Measurements of branching fraction and direct $CP$ asymmetry in $B^{\pm }\to K_S^0{K}_S^0{K}^{\pm }$ and a search for $B^{\pm }\to K_S^0{K}_S^0{\pi }^{\pm }$

We study charmless hadronic decays of charged $B$ mesons to the final states $K_S^0{K}_S^0{K}^{\pm }$ and $K_S^0{K}_S^0{\pi }^{\pm }$ using a $711{\mathrm{fb}}^{-1}$ data sample that contains $772\times {10}^6$ $B\overline{B}$ pairs and was collected at the $\mathrm{\Upsilon }(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. For $B^{\pm }\to K_S^0{K}_S^0{K}^{\pm }$, the measured branching fraction and direct $CP$ asymmetry are $[10.42\pm 0.43(\mathrm{stat})\pm 0.22(\mathrm{syst})]\times {10}^{-6}$ and $[+1.6\pm 3.9(\mathrm{stat})\pm 0.9(\mathrm{syst})]\%$, respectively. In the absence of a statistically significant signal for $B^{\pm }\to K_S^0{K}_S^0{\pi }^{\pm }$, we obtain a 90% confidence-level upper limit on its branching fraction as $8.7\times {10}^{-7}$.

Figure 1

Feynman diagrams of the dominant amplitudes that contribute to the decays $B^{\pm }\to K_S^0{K}_S^0{K}^{\pm }$ (left) and $B^{\pm }\to K_S^0{K}_S^0{\pi }^{\pm }$ (right).

Figure 2

Projections of the two-dimensional simultaneous fit to $\mathrm{\Delta }E$ for $C_{\mathrm{NB}}^{\prime }>0.0$ and $C_{\mathrm{NB}}^{\prime }$ for $|\mathrm{\Delta }E|<50\mathrm{MeV}$. Black points with error bars are the data, solid blue curves are the total PDF, long-dashed red curves are the signal, dashed green curves are the continuum background, dotted magenta curves are the combinatorial $B\overline{B}$ background, and dash-dotted cyan curves are the feed-across background.

Figure 3

Differential branching fraction (left) and ${\mathcal{A}}_{CP}$ (right) as functions of $M_{K_S^0{K}_S^0}$ for $B^{+}\to K_S^0{K}_S^0{K}^{+}$. Black points with error bars are the results from the two-dimensional fits to data and include systematic uncertainties. Blue squares in the left plot show the expectation from a phase-space MC sample, and the red line in the right plot indicates a zero $CP$ asymmetry.