Model-independent measurement of the CKM angle $\gamma$ using $B^0\to D{K}^{\ast 0}$ decays with $D\to K_S^0{\pi }^{+}{\pi }^{-}$ and $K_S^0{K}^{+}{K}^{-}$

A binned Dalitz plot analysis of the decays $B^0\to D{K}^{\ast 0}$, with $D \to K_{S}^{0} \pi^{+} \pi^{-}$and$K_{S}^{0} K^{+} K^{-}$, is performed to measure the observables $x_{\pm }$ and $y_{\pm }$, which are related to the CKM angle $\gamma$ and the hadronic parameters of the decays. The $D$ decay strong phase variation over the Dalitz plot is taken from measurements performed at the CLEO-c experiment, making the analysis independent of the $D$ decay model. With a sample of proton-proton collision data, corresponding to an integrated luminosity of $3.0{\mathrm{f}\mathrm{b}}^{-1}$, collected by the LHCb experiment, the values of the $CP$ violation parameters are found to be $x_+ = 0.05 \pm 0.35 \pm 0.02$,$x_-=-0.31\pm 0.20 \pm 0.04$,$y_+=-0.81\pm 0.28\pm 0.06$and$y_-=0.31\pm 0.21 \pm 0.05$, where the first uncertainties are statistical and the second systematic. These observables correspond to values $\gamma$ = $(71 \pm 20)^\circ$,$r_{B^0} = 0.56\pm 0.17$and$\delta_{B^0} = (204,^{+21}{-20})^\circ$\mathrm{.}Theparameters$r{B^0}$and$\delta_{B^0}$ are the magnitude ratio and strong phase difference between the suppressed and favoured $B^0$ decay amplitudes, and have been measured in a region of $\pm 50$ MeV/$c^2$ around the $K^{\ast }(892{)}^0$ mass and with the magnitude of the cosine of the $K^{\ast }(892{)}^0$ helicity angle larger than 0.4.