Search for muoproduction of $X(3872)$ at COMPASS and indication of a new state $\widetilde{X}(3872)$.

We have searched for exclusive production of exotic charmonia in the reaction $\mu^+~N \rightarrow \mu^+ (J\!/\!\psi\pi^+\pi^-)\pi^{\pm}~N'$ using COMPASS data collected with incoming muons of 160 GeV/$c$ and 200 GeV/$c$ momentum. In the $J\!/\!\psi\pi^+\pi^-$ mass distribution we observe a signal with a statistical significance of 4.1 $\sigma$. Its mass and width are consistent with those of the $X(3872)$. The shape of the $\pi^+\pi^-$ mass distribution from the observed decay into $J\!/\!\psi\pi^+\pi^-$ shows disagreement with previous observations for $X(3872)$. The observed signal may be interpreted as a possible evidence of a new charmonium state. It could be associated with a neutral partner of $X(3872)$ with $C = -1$ predicted by a tetraquark model. The product of cross section and branching fraction of the decay of the observed state into $J\!/\!\psi\pi^+\pi^-$ is determined to be 71$\pm$28(stat)$\pm$39(syst) pb.