Measurement of branching fraction and direct $CP$ asymmetry in charmless $B^{+}\to K^{+}{K}^{-}{\pi }^{+}$ decays at Belle

We report a study of the charmless hadronic decay of the charged $B$ meson to the three-body final state $K^{+}{K}^{-}{\pi }^{+}$. The results are based on a data sample that contains $772\times 10^{6}B\overline{B}$ pairs collected at the $\mathrm{\Upsilon }(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. The measured inclusive branching fraction and direct $CP$ asymmetry are $(5.38\pm 0.40\pm 0.35)\times {10}^{-6}$ and $-0.170\pm 0.073\pm 0.017$, respectively, where the first uncertainties are statistical and the second are systematic. The $K^{+}{K}^{-}$ invariant mass distribution of the signal candidates shows an excess in the region below $1.5\mathrm{GeV}/c^2$, which is consistent with the previous studies from BABAR and LHCb. In addition, strong evidence of a large direct $CP$ asymmetry is found in the low $K^{+}{K}^{-}$ invariant-mass region.

Figure 1

$B^{+}\to K^{+}{K}^{-}{\pi }^{+}$ Feynman diagrams (all Cabibbo-suppressed). (a) Tree diagram, (b) $W$-exchange diagram leading to $K{K}^{*}$ states, (c) strong-penguin diagram, and (d) electroweak penguin leading to the $\varphi \pi$ state.

Figure 2

The projections of the $M_{\mathrm{bc}}-\mathrm{\Delta }E$ fit to data in the first $M_{K^{+}{K}^{-}}$ bin. Points with error bars are the data, the red line is the fit result, the blue line is the sum of the signal and the self cross feed, the cyan dotted line is the continuum background, the brown dash-dotted line is the generic $B$ backgrounds, and the green dashed line is the sum of the rare $B$ backgrounds. The projection on $\mathrm{\Delta }E$ is with the requirement of $5.275<M_{\mathrm{bc}}<5.2835\mathrm{GeV}/c^2$, while the projection on $M_{\mathrm{bc}}$ is with the requirement of $-0.03<\mathrm{\Delta }E<0.03\mathrm{GeV}$.

Figure 3

Differential branching fractions (left) and measured ${\mathcal{A}}_{\mathit{C}P}$ (right) as a function of $M_{K^{+}{K}^{-}}$. Each point is obtained from a two-dimensional fit with systematic uncertainty included. Red squares with error bars in the left figure show the expected signal distribution in a three-body phase space MC. Note that the phase space hypothesis is rescaled to the total observed $B^{+}\to K^{+}{K}^{-}{\pi }^{+}$ signal yield.