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

TL;DR

This paper presents the first model-independent Dalitz analysis of $B^0 o DK^{*0}$ decays, measuring the amplitude ratio $r_S$ and setting an upper limit using a large data sample from the Belle experiment.

Contribution

It introduces a novel model-independent method for analyzing $B^0$ decays to determine the amplitude ratio $r_S$ with improved robustness against model assumptions.

Findings

Set an upper limit $r_S < 0.87$ at 68% CL.

Measured observables $x_ extpm$, $y_ extpm$ with uncertainties.

Utilized the full Belle dataset of $772\times10^6$ $B\bar{B}$ pairs.

Abstract

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 $D\to K_S^0\pi^+\pi^-$ 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 full data 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 is obtained 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 $B^0 \to D^0K^{*0}$ and $B^0 \to \bar{D^0}K^{*0}$.