First observation of the decays ${\bar{B}}_{(s)}^0\to D_s^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ and ${\bar{B}}_s^0\to D_{s1}(2536{)}^{+}{\pi }^{-}$

The first observation of the decays ${\bar{B}}_s^0\to D_s^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ and ${\bar{B}}^0\to D_s^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ are reported using an integrated luminosity of 1.0 fb${}^{-1}$ recorded by the LHCb experiment. The branching fractions, normalized with respect to ${\bar{B}}_s^0\to D_s^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ and ${\bar{B}}_s^0\to D_s^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$, respectively, are measured to be {\br(\bar{B}^0_{s}\to D_s^+K^-\pi^+\pi^-)\over\br(\bar{B}^0_{s}\to D_s^+\pi^-\pi^+\pi^-)} &= (5.2\pm0.5\pm0.3)\times10^{-2}, {\br(\bar{B}^0\to D_s^+K^-\pi^+\pi^-)\over\br(\bar{B}^0_{s}\to D_s^+K^-^\pi^+\pi^-)} &= 0.54\pm0.07\pm0.07, where the first uncertainty is statistical and the second is systematic. The ${\bar{B}}_s^0\to D_s^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ decay is of particular interest as it can be used to measure the weak phase $\gamma$. First observation of the $\bar{B}^0_s\to D_{s1}(2536)^+\pi^-, D_{s1}^+\to D_s^+\pi^-\pi^+$ decay is also presented, and its branching fraction relative to ${\bar{B}}_s^0\to D_s^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ is found to be {\br(\bar{B}^0_s\to D_{s1}(2536)^+\pi^-, D_{s1}^+\to D_s^+\pi^-\pi^+)\over\br(\bar{B}^0_{s}\to D_s^+\pi^-\pi^+\pi^-)} &= (4.0\pm1.0\pm0.4)\times10^{-3}.