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We investigate the $D\bar{D}$ production in $e^+e^-$ annihilations nearthreshold in an effective Lagrangian approach. This shows that the lineshape ofthe cross section near threshold is sensitive to the contributions from$\psi^\prime$, though it is below the $D\bar{D}$ threshold. The recentexperimental data from the BES and Belle collaborations allow us to determinethe $\psi^\prime D\bar{D}$ coupling constant which appears to be consistentwith other theoretical studies. As a consequence, the$\psi^\prime$-$\psi(3770)$ mixing parameter can be extracted around the$\psi(3770)$ mass region. Resonance parameters for $\psi(3770)$, X(3900),$\psi(4040)$, and $\psi(4160)$ are also investigated. The X(3900) appears as anenhancement at around 3.9 GeV in the Belle data. In addition to treating it asa resonance, we also study the mechanism that the enhancement is produced bythe $D\bar{D^*}+c.c.$ open channel effects. Our result shows that such apossibility cannot be eliminated.

The lineshape of $\psi(3770)$ and low-lying vector charmonium resonance parameters in $e^+ e^-\to D\bar D$