A modeldependent amplitude analysis of the decay $B^0\rightarrow D(K^0_S\pi^+\pi^) K^{*0}$ is performed using protonproton 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 $D\rightarrow K^0_S \pi^+\pi^$ amplitude model. These are the most precise measurements of these observables. They correspond to $\gamma=(80^{+21}_{22})^{\circ}$ and $r_{B^0}=0.39\pm0.13$, where $r_{B^0}$ is the magnitude of the ratio of the suppressed and favoured $B^0\rightarrow D K^+ \pi^$ decay amplitudes, in a $K\pi$ 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 $0.4$.
Variation of signal efficiency across the phase space for (left) long and (right) downstream candidates. 
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Invariant mass distribution for $ B ^0 \rightarrow D K ^{*0} $ long and downstream candidates. The fit result, including signal and background components, is superimposed (solid blue). The points are data, and the different fit components are given in the legend. The two vertical lines represent the signal region in which the $ C P$ fit is performed. 
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Selected $ B ^0 \rightarrow D K ^{*0} $ candidates, shown as (a) the Dalitz plot, and its projections on (b) $ m^2_$ , (c) $ m^2_+$ and (d) $ m^2_0$ {}. The line superimposed on the projections corresponds to the fit result and the points are data. 
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Selected $\overline{ B }{} {}^0 \rightarrow D \overline{ K }{} {}^{*0} $ candidates, shown as (a) the Dalitz plot, and its projections on (b) $ m^2_$ , (c) $ m^2_+$ and (d) $ m^2_0$ {}. The line superimposed on the projections corresponds to the fit result and the points are data. 
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Likelihood contours at 68.3% and 95.5% confidence level for $(x_{+},y_{+})$ (red) and $(x_{},y_{})$ (blue), obtained from the $ C P$ fit. 
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Confidence level curve on $\gamma$ , obtained using the "plugin" method [58]. 
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Confidence level curve on $ r_{ B ^0 }$ , obtained using the "plugin" method [58]. 
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Confidence level curve on $\delta_{ B ^0 }$ , obtained using the "plugin" method [58]. Only the $\delta_{ B ^0 }$ solution corresponding to $0<\gamma <180 ^{\circ} $ is highlighted; the other maximum is due to the $(\delta_{ B ^0 } ,\gamma )\rightarrow (\delta_{ B ^0 } +\pi,\gamma +\pi)$ ambiguity. 
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Twodimensional confidence level curves in the $(\gamma , r_{ B ^0 } )$ plane, obtained using the profilelikelihood method. 
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Twodimensional confidence level curves in the $(\gamma ,\delta_{ B ^0 } )$ plane, obtained using the profilelikelihood method. 
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Animated gif made out of all figures. 
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Signal and background yields in the signal region, $\pm25\mathrm{ Me V} $ around the $ B ^0$ mass, obtained from the invariant mass fit. Total yields, as well as separate yields for long and downstream candidates, are given. 
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Summary of the systematic uncertainties on $ z_{\pm}$ , in units of $(10^{3})$. The total experimental and total modelrelated uncertainties are also given as percentages of the statistical uncertainties. 
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Model related systematic uncertainties for each alternative model, in units of $(10^{3})$. The relative signs indicate full correlation or anticorrelation. 
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Created on 22 May 2020.