A possible explanation of the threshold enhancement in the process $e^{+}{e}^{-}\to \Lambda \bar{\Lambda }$

Abstract

Inspired by the recent measurement of the process $e^{+}{e}^{-}\to \Lambda \bar{\Lambda }$, we calculate the mass spectrum of the $\varphi$ meson with the GI model. For the excited vector strangeonium states $\varphi (3S,4S,5S,6S)$ and $\varphi (2D,3D,4D,5D)$, we further investigate the electronic decay width with the Van Royen-Weisskopf formula, and the partial widths of the $\Lambda \bar{\Lambda }$, ${\Xi }^{-(\ast )}{\bar{\Xi }}^{+}$, and ${\Sigma }^{+(\ast )}{\bar{\Sigma }}^{-(\ast )}$ decay modes with the extended quark pair creation model. We find that the electronic decay width of the $D$-wave vector strangeonium is about $3\sim 8$ times larger than that of the $S$-wave vector strangeonium. Around 2232 MeV the partial decay width of the $\Lambda \bar{\Lambda }$ mode can reach up to several MeV for $\varphi (3^3{S}_1)$, while the partial $\Lambda \bar{\Lambda }$ decay width of $\varphi (2^3{D}_1)$ is $\mathcal{O}(10^{-3})$ keV. If the threshold enhancement reported by the BESIII Collaboration arises from the strangeonium meson, this state is very likely to be the $\varphi (3^3{S}_1)$ state. We also note that the $\Lambda \bar{\Lambda }$ and ${\Sigma }^{+}{\bar{\Sigma }}^{-}$ partial decay widths of the states $\varphi (3^3{D}_1)$ and $\varphi (4^3{S}_1)$ are about several MeV, respectively, which are enough to be observed in future experiments.

arXiv comment9 pages, 5 figures, to be published in Chinese Physics C

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