}\bar{n}$ subprocess. However it is difficult to measure due to large background. On the other hand, although the cross section of the diagram with the $\bar{d^*}\to \bar{p}\bar{n}$ subprocess is small, only about $(3\sim 4)\%$ of the total cross section, the corresponding number of events is still large enough and can be measured at $\bar{\rm{P}}$anda, because the outgoing $\bar{p}$ and $\bar{n}$ come from the same source $\bar{d^*}$.
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