Study of the reactions $\bar{n} p \to 2π^{+}π^{-}$, $2π^{+}π^{-}π^{0}$, and $2π^{+}π^{-}2π^{0}$ using $J/ψ\to p π^{-}\bar{n}$

We report an experimental investigation of the reactions $\bar{n} p \to 2π^{+}π^{-}$, $\bar{n} p \to 2π^{+}π^{-}π^{0}$, and $\bar{n} p \to 2π^{+}π^{-}2π^{0}$ using $(10.087 \pm 0.044) \times 10^{9}$ $J/ψ$ events collected with the BESIII detector at the BEPCII storage ring. The antineutron ($\bar{n}$) is produced in the decay $J/ψ\to p π^{-} \bar{n}$ with studied momentum from 200~MeV/$c$ to 1174~MeV/$c$, while the target proton originates from the hydrogen nuclei in the cooling oil of the beam pipe. This novel method pioneers the study of $\bar{n}$-nucleon interactions at an $e^{+}e^{-}$ collider, providing the first experimental data for $\bar{n}$ momenta exceeding 800~MeV/$c$.