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 model-independent Dalitz plot analysis using $Dto K_S^0pi^+pi^-$ decays. Using the full data sample of $772times10^6$ $Bbar{B}$ pairs collected at the $Upsilon(4S)$ resonance with the Belle detector at KEKB accelerator the upper limit is $r_S < 0.87$ at the 68 % confidence level. This result is the first measurement of $r_S$ with a model-independent Dalitz analysis, and is consistent with results from other analyses. The value of $r_S$ indicates the sensitivity of the decay to $phi_3$ because the statistical uncertainty is proportional to $1/r_S$. The $r_S$ result is obtained from observables ($x_pm$, $y_pm$) begin{eqnarray} 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 y_+ &=& +0.3 ^{+0.5 +0.0}_{-0.8 -0.1} pm0.1 , end{eqnarray} where $x_pm = r_S cos(delta_S pm phi_3)$, $y_pm = r_S sin(delta_S pm phi_3)$ and $phi_3 (delta_S)$ are the weak (strong) phase difference between $B^0 to D^0K^{*0}$ and $B^0 to bar{D^0}K^{*0}$. The first uncertainty is statistical, the second is the experimental systematic and the third is the systematic due to the uncertainties on $c_i$ and $s_i$ parameters measured by CLEO.
Download