Branching fraction measurements of charged $B$ decays to $K^{*+}{K}^{+}{K}^{-}$, $K^{*+}{\pi }^{+}{K}^{-}$, $K^{*+}{K}^{+}{\pi }^{-}$ and $K^{*+}{\pi }^{+}{\pi }^{-}$ final states

Branching fraction and asymmetry measurements of charmless $B^{+}\to K^{*+}{h}_1^{+}{h}_2^{-}$ (where $h_{1,2}=K$, $\pi$) decays are presented, using a data sample of $232\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the SLAC PEP-II asymmetric-energy $B$ factory. Using a maximum likelihood fit, the following branching fraction results were obtained: $\mathcal{B}(B^{+}\to K^{*+}{K}^{+}{K}^{-})=(36.2\pm 3.3\pm 3.6)\times {10}^{-6}$ and $\mathcal{B}(B^{+}\to K^{*+}{\pi }^{+}{\pi }^{-})=(75.3\pm 6.0\pm 8.1)\times {10}^{-6}$. Upper limits were set for $\mathcal{B}(B^{+}\to K^{*+}{\pi }^{+}{K}^{-})<11.8\times {10}^{-6}$ and $\mathcal{B}(B^{+}\to K^{*+}{K}^{+}{\pi }^{-})<6.1\times {10}^{-6}$ at 90% confidence level. The charge asymmetries for the decays $B^{+}\to K^{*+}{K}^{+}{K}^{-}$ and $B^{+}\to K^{*+}{\pi }^{+}{\pi }^{-}$ were measured to be ${\mathcal{A}}_{K^{*}KK}=0.11\pm 0.08\pm 0.03$ and ${\mathcal{A}}_{K^{*}\pi \pi }=0.07\pm 0.07\pm 0.04$, respectively. The first error quoted on branching fraction and asymmetry measurements is statistical and the second systematic.

Figure 1

Penguin (a) and tree (b) Feynman diagrams for the decay $B^{+}\to K^{*+}{\pi }^{+}{K}^{-}$.

Figure 2

Maximum likelihood fit projections of $m_{ES}$ for signal-enhanced samples of charmless $B^{+}\to K^{*+}{h}_1^{+}{h}_2^{-}$ candidates. The dashed line is the fitted background PDF while the solid line is the sum of the signal and background PDFs. The points indicate the data. The plot labeled (a) shows a projection of $B^{+}\to K^{*+}{K}^{+}{K}^{-}$ candidates, (b) $B^{+}\to K^{*+}{\pi }^{+}{K}^{-}$ candidates, (c) $B^{+}\to K^{*+}{K}^{+}{\pi }^{-}$ candidates and (d) $B^{+}\to K^{*+}{\pi }^{+}{\pi }^{-}$ candidates.