Constraints on the CKM angle γ from B ^± → Dh ^± decays using D → h ^± h′ ^∓ π ⁰ final states

A data sample collected with the LHCb detector corresponding to an integrated luminosity of 9 fb ⁻¹ is used to measure eleven CP violation observables in B ^±→ Dh ^± decays, where h is either a kaon or a pion. The neutral D meson decay is reconstructed in the three-body final states: K ^±π ^∓π ⁰; π ⁺π ⁻π ⁰; K ⁺K ⁻π ⁰ and the suppressed π ^±K ^∓π ⁰ combination. The mode where a large CP asymmetry is expected, B ^±→ [π ^±K ^∓π ⁰] _DK ^±, is observed with a significance greater than seven standard deviations. The ratio of the partial width of this mode relative to that of the favoured mode, B ^±→ [K ^±π ^∓π ⁰] _DK ^±, is R _ADS(K) = (1.27 ± 0.16 ± 0.02) × 10 ⁻². Evidence for a large CP asymmetry is also seen: A _ADS(K) = −0.38 ± 0.12 ± 0.02. Constraints on the CKM angle γ are calculated from the eleven reported observables. [Figure not available: see fulltext.]