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

Abstract

We analyze the origin of the structures observed in the reactions $e^+e^-\to 3(π^+π^-)$, $2(π^+π^-π^0)$, $ωπ^+π^-π^0$, and $e^+e^-\to 2(π^+π^-)π^0$ around the antiproton-proton ($\bar pp$) threshold. We calculate the contribution of the two-step process $e^+e^-\to \bar NN \to$ multipions to the total reaction amplitude. The amplitude for $e^+e^-\to \bar NN$ is constrained from near-threshold data on the $e^+e^-\to \bar pp$ cross section and the one for $\bar NN \to$ multipions can be likewise fixed from available experimental information, for all those $5 π$ and $6π$ 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 $\bar NN$ threshold. The structures seen in the experiments emerges then as a threshold effect due to the opening of the $\bar NN$ channel.