Understanding oscillating features of the timelike nucleon electromagnetic form factors within the extending vector meson dominance model

We investigate the nonmonotonic behavior observed in the time-like nucleon electromagnetic form factors. Using a phenomenological extending vector meson dominance model, where the ground states $\rho$ and $\omega$ and their excited states $\rho(2D)$, $\omega(3D)$, and $\omega(5S)$ are taken into account, we have successfully reproduced the cross sections of $e^+ e^- \to p \bar{p}$ and $e^+ e^- \to n \bar{n}$ reactions. Furthermore, we have derived the nucleon electromagnetic form factors in the time-like region, and it is found that the so-called periodic behaviour of the nucleon effective form factors is not confirmed. However, there are indeed nonmonotonic structures in the line shape of nucleon effective form factors, which can be naturally reproduced by considering the contributions from the low-lying excited vector states.