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 $3.0,rm{fb}^{-1}$, collected by the LHCb experiment, the values of the $CP$ violation parameters are found to be $x_+ = 0.05 pm 0.35 pm 0.02$, $x_-=-0.31pm 0.20 pm 0.04$, $y_+=-0.81pm 0.28pm 0.06$ and $y_-=0.31pm 0.21 pm 0.05$, where the first uncertainties are statistical and the second systematic. These observables correspond to values $gamma$ = $(71 pm 20)^circ$, $r_{B^0} = 0.56pm 0.17$ and $delta_{B^0} = (204,^{+21}_{-20})^circ$. The parameters $r_{B^0}$ 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.