Time-dependent analysis of $B^0\to K_S^0\ddot{I}{€}^{-}\ddot{I}{€}^{+}{\hat{I}}^3$ decays and studies of the $K^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}$ system in $B^{+}\to K^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}{\hat{I}}^3$ decays

Abstract

We measure the time-dependent $CP$ asymmetry in the radiative-penguin decay $B^0\to K_S^0\ddot{I}{€}^{-}\ddot{I}{€}^{+}{\hat{I}}^3$, using a sample of $471$ million $\hat{I}\yen (4S)\to B\overline{B}$ events recorded with the BaBar detector at the PEP-II $e^{+}{e}^{-}$ storage ring at SLAC. Using events with $m_{K\ddot{I}€\ddot{I}€}<1.8\mathrm{Ge}V/c^2$, we measure the branching fractions of $B^{+}\to K^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}{\hat{I}}^3$ and $B^0\to K^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}{\hat{I}}^3$, the branching fractions of the kaonic resonances decaying to $K^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}$, as well as the overall branching fractions of the $B^{+}\to \ddot{I}{}^0{K}^{+}{\hat{I}}^3$, $B^{+}\to K^{\ast 0}\ddot{I}{€}^{+}{\hat{I}}^3$ and S-wave $B^{+}\to (K\ddot{I}€{)}_0^{\ast 0}\ddot{I}{€}^{+}{\hat{I}}^3$ components. For events from the $\ddot{I}$ mass band, we measure the $CP$-violating parameters ${\mathcal{S}}_{K_S^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}{\hat{I}}^3}=0.14\pm 0.25\pm 0.03$ and ${\mathcal{C}}_{K_S^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}{\hat{I}}^3}=-0.39\pm 0.20_{-0.02}^{+0.03}$, where the first uncertainties are statistical and the second are systematic. We extract from this measurement the time-dependent $CP$ asymmetry related to the $CP$ eigenstate $\ddot{I}{}^0{K}_S^0$ and obtain ${\mathcal{S}}_{K_S^0\ddot{I}{\hat{I}}^3}=-0.18\pm 0.32_{-0.05}^{+0.06}$, which provides information on the photon polarization in the underlying $b\to s{\hat{I}}^3$ transition.

33 pages, 8 figures, submitted to PRD