We present measurements of branching fractions and charge asymmetries for charmless $B$-meson decays to three-body final states of charged pions and kaons. The analysis uses $81.8{\mathrm{f}\mathrm{b}}^{-1}$ of data collected at the ${\rm Y}(4S)$ resonance with the BABAR detector at the SLAC PEP-II asymmetric $B$ Factory. We measure the branching fractions $\mathcal{B}(B^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+})=(10.9\pm 3.3\pm 1.6)\times {10}^{-6}$, $\mathcal{B}(B^{+}\to K^{+}{\pi }^{-}{\pi }^{+})=(59.1\pm 3.8\pm 3.2)\times {10}^{-6}$, and $\mathcal{B}(B^{+}\to K^{+}{K}^{-}{K}^{+})=(29.6\pm 2.1\pm 1.6)\times {10}^{-6}$ and provide 90% C.L. upper limits for other decays. We observe no charge asymmetries for these modes.

• Received 3 April 2003

DOI:https://doi.org/10.1103/PhysRevLett.91.051801