Origin of the structures observed in $e^{+}{e}^{-}$ annihilation into multipion states around the $\bar{p}p$ threshold

Abstract

We analyze the origin of the structures observed in the reactions $e^{+}{e}^{-}\to 3({\pi }^{+}{\pi }^{-})$, $2({\pi }^{+}{\pi }^{-}{\pi }^0)$, $\omega {\pi }^{+}{\pi }^{-}{\pi }^0$, and $e^{+}{e}^{-}\to 2({\pi }^{+}{\pi }^{-}){\pi }^0$ around the antiproton-proton ($\bar{p}p$) threshold. We calculate the contribution of the two-step process $e^{+}{e}^{-}\to \bar{N}N\to$ multipions to the total reaction amplitude. The amplitude for $e^{+}{e}^{-}\to \bar{N}N$ is constrained from near-threshold data on the $e^{+}{e}^{-}\to \bar{p}p$ cross section and the one for $\bar{N}N\to$ multipions can be likewise fixed from available experimental information, for all those $5\pi$ and $6\pi$ states. The resulting amplitude for $e^{+}{e}^{-}\to$ multipions turns out to be large enough to play a role for the considered $e^{+}{e}^{-}$ annihilation channels and, in three of the four reactions, even allows us to reproduce the data quantitatively near the $\bar{N}N$ threshold. The structures seen in the experiments emerges then as a threshold effect due to the opening of the $\bar{N}N$ channel.

Comments: 7 pages, 4 figures