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

We report measurements of the branching fractions and direct $CP$ asymmetries of the decays $B^0\to K^{+}{\pi }^{-}$, $B^{+}\to K^{+}{\pi }^0$, $B^{+}\to K^0{\pi }^{+}$, and $B^0\to K^0{\pi }^0$, and use these for testing the standard model through an isospin-based sum rule. In addition, we measure the branching fraction and direct $CP$ asymmetry of the decay $B^{+}\to {\pi }^{+}{\pi }^0$ and the branching fraction of the decay $B^0\to {\pi }^{+}{\pi }^{-}$. The data are collected with the Belle II detector from $e^{+}{e}^{-}$ collisions at the $\mathrm{{\rm Y}}(4S)$ 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.