Model-independent measurement of the CKM angle ${\hat{I}}^3$ using $B^0\to D{K}^{\ast 0}$ decays with $D\to K_S^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and $K_S^0{K}^{+}{K}^{-}$

Abstract

A binned Dalitz plot analysis of the decays $B^0\to D{K}^{\ast 0}$, with $D\to K_S^0\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and $K_S^0{K}^{+}{K}^{-}$, is performed to measure the observables $x_{\pm }$ and $y_{\pm }$, which are related to the CKM angle ${\hat{I}}^3$ and the hadronic parameters of the decays. The $D$ decay strong phase variation over the Dalitz plot is taken from measurements performed at the CLEO-c experiment, making the analysis independent of the $D$ decay model. With a sample of proton-proton collision data, corresponding to an integrated luminosity of $3.0{\mathrm{fb}}^{-1}$, collected by the LHCb experiment, the values of the $CP$ violation parameters are found to be $x_{+}=0.05\pm 0.35\pm 0.02$, $x_{-}=-0.31\pm 0.20\pm 0.04$, $y_{+}=-0.81\pm 0.28\pm 0.06$ and $y_{-}=0.31\pm 0.21\pm 0.05$, where the first uncertainties are statistical and the second systematic. These observables correspond to values ${\hat{I}}^3$ = $(71\pm 20{)}^{\circ }$, $r_{B^0}=0.56\pm 0.17$ and $\hat{I}{´}_{B^0}=(204{}_{-20}^{+21}{)}^{\circ }$. The parameters $r_{B^0}$ and $\hat{I}{´}_{B^0}$ are the magnitude ratio and strong phase difference between the suppressed and favoured $B^0$ decay amplitudes, and have been measured in a region of $\pm 50$ MeV/$c^2$ around the $K^{\ast }(892{)}^0$ mass and with the magnitude of the cosine of the $K^{\ast }(892{)}^0$ helicity angle larger than 0.4.

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-2016-006.html