Poles and Poltergeists in $e^{+}{e}^{-}\to D\bar{D}$ Data

Abstract

A recent report of $e^{+}{e}^{-}\to D\bar{D}$ events by the BESIII Collaboration suggests the presence of a structure $R$ at 3900~MeV\@. We argue that this structure, called $G(3900)$ in the past, is not in fact due to a new $c\bar{c}$ resonance, but rather naturally emerges as a threshold enhancement due to the opening of the $D^{\ast }\bar{D}$ channel. We further find that the appearance of this structure does not require suppression because of a radial node in the $\ddot{I}ˆ(4040)$ wave function, although a node improves fit quality. The measured $e^{+}{e}^{-}$ coupling of $\ddot{I}ˆ(4040)$ is found to be substantially smaller than previously estimated. In addition, we report new corrections to the measured cross section $\ddot{I}ƒ(e^{+}{e}^{-}\to D\bar{D})$ at energies near $\ddot{I}ˆ(3770)$.

Discussion of previous work updated. 9 pages, 8 figures