Search for the $D^*\bar{D}^*$ molecular state $Z_c(4000)$ in the reaction $B^{-} \rightarrow J/\psi \rho^0 K^{-}$

Based on the prediction of a $D^*\bar{D}^*$ molecular state $Z_c(4000)$ with isospin $I=1$ in the coupled channel approach, we suggest to search for this state in the reaction $B^- \to J/\psi \rho^0 K^-$. By taking into account the final state interactions of $J/\psi \rho$ and $D^{*0}\bar{D}^{*0}$, and the contribution from 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 $Z_c(4000)$. Searching for the $Z_c(4000)$ in the reaction $B^- \to J/\psi \rho^0 K^-$ is crucial to understand the internal structures of the exotic hadrons, and our predictions can be tested by the Belle II and LHCb in future.