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

TL;DR

This paper investigates the structures observed in certain $e^+e^-$ annihilation multipion production channels near the $ar pp$ threshold, attributing them to threshold effects from the opening of the $ar NN$ channel.

Contribution

It provides a quantitative analysis of the two-step process involving $ar NN$ intermediate states, explaining the observed structures as threshold effects.

Findings

The two-step process significantly contributes to the reaction amplitude.

The model reproduces experimental data near the $ar NN$ threshold.

Structures are explained as threshold effects from $ar NN$ channel opening.

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 ($\bar pp$) 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 $5 \pi$ 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 $\bar NN$ threshold. The structures seen in the experiments emerges then as a threshold effect due to the opening of the $\bar NN$ channel.