Mass shift of charmonium states in $\bar p A$ collisions

The masses of the low lying charmonium states, namely, the $J/\Psi$, $\Psi(3686)$, and $\Psi(3770)$ are shifted downwards due to the second order Stark effect. In $\bar p + \text{Au}$ collisions at $6-10$~GeV we study their in\,-\,medium propagation. The time evolution of the spectral functions of these charmonium states is studied with a Boltzmann\,-\,Uehling\,-\,Uhlenbeck (BUU) type transport model. We show that their in\,-\,medium mass shift can be observed in the dilepton spectrum. Therefore, by observing the dileptonic decay channel of these low lying charmonium states, especially for $\Psi(3686)$, we can gain information about the magnitude of the gluon condensate in nuclear matter. This measurement could be performed at the upcoming PANDA experiment at FAIR.