Measurement of branching-fraction ratios and CP asymmetries in B^± → D_CP±K^± decays at Belle and Belle II

We report results from a study of B^±→ DK^± decays followed by D decaying to the CP-even final state K⁺K⁻ and CP-odd final state K_S⁰π⁰, where D is an admixture of D⁰ and D¯⁰ states. These decays are sensitive to the Cabibbo-Kobayashi-Maskawa unitarity-triangle angle ϕ₃. The results are based on a combined analysis of the final data set of 772 × 10⁶BB¯ pairs collected by the Belle experiment and a data set of 198 × 10⁶BB¯ pairs collected by the Belle II experiment, both in electron-positron collisions at the Υ(4S) resonance. We measure the CP asymmetries to be A_CP+ = (+12.5 ± 5.8 ± 1.4)% and A_CP− = (−16.7 ± 5.7 ± 0.6)%, and the ratios of branching fractions to be R_CP+ = 1.164 ± 0.081 ± 0.036 and R_CP− = 1.151 ± 0.074 ± 0.019. The first contribution to the uncertainties is statistical, and the second is systematic. The asymmetries A_CP+ and A_CP− have similar magnitudes and opposite signs; their difference corresponds to 3.5 standard deviations. From these values we calculate 68.3% confidence intervals of (8.5^° < ϕ₃ < 16.5^°) or (84.5^° < ϕ₃ < 95.5^°) or (163.3^° < ϕ₃ < 171.5^°) and 0.321 < r_B < 0.465.