Dalitz-plot analysis of the decays $B^{\pm }\to K^{\pm }{\pi }^{\mp }{\pi }^{\pm }$

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 $226.0\pm 2.5$ million $B\overline{B}$ pairs collected by the BABAR detector, we measure the magnitudes and phases of the intermediate resonant and nonresonant amplitudes for both charge-conjugate decays. We present measurements of the corresponding branching fractions and their charge asymmetries that supersede those of previous BABAR analyses. We find the charge asymmetries to be consistent with zero.

Figure 1

The $m_{\mathrm{ES}}$ distribution, together with the fitted PDFs: the data are the black points with statistical error bars, the lower solid (red/dark) area is the $q\overline{q}$ component, the middle solid (green/light) area is the $B\overline{B}$ background contribution, while the upper blue line shows the total fit result. The upper (lower) plot is for negatively charged (positively charged) events.

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 being proportional to the number of entries.

Figure 3

Invariant mass projections for the data in the signal region and the fit results. The upper (lower) plots are for the $B^{-}$ ($B^{+}$) sample. The left-hand (right-hand) plots show the $m_{K^{\pm }{\pi }^{\mp }}$ ($m_{{\pi }^{\pm }{\pi }^{\mp }}$) spectrum. 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 histogram shows the total fit result. The large dips in the spectra correspond to the charm vetoes. 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.