Measurements of isospin asymmetry and difference of direct C P asymmetries in inclusive B → X s γ decays

We report measurements of isospin asymmetry ${\mathrm{{\Delta}}}_{0{-}}$ and difference of direct $CP$ asymmetries $\mathrm{{\Delta}}{A}_{CP}$ between charged and neutral $B{\rightarrow}{X}_{s}{\gamma}$ decays. This analysis is based on the data sample containing $772\times{}{10}^{6}B\overline{B}$ 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 $2.8\text{ }\text{ }\mathrm{GeV}/{c}^{2}$, we obtain ${\mathrm{{\Delta}}}_{0{-}}=[{-}0.48\pm{}1.49(\mathrm{stat})\pm{}0.97(\mathrm{syst})\pm{}1.15({f}_{+{-}}/{f}_{00})]$% and $\mathrm{{\Delta}}{A}_{CP}=[+3.69\pm{}2.65(\mathrm{stat})\pm{}0.76(\mathrm{syst})]$%, where the last uncertainty for ${\mathrm{{\Delta}}}_{0{-}}$ is due to the uncertainty on the production ratio of ${B}^{+}{B}^{{-}}$ to ${B}^{0}{\overline{B}}^{0}$ in $\mathrm{{\Upsilon}}(4S)$ decays. The measured value of ${\mathrm{{\Delta}}}_{0{-}}$ is consistent with zero, allowing us to constrain the resolved photon contribution in the $B{\rightarrow}{X}_{s}{\gamma}$, and improve the branching fraction prediction. The result for $\mathrm{{\Delta}}{A}_{CP}$ is consistent with the prediction of the SM. We also measure the direct $CP$ asymmetries for charged and neutral $B{\rightarrow}{X}_{s}{\gamma}$ decays. All the measurements are the most precise to date.