Measurements of isospin asymmetry and difference of direct $CP$ asymmetries in inclusive $B\to X_s{\hat{I}}^3$ decays

Abstract

We report measurements of isospin asymmetry $\hat{I}{”}_{0-}$ and difference of direct $CP$ asymmetries $\hat{I}”A_{CP}$ between charged and neutral $B\to X_s{\hat{I}}^3$ decays. This analysis is based on the data sample containing $772\times 10^{6}B\bar{B}$ pairs that was collected with the Belle detector at the KEKB energy-asymmetric $e^{+}{e}^{-}$ collider. Using a sum-of-exclusive technique with invariant $X_s$ mass up to 2.8~GeV/$c^2$, we obtain $\hat{I}{”}_{0-}=[-0.48\pm 1.49(stat.)\pm 0.97(syst.)\pm 1.15(f_{+-}/f_{00})]$\% and $\hat{I}”A_{CP}=[+3.69\pm 2.65(stat.)\pm 0.76(syst.)]$\%, where the last uncertainty for $\hat{I}{”}_{0-}$ is due to the uncertainty on the production ratio of $B^{+}{B}^{-}$ to $B^0{\bar{B}}^0$ in $\hat{I}\yen (4S)$ decays. The measured value of $\hat{I}{”}_{0-}$ is consistent with zero, allowing us to constrain the resolved photon contribution in the $B\to X_s{\hat{I}}^3$, and improve the branching fraction prediction. The result for $\hat{I}”A_{CP}$ is consistent with the prediction of the SM. We also measure the direct $CP$ asymmetries for charged and neutral $B\to X_s{\hat{I}}^3$ decays. All the measurements are the most precise to date.

20 pages, 10 figures, submitted to PRD