Mass shift of charmonium states in $\bar{p}A$ collision

The masses of the low lying charmonium states, namely, the $J\mathrm{/}\mathrm{\Psi }$, $\mathrm{\Psi }(3686)$, and $\mathrm{\Psi }(3770)$ 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 $\mathrm{\Psi }(3686)$, 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.