We report on a study of three-body charmless decays $B^{+}\to K^{+}{h}^{+}{h}^{-}$ based on a $29.1\hspace{0.5em}{\mathrm{fb}}^{-1}$ data sample collected with the Belle detector. With no assumptions on the intermediate mechanisms, the following three-body branching fractions have been measured for the first time: $\mathcal{B}{(B}^{+}\to K^{+}{\pi }^{-}{\pi }^{+})=(55.6\mathrm{}\pm 5.8\pm 7.7)\times {10}^{-6}$ and $\mathcal{B}{(B}^{+}\to K^{+}{K}^{-}{K}^{+})=(35.3\mathrm{}\pm 3.7\pm 4.5)\times {10}^{-6}.$ We present the first observation of the decay $B^{+}\to f_0{\mathrm{}\left(980\right)K}^{+}$ with a branching fraction product of $\mathcal{B}(B^{+}\to f_0{\mathrm{}\left(980\right)K}^{+})\times \mathcal{B}\left(f_0\mathrm{}\right(980)\mathrm{}\to {\pi }^{+}{\pi }^{-}){=(9.6\mathrm{}}_{-2.3-1.5-0.8}^{+2.5+1.5+3.4\mathrm{}})\times {10}^{-6}.$ This is the first reported example of a B meson decay to a scalar pseudoscalar final state. We also report the first observation of $B^{+}\to K^{*}{\mathrm{}\left(892\right)\mathrm{}}^0{\pi }^{+}$ decay with a branching fraction of $\mathcal{B}(B^{+}\to K^{*}{\mathrm{}\left(892\right)\mathrm{}}^0{\pi }^{+}){=(19.4\mathrm{}}_{-3.9-2.1-6.8}^{+4.2+2.1+3.5\mathrm{}})\times {10}^{-6}.$

• Received 27 December 2001

DOI:https://doi.org/10.1103/PhysRevD.65.092005