Measurement of Branching Fractions and Search for $\mathit{CP}$-Violating Charge Asymmetries in Charmless Two-Body $\mathit{B}$ Decays into Pions and Kaons

We present measurements, based on a sample of approximately $23\times {10}^6$ $B\overline{B}$ pairs, of the branching fractions and a search for $\mathrm{CP}$-violating charge asymmetries in charmless hadronic decays of $B$ mesons into two-body final states of kaons and pions. We find the branching fractions $B(B^0\to {\pi }^{+}{\pi }^{-})=(4.1\pm 1.0\pm 0.7)\times {10}^{-6\mathrm{}}$, $B(B^0\to K^{+}{\pi }^{-})=(16.7\pm 1.6\pm 1.3)\times {10}^{-6\mathrm{}}$, $B(B^{+}\to K^{+}{\pi }^0)=({10.8}_{-1.9\mathrm{}}^{+2.1\mathrm{}}\pm 1.0)\times {10}^{-6\mathrm{}}$, $B(B^{+}\to K^0{\pi }^{+})=({18.2}_{-3.0\mathrm{}}^{+3.3\mathrm{}}\pm 2.0)\times {10}^{-6\mathrm{}}$, $B(B^0\to K^0{\pi }^0)=({8.2}_{-2.7\mathrm{}}^{+3.1\mathrm{}}\pm 1.2)\times {10}^{-6\mathrm{}}$. We also report $90\%$ confidence level upper limits for $B$ meson decays to the ${\pi }^{+}{\pi }^0$, $K^{+}{K}^{-}$, and ${\overline{K}}^0{K}^{+}$ final states. In addition, charge asymmetries have been found to be consistent with zero, where the statistical precision is in the range of $\pm 0.10$ to $\pm 0.18$, depending on the decay mode.