Study of $B^{-}\to D{K}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and $B^{-}\to D\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ decays and determination of the CKM angle ${\hat{I}}^3$

Abstract

We report a study of the suppressed $B^{-}\to D{K}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and favored $B^{-}\to D\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ decays, where the neutral $D$ meson is detected through its decays to the $K^{\mp }\ddot{I}{€}^{\pm }$ and CP-even $K^{+}{K}^{-}$ and $\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ final states. The measurement is carried out using a proton-proton collision data sample collected by the LHCb experiment, corresponding to an integrated luminosity of 3.0~fb${}^{-1}$. We observe the first significant signals in the CP-even final states of the $D$ meson for both the suppressed $B^{-}\to D{K}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and favored $B^{-}\to D\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ modes, as well as in the doubly Cabibbo-suppressed $D\to K^{+}\ddot{I}{€}^{-}$ final state of the $B^{-}\to D\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ decay. Evidence for the ADS suppressed decay $B^{-}\to D{K}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$, with $D\to K^{+}\ddot{I}{€}^{-}$, is also presented. From the observed yields in the $B^{-}\to D{K}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$, $B^{-}\to D\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and their charge conjugate decay modes, we measure the value of the weak phase to be ${\hat{I}}^3=(74_{-19}^{+20}{)}^{\mathrm{o}}$. This is one of the most precise single-measurement determinations of ${\hat{I}}^3$ to date.

22 pages, 9 figures; All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-020.html