Evidence for Large Direct $CP$ Violation in $B^{\pm }\to \rho (770{)}^0{K}^{\pm }$ from Analysis of Three-Body Charmless $B^{\pm }\to K^{\pm }{\pi }^{\pm }{\pi }^{\pm }$ Decays

We report results on a Dalitz analysis of three-body charmless $B^{\pm }\to K^{\pm }{\pi }^{\pm }{\pi }^{\mp }$ decay including searches for direct $CP$ violation. We report the first observation of the decay $B^{\pm }\to f_2(1270)K^{\pm }$ with a statistical significance above $6\sigma$. We also observe first evidence for large direct $CP$ violation in the $B^{\pm }\to \rho (770{)}^0{K}^{\pm }$ channel. The results are obtained with a data sample that contains $386\times {10}^6$ $B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider.

Figure 1

$\Delta E$ distributions for (a) $B^{-}\to K^{-}{\pi }^{-}{\pi }^{+}$ and (b) $B^{+}\to K^{+}{\pi }^{+}{\pi }^{-}$ events with $|M_{\mathrm{bc}}-M_B|<7.5\mathrm{MeV}/c^2$. Points with error bars are data; the smooth curve is the fit result; the hatched areas are various background components.

Figure 2

Results of the fit to $K^{\pm }{\pi }^{\pm }{\pi }^{\mp }$ events in the $B$ signal region: (a) $M(K^{+}{\pi }^{-})$ distribution with $M({\pi }^{+}{\pi }^{-})>1.5\mathrm{GeV}/c^2$; (b) $M({\pi }^{+}{\pi }^{-})$ distribution with $M(K^{+}{\pi }^{-})>1.5\mathrm{GeV}/c^2$. Points with error bars are data, the open histogram is the fit result and hatched histogram is the background component. Inset in (a) shows the $K^{*}(892)-K_0^{*}(1430)$ mass region in $20\mathrm{MeV}/c^2$ bins. Inset in (b) shows the ${\chi }_{c0}$ mass region in $10\mathrm{MeV}/c^2$ bins.

Figure 3

${\pi }^{+}{\pi }^{-}$ mass spectra for $B^{-}$ (left column) and $B^{+}$ (right column) events for different helicity regions: (a), (b) no helicity cuts; (c), (d) $\cos {\theta }_H^{\pi \pi }<0$; (e), (f) $\cos {\theta }_H^{\pi \pi }>0$; Points with error bars are data, the open histogram is the fit result, and the hatched histogram is the background component.