Evidence for Isospin Violation and Measurement of $CP$ Asymmetries in $B\to K^{\ast }(892){\hat{I}}^3$

Abstract

We report the first evidence for isospin violation in $B\to K^{\ast }{\hat{I}}^3$ and the first measurement of difference of $CP$ asymmetries between $B^{+}\to K^{\ast +}{\hat{I}}^3$ and $B^0\to K^{\ast 0}{\hat{I}}^3$. 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$\ddot{I}ƒ$, $\hat{I}{”}_{0+}=(+6.2\pm 1.5(stat.)\pm 0.6(syst.)\pm 1.2(f_{+-}/f_{00}))$\%, where the third uncertainty is due to the uncertainty on the fraction of $B^{+}{B}^{-}$ to $B^0{\bar{B}}^0$ production in $\hat{I}\yen (4S)$ decays. The measured value is consistent with predictions of the SM. The result for the difference of $CP$ asymmetries is $\hat{I}”A_{CP}=(+2.4\pm 2.8(stat.)\pm 0.5(syst.))$\%, 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 $B^0\to K^{\ast 0}{\hat{I}}^3$ to $B_s^0\to \ddot{I}•{\hat{I}}^3$.

11 pages, 7 figures. shown at FPCP2017. accepted by PRL