Measurements of charmless hadronic $b\to s$ penguin decays in the ${\pi }^{+}{\pi }^{-}{K}^{+}{\pi }^{-}$ final state and first observation of $B^0\to {\rho }^0{K}^{+}{\pi }^{-}$

We report measurements of charmless hadronic $B^0$ decays into the ${\pi }^{+}{\pi }^{-}{K}^{+}{\pi }^{-}$ final state. The analysis uses a sample of $657\times {10}^6$ $B\overline{B}$ pairs collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider at the resonance. The decay $B^0\to {\rho }^0{K}^{+}{\pi }^{-}$ is observed for the first time; the significance is $5.0\sigma$ and the corresponding partial branching fraction for $M_{K\pi }\in (0.75,1.20)\mathrm{GeV}/c^2$ is $[2.8\pm 0.5(\mathrm{stat})\pm 0.5(\mathrm{syst})]\times {10}^{-6}$. We also obtain the first evidence for $B^0\to f_0(980)K^{+}{\pi }^{-}$ with $3.5\sigma$ significance and for $B^0\to {\pi }^{+}{\pi }^{-}{K}^{*0}$ with $4.5\sigma$ significance. For the two-body decays $B^0\to {\rho }^0{K}^{*0}$ and $B^0\to f_0(980)K^{*0}$, the significances are $2.7\sigma$ and $2.5\sigma$, respectively, and the upper limits on the branching fractions are $3.4\times {10}^{-6}$ and $2.2\times {10}^{-6}$ at 90% confidence level.

Figure 1

Feynman diagrams for charmless hadronic $B$ decays pertaining to $B^0\to {\rho }^0{K}^{*0}$: (a) $b\to s$ penguin diagram, and (b) $b\to u$ tree diagram.

Figure 2

Projection of the 4D fit results onto (a) $M_{\mathrm{bc}}$, (b) $\Delta E$, (c) $M_{\pi \pi }$, and (d) $M_{K\pi }$, with the other variables required to satisfy (except for the variable plotted) $M_{\mathrm{bc}}\in (5.27,5.29)\mathrm{GeV}/c^2$, $\Delta E\in (-0.045,0.045)\mathrm{GeV}$, $M_{\pi \pi }\in (0.62,1.04)\mathrm{GeV}/c^2$, and $M_{K\pi }\in (0.84,0.94)\mathrm{GeV}/c^2$. The curves are for the ${\rho }^0{K}^{+}{\pi }^{-}$ (solid shaded regions), the sum of ${\rho }^0{K}^{*0}$ and $f_0(980)K^{*0}$ (dashed lines), $f_2(1270)K^{*0}$ and the sum of feed-down modes (dot-dashed lines), the sum of the backgrounds (dotted lines), and the total (solid lines).

Figure 3

Signal yields obtained from the two-dimensional fits to $M_{\mathrm{bc}}$ and $\Delta E$ in bins of $M_{\pi \pi }$ (left panel) and $M_{K\pi }$ (right panel) up to the higher-mass regions. Solid curves show the results of the two-dimensional binned fit, and dashed curves show the contributions of nonresonant ${\pi }^{+}{\pi }^{-}$ (left panel) and the sum of nonresonant $K^{+}{\pi }^{-}$ and $K_0^{*}(1430{)}^0$ (right panel). The vertical lines show the nominal 4D fit regions.