Evidence for Isospin Violation and Measurement of $CP$ Asymmetries in $B \to K^{\ast}(892) \gamma$

We report the first evidence for isospin violation in $B \to K^* \gamma$ and the first measurement of difference of $CP$ asymmetries between $B^+ \to K^{*+} \gamma$ and $B^0 \to K^{*0} \gamma$. 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. We find evidence for the isospin violation with a significance of 3.1$\sigma$, $\Delta_{0+} = (+6.2 \pm 1.5 ({\rm stat.}) \pm 0.6 ({\rm syst.}) \pm 1.2 (f_{+-}/f_{00}))$\%, where the third uncertainty is due to the uncertainty on the fraction of $B^+B^-$ to $B^0\bar{B}^0$ production in $\Upsilon(4S)$ decays. The measured value is consistent with predictions of the SM. The result for the difference of $CP$ asymmetries is $\Delta A_{CP} = (+2.4 \pm 2.8({\rm stat.}) \pm 0.5({\rm syst.}))$\%, consistent with zero. The measured branching fractions and $CP$ asymmetries for charged and neutral $B$ meson decays are the most precise to date. We also calculate the ratio of branching fractions of $B^0 \to K^{*0} \gamma$ to $B_s^0 \to \phi \gamma$.