Measurement of CP observables in B+- --> D_CP K+- decays and constraints on the CKM angle gamma

Using the entire sample of 467 million Y(4S) --> BBbar decays collected with the BaBar detector at the PEP-II asymmetric-energy B factory at SLAC, we perform a "GLW" analysis of B+- --> D K+- 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 A_CP+ = 0.25+-0.06+-0.02 and A_CP- = -0.09+-0.07+-0.02, respectively, where the first error is the statistical and the second is the systematic uncertainty. The parameter A_CP+ 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, R_CP+ = 1.18+-0.09+-0.05 and R_CP- = 1.07+-0.08+-0.04. We infer frequentist confidence intervals for the angle gamma of the (db) unitarity triangle, for the strong phase difference delta_B, and for the amplitude ratio r_B, which are related to the B- --> DK- decay amplitude by r_Be^{i(delta_B-gamma)} = A(B- --> anti-D0 K^-)/A(B- --> D0 K-). Including statistical and systematic uncertainties, we obtain 0.24r_B(0.06r_B