Measurement of the CKM angle $gamma$ using $B^0 rightarrow D K^{*0}$ with $D rightarrow K^0_S pi^+ pi^-$ decays

A model-dependent amplitude analysis of the decay $B^0rightarrow D(K^0_Spi^+pi^-) K^{*0}$ is performed using proton-proton collision data corresponding to an integrated luminosity of 3.0fb$^{-1}$, recorded at $sqrt{s}=7$ and $8 TeV$ by the LHCb experiment. The CP violation observables $x_{pm}$ and $y_{pm}$, sensitive to the CKM angle $gamma$, are measured to be begin{eqnarray*} x_- &=& -0.15 pm 0.14 pm 0.03 pm 0.01, y_- &=& 0.25 pm 0.15 pm 0.06 pm 0.01, x_+ &=& 0.05 pm 0.24 pm 0.04 pm 0.01, y_+ &=& -0.65^{+0.24}_{-0.23} pm 0.08 pm 0.01, end{eqnarray*} where the first uncertainties are statistical, the second systematic and the third arise from the uncertainty on the $Drightarrow K^0_S pi^+pi^-$ amplitude model. These are the most precise measurements of these observables. They correspond to $gamma=(80^{+21}_{-22})^{circ}$ and $r_{B^0}=0.39pm0.13$, where $r_{B^0}$ is the magnitude of the ratio of the suppressed and favoured $B^0rightarrow D K^+ pi^-$ decay amplitudes, in a $Kpi$ mass region of $pm50 MeV$ around the $K^*(892)^0$ mass and for an absolute value of the cosine of the $K^{*0}$ decay angle larger than $0.4$.