Dalitz analysis of three-body charmless $B^0\to K^0{\pi }^{+}{\pi }^{-}$ decay

We report results of a Dalitz plot analysis of the three-body charmless $B^0\to K^0{\pi }^{+}{\pi }^{-}$ decay. The analysis is performed with a data sample that contains $388\times {10}^6$ $B\overline{B}$ pairs collected near the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. Measurements of branching fractions for the quasi-two-body decays $B^0\to \rho (770{)}^0{K}^0$, $B^0\to f_0(980)K^0$, $B^0\to K^{*}(892{)}^{+}{\pi }^{-}$, $B^0\to K^{*}(1430{)}^{+}{\pi }^{-}$, and upper limits on several other quasi-two-body decay modes are reported.

Figure 1

$\Delta E$ distribution for the $B^0\to K^0{\pi }^{+}{\pi }^{-}$ candidate events with $|M_{\mathrm{bc}}-M_B|<7.5\mathrm{MeV}/c^2$. Points with error bars are data; the upper curve is the fit result; the hatched histograms are various background components.

Figure 2

Dalitz plots for events in the (a) $M_{\mathrm{bc}}-\Delta E$ sidebands and in the (b) $B$ signal region.

Figure 3

Results of the best fit to events in the $\Delta E-M_{\mathrm{bc}}$ sidebands. Points with error bars are data; histograms are fit results.

Figure 4

Results of the fit to $K_S^0{\pi }^{+}{\pi }^{-}$ events in the signal region. Points with error bars are data, the open histograms are the fit result, and hatched histograms are the background components. Insets in (a) and (b) show the $K^{*}(892)-K_0^{*}(1430)$ mass region in $20\mathrm{MeV}/c^2$ bins; inset in (c) shows the ${\chi }_{c0}$ mass region in $25\mathrm{MeV}/c^2$ bins. When plotting a two-particle mass projection we require the invariant mass of the other two two-particle combinations to be greater than $1.5\mathrm{GeV}/c^2$.

Figure 5

Helicity angle distributions for (a) $K^{*}(892)$ ($0.82\mathrm{GeV}/c^2<M(K_S^0\pi )<0.97\mathrm{GeV}/c^2$); (b) $\rho (770)$ ($0.60\mathrm{GeV}/c^2<M(\pi \pi )<0.90\mathrm{GeV}/c^2$); (c) $f_0(980)$ ($0.90\mathrm{GeV}/c^2<M(\pi \pi )<1.06\mathrm{GeV}/c^2$). Points with error bars are data, the open histogram is the fit result, and the hatched histogram is the background component. Note that there are two entries per $B$ candidate in plot (a).