Study of ${\mathbf{B}}^0\to \ddot{\mathbf{I}}{}^{+}\ddot{\mathbf{I}}{}^{-}$ decays and implications for the CKM angle $\ddot{\mathbf{I}}{•}_2$

Abstract

We present a measurement of the branching fraction and the longitudinal polarization fraction of $B^0\to \ddot{I}{}^{+}\ddot{I}{}^{-}$ decays, as well as the time-dependent $CP$ violating parameters in decays into longitudinally polarized $\ddot{I}{}^{+}\ddot{I}{}^{-}$ pairs with Belle's final data set of $772\times 10^6$ $B\bar{B}$ pairs, at the $\hat{I}\yen (4S)$ resonance, collected at the asymmetric-energy $e^{+}{e}^{-}$ collider KEKB. We obtain $\mathcal{B}(B^0\to \ddot{I}{}^{+}\ddot{I}{}^{-})=(28.3\pm 1.5(\mathrm{stat})\pm 1.5(\mathrm{syst}))\times 10^{-6}$, $f_L=0.988\pm 0.012(\mathrm{stat})\pm 0.023(\mathrm{syst})$, ${\mathcal{A}}_{CP}=0.00\pm 0.10(\mathrm{stat})\pm 0.06(\mathrm{syst})$, ${\mathcal{S}}_{CP}=-0.13\pm 0.15(\mathrm{stat})\pm 0.05(\mathrm{syst}).$ We perform an isospin analysis to constrain the CKM angle $\ddot{I}{•}_2$ and obtain two solutions with \begin{eqnarray} ϕ_{2} = (93.7\pm10.6)^{\circ},\nonumber \end{eqnarray} being most compatible with other Standard-Model based fits to the data.

26 pages, 7 figures, submitted to PRD