  In this work, we apply the vector meson dominance (VMD) model to extract the
electromagnetic time-like form factor of the $D^*\to D$ transition combining
the recent Belle data for $e^+ e^-\to D^{*+} D^- + c.c.$ and data for $D^*\to
D\gamma$. Two solutions are obtained in the interpretation of the cross section
lineshape: i) With a relatively large coupling for $\psi D^*\bar{D}$ determined
by experiment, destructive interferences among those charmonium components are
required to bring down the overall cross sections, and then account for the
cross section lineshape. ii) With a relatively small value for the $\psi
D^*\bar{D}$ coupling based on heavy quark theory, an apparent cross section
deficit near threshold is observed, and contributions from other mechanisms are
needed. It might imply the presence of an additional resonance X(3900).
Meanwhile, we also point out that an enhancement like that could be produced by
the $D_s^*\bar{D_s}+c.c.$ open channel effects.

High Energy Physics - Phenomenology;High Energy Physics - Experiment