  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 $x_+ = 0.05 \pm 0.35 \pm
0.02$, $x_-=-0.31\pm 0.20 \pm 0.04$, $y_+=-0.81\pm 0.28\pm 0.06$ 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 $\delta_{B^0} =
(204\,^{+21}_{-20})^\circ$. 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.

High Energy Physics - Experiment