Lineshape ofψ(3770)and low-lying vector charmonium resonance parameters ine+e−→DD¯

Abstract

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