Measurement of time-dependent $CP$ violation parameters in $B^0\to K_S^0\ddot{I}{€}^0{\hat{I}}^3$ decays at Belle and Belle II

Abstract

We perform a measurement of time-dependent $CP$ violation parameters in $B^0\to K_S^0\ddot{I}{€}^0{\hat{I}}^3$ decays using a dataset of approximately $772\times 10^6$ and $521\times 10^6$ $\hat{I}\yen (4S)$ decays collected by the Belle and Belle II experiments, respectively. The measured parameters for the combined dataset in the $K^{\ast 0}(892)$ dominated region ($M_{K_S^0\ddot{I}{€}^0}\in [0.8,1.0]\mathrm{GeV}/c^2$) are $S=0.09\pm 0.16\pm 0.02$ and $C=-0.09\pm 0.08\pm 0.04$. For the non-$K^{\ast 0}(892)$ region ($M_{K_S^0\ddot{I}{€}^0}\in [1.0,1.8]\mathrm{GeV}/c^2$), the corresponding values are $S=-0.32\pm 0.33\pm 0.09$ and $C=-0.07\pm 0.17\pm 0.08$. The first quoted uncertainties are statistical, while the second ones are systematic. These results are consistent with Standard Model predictions and more precise than previous measurements.