Improved measurement of the CKM angle γ in B^{∓}→D^{(*)}K^{(*)∓} decays with a Dalitz plot analysis of D decays to K_{S}^{0}π^{+}π^{-} and K_{S}^{0}K^{+}K^{-}

We report on an improved measurement of the Cabibbo-Kobayashi-Maskawa CP-violating phase γ through a Dalitz plot analysis of neutral D meson decays to KS0π+π- and KS0K+K- produced in the processes B∓→DK∓, B∓→D*K∓ with D*→Dπ0, Dγ, and B∓→DK*∓ with K*∓→KS0π∓. Using a sample of 383×106 BB̅ pairs collected by the BABAR detector, we measure γ=(76±22±5±5)° (mod 180°), where the first error is statistical, the second is the experimental systematic uncertainty, and the third reflects the uncertainty on the description of the Dalitz plot distributions. The corresponding 2-standard-deviation region is 29°<γ<122°. This result has a significance of direct CP violation (γ≠0) of 3.0 standard deviations.