Test of the $X(3872)$ Structure in Antiproton-Nucleus Collisions

The present day experimental data on the $X(3872)$ decays do not allow to make clear conclusions on the dominating structure of this state. We discuss here an alternative way to study its structure by means of the two-step $\bar D^*$ (or $D$) production in $\bar p A$ reactions. If this process is mediated by $X(3872)$, the characteristic narrow peaks of the $\bar D^*$ (or $D$) distributions in the light cone momentum fraction at small transverse momenta will appear. This would unambiguously signal the $D \bar D^*$ + c.c. molecular composition of the $X(3872)$ state.