Search for b → u transitions in B ± → [K∓π±π0]DK± decays

We present a study of the decays B ± → D K ± with D mesons reconstructed in the K + π − π 0 or K − π + π 0 final states, where D indicates a D 0 or a ¯¯¯ D 0 meson. Using a sample of 474 × 10 6 B ¯¯¯ B pairs collected with the BABAR detector at the PEP-II asymmetric-energy e + e − collider at SLAC, we measure the ratios R ± ≡ Γ ( B ± → [ K ∓ π ± π 0 ] D K ± ) Γ ( B ± → [ K ± π ∓ π 0 ] D K ± ) . We obtain R + = ( 5 + 12 − 10 ( stat ) + 2 − 4 ( syst ) ) × 10 − 3 and R − = ( 12 + 12 − 10 ( stat ) + 3 − 5 ( syst ) ) × 10 − 3 , from which we extract the upper limits at 90% probability: R + < 23 × 10 − 3 and R − < 29 × 10 − 3 . Using these measurements, we obtain an upper limit for the ratio r B of the magnitudes of the b → u and b → c amplitudes r B < 0.13 at 90% probability