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

## TL;DR

This paper calculates the meson-meson components of the $ ext{psi}(3770)$ wave function using a coupled-channel approach and experimental data, revealing a dominant quark-antiquark core with small meson cloud contributions.

## Contribution

It introduces a method to determine the meson-meson probabilities in $ ext{psi}(3770)$ using the $^3P_0$ model and experimental data, providing new empirical insights.

## Key findings

- $Z$ probability of a quark-antiquark core is about 80-85%.
- Meson-meson components are relatively small in the $ ext{psi}(3770)$.
- Supports the largely $qar q$ nature of vector mesons, especially $ ext{psi}(3770)$.

## 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 $^3P_0$ 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 $80\sim85\%$, 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.