Study of three-body charmless<i>B</i>decays

We report on a study of three-body charmless decays ${B}^{+}\ensuremath{\rightarrow}{K}^{+}{h}^{+}{h}^{\ensuremath{-}}$ based on a $29.1 {\mathrm{fb}}^{\ensuremath{-}1}$ 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: $\mathcal{B}{(B}^{+}\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+})=(55.6\ifmmode\pm\else\textpm\fi{}5.8\ifmmode\pm\else\textpm\fi{}7.7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ and $\mathcal{B}{(B}^{+}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}}{K}^{+})=(35.3\ifmmode\pm\else\textpm\fi{}3.7\ifmmode\pm\else\textpm\fi{}4.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}.$ We present the first observation of the decay ${B}^{+}\ensuremath{\rightarrow}{f}_{0}{(980)K}^{+}$ with a branching fraction product of $\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{f}_{0}{(980)K}^{+})\ifmmode\times\else\texttimes\fi{}\mathcal{B}({f}_{0}(980)\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}){=(9.6}_{\ensuremath{-}2.3\ensuremath{-}1.5\ensuremath{-}0.8}^{+2.5+1.5+3.4})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}.$ This is the first reported example of a B meson decay to a scalar pseudoscalar final state. We also report the first observation of ${B}^{+}\ensuremath{\rightarrow}{K}^{*}{(892)}^{0}{\ensuremath{\pi}}^{+}$ decay with a branching fraction of $\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{K}^{*}{(892)}^{0}{\ensuremath{\pi}}^{+}){=(19.4}_{\ensuremath{-}3.9\ensuremath{-}2.1\ensuremath{-}6.8}^{+4.2+2.1+3.5})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}.$