Measurement of the CKM angle γusing B^\pm --> D K^\pm with D-->K_Sπ^+π^-, K_SK^+K^- decays

Abstract

A binned Dalitz plot analysis of $B^{\pm }\to D{K}^{\pm }$ decays, with $D\to K_S\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ 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 ${\hat{I}}^3$. 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 ${\hat{I}}^3=(62_{-14}^{+15}{)}^{\circ }$, with a second solution at ${\hat{I}}^3\to {\hat{I}}^3+180^{\circ }$, and $r_B=0.080_{-0.021}^{+0.019}$, where $r_B$ is the ratio between the suppressed and favoured $B$ decay amplitudes.