Search for the $D^*\bar{D}^*$ molecular state $Z_c(4000)$ in the reaction of $B^{-} \rightarrow J/\psi \rho K^{-}$.

Based on the prediction of a $D^*\bar{D}^*$ molecular state $Z_c(4000)$ with isospin $I=1$ in the coupled channels unitary chiral approach, and that the existence of the $Z_c(4000)$ is crucial to understand the near threshold enhancement in the $e^+e^-\to (D^*\bar{D}^*)^\pm \pi^\mp$ process reported by the BESIII Collaboration, we suggest to search for this state in the reaction of $B^- \to J/\psi \rho K^-$. By taking into account the final state interactions of $J/\psi \rho$ and $D^{*0}\bar{D}^{*0}$, and the contribution of the $K_1(1270)$ resonance, we find that the $J/\psi\rho$ mass distribution shows a peak around 4000 MeV, which could be associated to the $D^*\bar{D}^*$ molecular state $Z_c(4000)$.