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

We report measurements of isospin asymmetry ${\mathrm{\Delta }}_{0-}$ and difference of direct $CP$ asymmetries $\mathrm{\Delta }{A}_{CP}$ between charged and neutral $B\to X_s\gamma$ 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 $2.8\mathrm{GeV}/c^2$, 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 $B\to X_s\gamma$, 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 $B\to X_s\gamma$ decays. All the measurements are the most precise to date.

Figure 1

Neural Network output in simulated data that ranges from $-1$ for the $q\overline{q}$ background-like events to $+1$ for the signal-like events. The solid (brown) curve shows signal, the dotted-dashed (orange) curve represents cross-feed, the dashed (blue) curve is $q\overline{q}$ background, and the long dashed (green) curve shows $B\overline{B}$ background.

Figure 2

$M_{\mathrm{bc}}$ distributions for (a) $B^{-}$, (b) $B^{+}$, (c) ${\overline{B}}^0$, (d) $B^0$, and (e) $B_{\mathrm{fns}}$ in on-resonance data, and (f) charged $B$, (g) neutral $B$ and (h) $B_{\mathrm{fns}}$ in off-resonance data. The points with error bars show the data and the lines show different contributions as obtained from the fit. The long dashed (brown) curves represent signal, the dotted (blue) curves show continuum, the dotted-dashed (green) curves are $B\overline{B}$ background, the dashed (orange) curves show cross-feed, and solid (red) curves are the sum of all contributions.

Figure 3

The solid (black), dashed (red) and dotted (blue) curves show the most probable value, $1\sigma$ and $2\sigma$ confidence intervals for $\mathrm{Im}(C_8/C_7)$ as a function of ${\tilde{\mathrm{\Lambda }}}_{78}$, respectively. The range of ${\tilde{\mathrm{\Lambda }}}_{78}$ is chosen to be $17\mathrm{MeV}<{\tilde{\mathrm{\Lambda }}}_{78}<190\mathrm{MeV}$.