Testing the predicted dynamically generated hidden charm $X$ scalar state through the $D\bar D$ invariant mass spectrum and the radiative decay of the $\psi(3770)$

Abstract

In this work we present our model that dynamically generates resonances from charmed and light pseudoscalar and vector mesons. The model generates a rich spectrum of charmed and hidden charm scalar and axial resonances, most of them which can be associated with observed states. Other states are predicted, in particular a hidden charm scalar resonance with mass close to the $D\bar D$ threshold. For this resonance we present calculations which show that an observed enhancement in the $D\bar D$ mass spectrum measured by Belle in reactions producing $D\bar D J/\psi$ in the final state could be originated by this predicted state. We also present theoretical calculations on the radiative decay width of the $\psi(3770)$ into this state. The predicted branching fractions suggest that this predicted state could be observed by BES with statistics of one year run in the $\psi(3770)$ peak.