Measurement of CP observables in B^± → DK^± and B^± → Dπ^± with two- and four-body D decays

Measurements of CP observables in B ^±→DK ^± and B ^±→Dπ ^± decays are presented where the D meson is reconstructed in the final states K ^±π ^∓, π ^±K ^∓, K ⁺K ⁻, π ⁺π ⁻, K ^±π ^∓π ⁺π ⁻, π ^±K ^∓π ⁺π ⁻ and π ⁺π ⁻π ⁺π ⁻. This analysis uses a sample of charged B mesons from pp collisions collected by the LHCb experiment in 2011 and 2012, corresponding to an integrated luminosity of 3.0 fb ⁻¹. Various CP-violating effects are reported and together these measurements provide important input for the determination of the unitarity triangle angle γ. The analysis of the four-pion D decay mode is the first of its kind.