Wave-like amplification of near-threshold two-particle reactions: from muon-catalyzed fusion to $\Lambda\bar{\Lambda}$ production at $e^-e^+$ annihilation

Abstract

A simple model is proposed to explain the recently found wave-like enhancement of the $\Lambda\bar{\Lambda}$ pair production near the threshold at the $e^-e^+$ annihilation, which allows extracting model-independent scattering parameters and spectral information for the $\Lambda\bar{\Lambda}$ pair from the oscillatory nature of the measured cross section. In particular, it predicts a single bound state of $\Lambda\bar{\Lambda}$ with a binding energy of $\varepsilon_{\Lambda\bar{\Lambda}}=(36\pm5)$MeV. The model is a generalization of the formulas obtained in our earlier work [1] to explain the effect of wave-like amplification found in it near the threshold of fusion reactions screened by a muon or electron. The analysis allows us to conclude that the effect of wave-like amplification is an integral feature of any two-particle near-threshold reaction. In this regard, it seems promising to investigate, within the framework of our model, the oscillatory nature of the electromagnetic form factors of hyperons and nucleons extracted in experiments on $e^- e^+$ annihilation. A natural further development of the model could be its generalization to processes of producing various hadron pairs in $e^-e^+$ annihilation.