Line shape and $D^{(\ast )}{\bar{D}}^{(\ast )}$ probabilities of $\psi (3770)$ from the $e^{+}{e}^{-}\to D\bar{D}$ reaction

Abstract

We have performed a calculation of the $D\bar{D}$, $D{\bar{D}}^{\ast }$, $D^{\ast }\bar{D}$, $D^{\ast }{\bar{D}}^{\ast }$ components in the wave function of the $\psi (3770)$. For this we make use of the ${}^3{P}_0$ model to find the coupling of $\psi (3770)$ to these components, that with an elaborate angular momentum algebra can be obtained with only one parameter. Then we use data for the $e^{+}{e}^{-}\to D\bar{D}$ reaction, from where we determine a form factor needed in the theoretical frame work, as well as other parameters needed to evaluate the meson-meson selfenergy of the $\psi (3770)$. Once this is done we determine the $Z$ probability to still have a vector core and the probability to have the different meson components. We find $Z$ about $80\sim 85\%$, and the individual meson-meson components are rather small, providing new empirical information to support the largely $q\bar{q}$ component of vector mesons, and the $\psi (3770)$ in particular.

arXiv comment30 pages, 12 figures

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