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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 tomeasure 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 phasevariation over the Dalitz plot is taken from measurements performed at theCLEO-c experiment, making the analysis independent of the $D$ decay model. Witha sample of proton-proton collision data, corresponding to an integratedluminosity of $3.0\,\rm{fb}^{-1}$, collected by the LHCb experiment, the valuesof the $CP$ violation parameters are found to be $x_+ = 0.05 \pm 0.35 \pm0.02$, $x_-=-0.31\pm 0.20 \pm 0.04$, $y_+=-0.81\pm 0.28\pm 0.06$ and$y_-=0.31\pm 0.21 \pm 0.05$, where the first uncertainties are statistical andthe second systematic. These observables correspond to values $\gamma$ = $(71\pm 20)^\circ$, $r_{B^0} = 0.56\pm 0.17$ and $\delta_{B^0} =(204\,^{+21}_{-20})^\circ$. The parameters $r_{B^0}$ and $\delta_{B^0}$ are themagnitude 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 thecosine of the $K^{\ast}(892)^{0}$ helicity angle larger than 0.4.

the journal of high energy physics/the journal of high energy physics

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 $K_{S}^{0}  K^{+} K^{-}$