Electromagnetic form factors of $\Lambda$ hyperon in the vector meson dominance model and a possible explanation of the near-threshold enhancement of the $e^+e^- \to \Lambda\bar{\Lambda}$ reaction

Abstract

The near-threshold $e^+e^- \to \Lambda\bar{\Lambda}$ reaction is studied with the assumption that the production mechanism is due to a near-$\Lambda \bar{\Lambda}$-threshold bound state. The cross section of $e^+e^- \to \Lambda\bar{\Lambda}$ reaction is parametrized in terms of the electromagnetic form factors of $\Lambda$ hyperon, which are obtained with the vector meson dominance model. It is shown that the contribution to the $e^+e^- \to \Lambda\bar{\Lambda}$ reaction from a new narrow state with quantum numbers $J^{PC}=1^{--}$ is dominant for energies very close to threshold. The mass of this new state is around 2231 MeV, which is very close to the mass threshold of $\Lambda \bar{\Lambda}$, while its width is just a few MeV. This gives a possible solution to the problem that all previous calculations seriously underestimate the near-threshold total cross section of the $e^+e^- \to \Lambda\bar{\Lambda}$ reaction. We also note that the near-threshold enhancement can be also reproduced by including these well established vector resonances $\omega(1420)$, $\omega(1650)$, $\phi(1680)$, or $\phi(2170)$ with a Flatt${\rm\acute{e}}$ form for their total decay width, and a strong coupling to the $\Lambda\bar{\Lambda}$ channel.