Measurements of isospin asymmetry and difference of direct $CP$ asymmetries in inclusive $B to X_s gamma$ decays

We report measurements of isospin asymmetry $Delta_{0-}$ and difference of direct $CP$ asymmetries $Delta A_{CP}$ between charged and neutral $B to X_s gamma$ decays. This analysis is based on the data sample containing $772 times 10^6 Bbar{B}$ 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 $Delta_{0-} = bigl[-0.48 pm 1.49 {rm (stat.)} pm 0.97 {rm (syst.)} pm 1.15 {(f_{+-}/f_{00})}bigr]$% and $Delta A_{CP} = bigl[+3.69 pm 2.65 {rm (stat.)} pm 0.76{rm (syst.)}bigr]$%, where the last uncertainty for $Delta_{0-}$ is due to the uncertainty on the production ratio of $B^+B^-$ to $B^0bar{B}^0$ in $Upsilon(4S)$ decays. The measured value of $Delta_{0-}$ is consistent with zero, allowing us to constrain the resolved photon contribution in the $B to X_s gamma$, and improve the branching fraction prediction. The result for $Delta A_{CP}$ is consistent with the prediction of the SM. We also measure the direct $CP$ asymmetries for charged and neutral $B to X_s gamma$ decays. All the measurements are the most precise to date.