Study of CP violation in B^∓ → Dh^∓ (h = K, π) with the modes D → K^∓π^±π⁰, D → π⁺ π^- π⁰ and D → K⁺ K^- π⁰

An analysis of the decays of B ^∓ → DK ^∓ and B ^∓ → Dπ ^∓ is presented in which the D meson is reconstructed in the three-body final states K ^∓ π ^±π ⁰, π ⁺π ^-π ⁰ and K ⁺K ^-π ⁰. Using data from LHCb corresponding to an integrated luminosity of 3.0fb ^-1 of pp collisions, measurements of several CP observables are performed. First observations are obtained of the suppressed Atwood-Dunietz-Soni decay B ^∓ → [π ^∓ K ^± π ⁰] _Dπ ^∓ and the quasi-Gronau-London-Wyler decay B ^∓ → [K ⁺ K ^- π ⁰] _Dπ ^∓. The results are interpreted in the context of the unitarity triangle angle γ and related parameters.