Study of the branching ratio of $\psi(3770)\to D\bar{D}$ in $e^+e^-\to D\bar{D}$ scattering

Abstract

Based on the data of BES and Belle, the production of $D\bar{D}$ in the $e^+e^-\to D\bar{D}$ scattering process is studied in this paper. We analyze the continuum and resonant contributions in the energy region from 3.7 to 4.4 GeV. In the $\chi^2$ fit to data, we obtain the resonance parameters of $\psi(3770)$, the branching ratio of $\psi(3770)\to D\bar{D}$ decay by confronting the data to the theoretical formula where both the contributions of the resonances, continuum and interference effects are included. We obtain the branching ratio of $\psi(3770)\to D\bar{D}$ decay is $97.2%\pm 8.9%$, as well as the branching ratio of $\psi(4040)$, $\psi(4160)\to D\bar{D}$ decays.