Measurement of CP observables in B^{±}→D_{CP}K^{±} decays and constraints on the CKM angle γ

Using the entire sample of 467×106 Υ(4S)→BB̅ decays collected with the BABAR detector at the PEP-II asymmetric-energy B factory at the SLAC National Accelerator Laboratory, we perform an analysis of B±→DK± decays, using decay modes in which the neutral D meson decays to either CP-eigenstates or non-CP-eigenstates. We measure the partial decay rate charge asymmetries for CP-even and CP-odd D final states to be ACP+=0.25±0.06±0.02 and ACP-=-0.09±0.07±0.02, respectively, where the first error is the statistical and the second is the systematic uncertainty. The parameter ACP+ is different from zero with a significance of 3.6 standard deviations, constituting evidence for direct CP violation. We also measure the ratios of the charged-averaged B partial decay rates in CP and non-CP decays, RCP+=1.18±0.09±0.05 and RCP-=1.07±0.08±0.04. We infer frequentist confidence intervals for the angle γ of the unitarity triangle, for the strong phase difference δB, and for the amplitude ratio rB, which are related to the B-→DK- decay amplitude by rBei(δB-γ)=A(B-→D̅ 0K-)/A(B-→D0K-). Including statistical and systematic uncertainties, we obtain 0.24<rB<0.45 (0.06<rB<0.51) and, modulo 180°, 11.3°<γ<22.7° or 80.8°<γ<99.2° or 157.3°<γ<168.7° (7.0°<γ<173.0°) at the 68% (95%) confidence level.