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Measurement of branching fractions and direct $CP$ asymmetries for $B \to Kπ$ and $B\toππ$ decays at Belle II

We report measurements of the branching fractions and direct $\it{CP}$ asymmetries of the decays $B^0 \to K^+ π^-$, $B^+ \to K^+ π^0$, $B^+ \to K^0 π^+$, and $B^0 \to K^0 π^0$, and use these for testing the standard model through an isospin-based sum rule. In addition, we measure the branching fraction and direct $\it{CP}$ asymmetry of the decay $B^+ \to π^+π^0$ and the branching fraction of the decay $B^0 \to π^+π^-$. The data are collected with the Belle II detector from $e^+e^-$ collisions at the $Υ(4S)$ resonance produced by the SuperKEKB asymmetric-energy collider and contain $387\times 10^6$ bottom-antibottom meson pairs. Signal yields are determined in two-dimensional fits to background-discriminating variables, and range from 500 to 3900 decays, depending on the channel. We obtain $-0.03 \pm 0.13 \pm 0.04$ for the sum rule, in agreement with the standard model expectation of zero and with a precision comparable to the best existing determinations.