Observation of $B^0_s \to K^{*\pm}K^\mp$ and evidence for $B^0_s \to K^{*-}\pi^+$ decays

Measurements of the branching fractions of $B^0_s \to K^{*\pm}K^\mp$ and $B^0_s \to K^{*\pm}\pi^\mp$ decays are performed using a data sample corresponding to $1.0 \ {\rm fb}^{-1}$ of proton-proton collision data collected with the LHCb detector at a centre-of-mass energy of $7\mathrm{\,TeV}$, where the $K^{*\pm}$ mesons are reconstructed in the $K^0_{\rm S}\pi^\pm$ final state. The first observation of the $B^0_s \to K^{*\pm}K^\mp$ decay and the first evidence for the $B^0_s \to K^{*-}\pi^+$ decay are reported with branching fractions \begin{eqnarray} {\cal B}(B^0_s \to K^{*\pm}K^\mp) & = & (12.7\pm1.9\pm1.9) \times 10^{-6}, \\ {\cal B}(B^0_s \to K^{*-}\pi^+) & = & ~(3.3\pm1.1\pm0.5) \times 10^{-6}, \end{eqnarray} where the first uncertainties are statistical and the second are systematic. In addition, an upper limit of ${\cal B}(B^0 \to K^{*\pm}K^\mp) < 0.4 \ (0.5) \times 10^{-6}$ is set at $90\,% \ (95\,%)$ confidence level.