First model-independent Dalitz analysis of $B^0\to D{K}^{\ast 0}$, $D\to K_S^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ decay

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 Dalitz analysis of $D\to K_S^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ 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 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 the KEKB $e^{+}{e}^{-}$ collider. This result is obtained from observables $x_{-}=+0.4_{-0.6-0.1}^{+1.0+0.0}\pm 0.0$, $y_{-}=-0.6_{-1.0-0.0}^{+0.8+0.1}\pm 0.1$, $x_{+}=+0.1_{-0.4-0.1}^{+0.7+0.0}\pm 0.1$ and $y_{+}=+0.3_{-0.8-0.1}^{+0.5+0.0}\pm 0.1$, 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 $\ddot{I}{•}_3(\hat{I}{´}_S)$ is the weak (strong) phase difference between $B^0\to D^0{K}^{\ast 0}$ and $B^0\to \overline{D^0}{K}^{\ast 0}$.

arXiv admin note: substantial text overlap with arXiv:1502.07550