The first observation of the decays ${\overline{B}}_s^0\to D_s^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ and ${\overline{B}}^0\to D_s^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ are reported using an integrated luminosity of $1.0{\mathrm{fb}}^{-1}$ recorded by the LHCb experiment. The branching fractions, normalized with respect to ${\overline{B}}_s^0\to D_s^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ and ${\overline{B}}_s^0\to D_s^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$, respectively, are measured to be $\frac{\mathcal{B}({\overline{B}}_s^0\to D_s^{+}{K}^{-}{\pi }^{+}{\pi }^{-})}{\mathcal{B}({\overline{B}}_s^0\to D_s^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-})}=(5.2\pm 0.5\pm 0.3)\times {10}^{-2}$ and $\frac{\mathcal{B}({\overline{B}}^0\to D_s^{+}{K}^{-}{\pi }^{+}{\pi }^{-})}{\mathcal{B}({\overline{B}}_s^0\to D_s^{+}{K}^{-}{\pi }^{+}{\pi }^{-})}=0.54\pm 0.07\pm 0.07$, where the first uncertainty is statistical and the second is systematic. The ${\overline{B}}_s^0\to D_s^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ decay is of particular interest as it can be used to measure the weak phase $\gamma$. First observation of the ${\overline{B}}_s^0\to D_{s1}(2536{)}^{+}{\pi }^{-}$, $D_{s1}^{+}\to D_s^{+}{\pi }^{-}{\pi }^{+}$ decay is also presented, and its branching fraction relative to ${\overline{B}}_s^0\to D_s^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ is found to be $\frac{\mathcal{B}({\overline{B}}_s^0\to D_{s1}(2536{)}^{+}{\pi }^{-},D_{s1}^{+}\to D_s^{+}{\pi }^{-}{\pi }^{+})}{\mathcal{B}({\overline{B}}_s^0\to D_s^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-})}=(4.0\pm 1.0\pm 0.4)\times {10}^{-3}$.

• Received 7 November 2012

DOI:https://doi.org/10.1103/PhysRevD.86.112005

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© 2012 CERN, for the LHCb Collaboration