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We report a measurement of the amplitude ratio $r_S$ of $B^0 \to D^0K^{*0}$and $B^0 \to \bar{D^0}K^{*0}$ decays with a Dalitz analysis of $D\toK_S^0\pi^+\pi^-$ decays, for the first time using a model-independent method.We set an upper limit $r_S < 0.87$ at the 68\% confidence level, using the fulldata sample of $772\times10^6$ $B\bar{B}$ pairs collected at the $\Upsilon(4S)$resonance with the Belle detector at the KEKB $e^+e^-$ collider. This result isobtained from observables $x_- = +0.4 ^{+1.0 +0.0}_{-0.6 -0.1} \pm0.0$, $y_- =-0.6 ^{+0.8 +0.1}_{-1.0 -0.0} \pm0.1$, $x_+ = +0.1 ^{+0.7 +0.0}_{-0.4 -0.1}\pm0.1$ and $y_+ = +0.3 ^{+0.5 +0.0}_{-0.8 -0.1} \pm0.1$, where $x_\pm = r_S\cos(\delta_S \pm \phi_3)$, $y_\pm = r_S \sin(\delta_S \pm \phi_3)$ and$\phi_3~(\delta_S)$ is the weak (strong) phase difference between $B^0 \toD^0K^{*0}$ and $B^0 \to \bar{D^0}K^{*0}$.

First model-independent Dalitz analysis of $B^0 \to DK^{*0}$, $D\to K_S^0\pi^+\pi^-$ decay