Measurement of the CKM angle \gamma using B^\pm --> D K^\pm with D-->K_S\pi^+\pi^-, K_SK^+K^- decays

A binned Dalitz plot analysis of $B^{\pm }\to D{K}^{\pm }$ decays, with $D \to K_S \pi^+\pi^-$and$D \to K_S K^+ K^-$, is performed to measure the \CP-violating observables $x_{\pm }$ and $y_{\pm }$, which are sensitive to the Cabibbo-Kobayashi-Maskawa angle $\gamma$. The analysis exploits a sample of proton-proton collision data corresponding to 3.0\invfb collected by the LHCb experiment. Measurements from CLEO-c of the variation of the strong-interaction phase of the $D$ decay over the Dalitz plot are used as inputs. The values of the parameters are found to be $x_+ = (-7.7 \pm 2.4 \pm 1.0 \pm 0.4)\times 10^{-2}$,$x_- = (2.5 \pm 2.5 \pm 1.0 \pm 0.5) \times 10^{-2}$,$y_+ = (-2.2 \pm 2.5 \pm 0.4 \pm 1.0)\times 10^{-2}$,and$y_- = (7.5 \pm 2.9 \pm 0.5 \pm 1.4) \times 10^{-2}$. The first, second, and third uncertainties are the statistical, the experimental systematic, and that associated with the precision of the strong-phase parameters. These are the most precise measurements of these observables and correspond to $\gamma = (62^{,+15}{,-14})^\circ$,withasecondsolutionat$\gamma \to \gamma + 180^\circ$,and$r_B = 0.080^{+ 0.019}{-0.021}$,where$r_B$ is the ratio between the suppressed and favoured $B$ decay amplitudes.