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

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.