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

Measurements of CP   observables in B±→DK±B±→DK± and B±→Dπ±B±→Dπ± decays are presented where the D   meson is reconstructed in the final states K±π∓K±π∓, π±K∓π±K∓, K+K−K+K−, π+π−π+π−, K±π∓π+π−K±π∓π+π−, π±K∓π+π−π±K∓π+π− and π+π−π+π−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−13.0 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.