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Phenomenological study on the $\bar p N\to \bar NNππ$ reactions

We extend our recent phenomenological study of $pN \to NNππ$ reactions to the $\bar{p}N \to \bar{N}Nππ$ reactions for anti-proton beam momenta up to 3.0 GeV within an effective Lagrangian approach. The contribution of $N^*(1440)$ with its $Nσ$ decay mode is found to be dominant at the energies close to threshold for $\bar NNπ^+π^-$ and $\bar NNπ^0π^0$ channels. At higher energies or for $p\bar nπ^-π^-$ and $\bar NNπ^\pmπ^0$ channels where $N^*(1440)\to Nσ$ mode cannot contribute, large contributions from double-$Δ$, $Δ(1600) \to N^*(1440)π$, $Δ(1600) \to Δπ$ and $Δ(1620) \to Δπ$ are found. In the near-threshold region, sizeable contributions from $Δ\to Δπ$, $Δ\to Nπ$, $N \to Δπ$ and nucleon pole are also indicated. Although these results are similar to those for $pN\to NNππ$ reactions, the antinucleon-nucleon collisions are shown to be complementary to the nucleon-nucleon collisions and may even have advantages in some aspects. The PANDA/FAIR experiment is suggested to be an excellent place for studying the properties of relevant $N^*$ and $Δ^*$ resonances.