Measurement of the amplitude ratio of $B^0\to D^0{K}^{\ast 0}$ and $B^0\to \overline{D^0}{K}^{\ast 0}$ decays with a model-independent Dalitz plot analysis using $D\to K_S^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ decays

Abstract

We report a measurement of the amplitude ratio $r_S$ of $B^0\to D^0{K}^{\ast 0}$ and $B^0\to \overline{D^0}{K}^{\ast 0}$ decays with a model-independent Dalitz plot analysis using $D\to K_S^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ decays. Using the full data sample of $772\times 10^6$ $B\bar{B}$ pairs collected at the $\hat{I}\yen (4S)$ 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 $\ddot{I}{•}_3$ 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 $x_{\pm }=r_S\cos (\hat{I}{´}_S\pm \ddot{I}{•}_3)$, $y_{\pm }=r_S\sin (\hat{I}{´}_S\pm \ddot{I}{•}_3)$ and $\ddot{I}{•}_3(\hat{I}{´}_S)$ are the weak (strong) phase difference between $B^0\to D^0{K}^{\ast 0}$ and $B^0\to \overline{D^0}{K}^{\ast 0}$. 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.