Observation of $B_{c}^{+} to J/psi D^{(*)} K^{(*)}$ decays

A search for the decays $B_c^+ to J/psi D^{(*)0} K^+$ and $B_c^+ to J/psi D^{(*)+} K^{*0}$ is performed with data collected at the LHCb experiment corresponding to an integrated luminosity of 3 fb$^{-1}$. The decays $B_c^+ to J/psi D^0 K^+$ and $B_c^+ to J/psi D^{*0} K^+$ are observed for the first time, while first evidence is reported for the $B_c^+ to J/psi D^{*+} K^{*0}$ and $B_c^+ to J/psi D^+ K^{*0}$ decays. The branching fractions of these decays are determined relative to the $B_c^+ to J/psi pi^+$ decay. The $B_c^+$ mass is measured, using the $J/psi D^0 K^+$ final state, to be $6274.28 pm 1.40 (stat) pm 0.32 (syst)$ MeV/$c^2$. This is the most precise single measurement of the $B_c^+$ mass to date.