The electromagnetic form factors of $$\Lambda _c$$ hyperon in the vector meson dominance model

Abstract

We apply a modified vector meson dominance (VMD) model to analyze the electromagnetic form factors of the $\Lambda_c$ hyperon in the time-like reaction $e^+e^-\rightarrow \Lambda_c^+ \bar{\Lambda}_c^-$. In the model, we include the contributions from the vector charmed mesons and their excitations $\psi(1S)$, $\psi(2S)$, $\psi(3770)$, $\psi(4040)$, $\psi(4160)$ and $\psi(4415)$. We perform a combined fit to the available data on the Born cross section in reaction $e^+e^-\rightarrow \Lambda_c^+ \bar{\Lambda}_c^-$ and the ratio of the electromagnetic form factors $|G_E/G_M|$ to obtain the values of the model parameters. Our results show that the VMD model can simultaneously describe the data of electromagnetic form factors from the Belle and BESIII Collaborations, and the behavior of $|G_E/G_M|$ for the BESIII data can be qualitatively reproduced by the VMD model prediction at the threshold region. Moreover, we predict the single and double polarization observables in $e^+e^-\rightarrow \Lambda_c^+ \bar{\Lambda}_c^-$ reactions, which are experimentally accessible in the polarized process. We also obtain the form factors of the $\Lambda_c$ hyperon in the space-like region via analytic continuing the time-like form factors.