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^±π⁰, π⁺π^-π⁰ and K⁺K^-π⁰. 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^± π⁰]_Dπ^∓ and the quasi-Gronau-London-Wyler decay B^∓ → [K⁺ K^- π⁰]_Dπ^∓. The results are interpreted in the context of the unitarity triangle angle γ and related parameters.