Evidence for direct $CP$ violation from Dalitz-plot analysis of $B^{\pm }\to K^{\pm }{\pi }^{\mp }{\pi }^{\pm }$

We report a Dalitz-plot analysis of the charmless hadronic decays of charged $B$ mesons to the final state $K^{\pm }{\pi }^{\mp }{\pi }^{\pm }$. Using a sample of $(383.2\pm 4.2)\times {10}^6$ $B\overline{B}$ pairs collected by the BABAR detector, we measure $CP$-averaged branching fractions and direct $CP$ asymmetries for intermediate resonant and nonresonant contributions. We find evidence for direct $CP$ violation in the decay $B^{\pm }\to {\rho }^0(770)K^{\pm }$, with a $CP$-violation parameter $A_{CP}=(+44\pm 10\pm 4_{-13}^{+5})\%$.

Figure 1

Regions of the $\Delta E^{\prime }-m_{\mathrm{ES}}$ plane. The red/horizontal hatching is the “upper sideband,” the green/crossed hatching is the “left sideband,” and the blue/vertical hatching is the “signal region.”

Figure 2

Background-subtracted Dalitz plot of the combined $B^{\pm }\to K^{\pm }{\pi }^{\mp }{\pi }^{\pm }$ data sample in the signal region. The plot shows bins with greater than zero entries. The area of the boxes is proportional to the number of entries. The depleted horizontal bands are the charmonium vetoes.

Figure 3

Invariant mass projections for the data in the signal region and the fit results. The left-hand plot shows the $m_{K^{\pm }{\pi }^{\mp }}$ spectrum up to $1.7\mathrm{GeV}/c^2$. The right-hand plot shows the $m_{{\pi }^{\pm }{\pi }^{\mp }}$ spectrum up to $1.6\mathrm{GeV}/c^2$. The bottom plot shows the $m_{{\pi }^{\pm }{\pi }^{\mp }}$ spectrum in the region of the ${\chi }_{c0}$. The data are the black points with statistical error bars, the lower solid (red/dark) histogram is the $q\overline{q}$ component, the middle solid (green/light) histogram is the $B\overline{B}$ background contribution, while the upper blue curve shows the total fit result. For the $m_{K^{\pm }{\pi }^{\mp }}$ plots the requirement is made that $m_{{\pi }^{\pm }{\pi }^{\mp }}$ is greater than $2\mathrm{GeV}/c^2$ and vice versa.

Figure 4

Projection plots of the ${\pi }^{+}{\pi }^{-}$ invariant mass in the region of the ${\rho }^0(770)$ and $f_0(980)$ resonances. The left (right) plots are for $B^{-}$ ($B^{+}$) candidates. The top row shows all candidates, the middle row shows those where $\cos {\theta }_H>0$, and the bottom row shows those where $\cos {\theta }_H<0$. The data are the black points with statistical error bars, the lower solid (red/dark) histogram is the $q\overline{q}$ component, the middle solid (green/light) histogram is the $B\overline{B}$ background contribution, while the blue open histogram shows the total fit result.