Model-independent measurement of $CP$ violation parameters in $B^{\pm}\to(K^{0}_{\rm S}h^{+}h^{-})_{D}K^{\pm}$ decays

The following $CP$ violating observables are measured in a model-independent analysis of $B^{\pm}\to(K^{0}_{\rm S}h^{+}h^{-})_{D}K^{\pm}$ (where $h = \pi, K$) decays reconstructed in a data sample corresponding to an integrated luminosity of 2.0~fb$^{-1}$ of $pp$ interactions collected by the LHCb experiment at a centre-of-mass energy of 8~TeV in 2012 \begin{align*} x_+ & = (-8.7 \pm 3.1 \pm 1.6 \pm 0.6) \times 10^{-2}, \\ x_- & = \phantom{-} ( 5.3 \pm 3.2 \pm 0.9 \pm 0.9) \times 10^{-2}, \\ y_+ & = \phantom{-} ( 0.1 \pm 3.6 \pm 1.4 \pm 1.9) \times 10^{-2}, \\ y_- & = \phantom{-} ( 9.9 \pm 3.6 \pm 2.2 \pm 1.6) \times 10^{-2}, \end{align*} where the first uncertainty is statistical, the second arises from systematic effects from the method or detector considerations and the third from external strong-phase measurements used in the fit. These results are combined with those obtained in the equivalent analysis of LHCb data collected in 2011. The best-fit value of the CKM unitarity triangle angle $\gamma$ is determined to be $(57 \pm 16)^{\circ}$ and the parameters $r_B$ and $\delta_B$ are determined to be $(8.8^{+2.3}_{-2.4}) \times 10^{-2}$ and $(124^{+15}_{-17})^{\circ}$, respectively.