Measurement of CP observables in B± → DCPK± decays and constraints on the CKM angle γ

Using the entire sample of 467 million Υ(4S) → B(bar B) decays collected with the BABAR detector at the PEP-II asymmetric-energy B factory at SLAC, we perform a 'GLW' analysis of B± → D± 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 (db) unitarity triangle, for the strong phase difference (delta)B, and for the amplitude ratio rB, which are related to the B- → D- decay amplitude by rBei(δb-#gamma#) = A(B- → (bar D)0K-)/A(B- → D0K0-). Including statistical and systematic uncertainties, they obtain 0.24 < rB < 0.45 (0.06 < rB < 0.51) and, modulo 180o, 11.3o < γ < 22.7o or 80.9o < γ < 99.1o or 157.3o < γ 168.7o (7.0o < γ < 173.0o) at the 68% (95%) confidence level.