Constraints on the CKM angle γγ from B±→Dh±B±→Dh± decays using D→h±h′∓π0D→h±h′∓π0 final states

A data sample collected with the LHCb detector corresponding to an integrated luminosity of 9 fb−1−1 is used to measure eleven CPCP violation observables in B±→Dh±B±→Dh± decays, where hh is either a kaon or a pion. The neutral DD meson decay is reconstructed in the three-body final states: K±π∓π0K±π∓π0; π+π−π0π+π−π0; K+K−π0K+K−π0 and the suppressed π±K∓π0π±K∓π0 combination. The mode where a large CPCP asymmetry is expected, B±→[π±K∓π0]DK±B±→[π±K∓π0]D​K±, 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∓π0]DK±B±→[K±π∓π0]D​K±, is RADS(K)=(1.27±0.16±0.02)×10−2RADS(K)​=(1.27±0.16±0.02)×10−2. Evidence for a large CPCP asymmetry is also seen: AADS(K)=−0.38±0.12±0.02AADS(K)​=−0.38±0.12±0.02. Constraints on the CKM angle γγ are calculated from the eleven reported observables.