Search for the decay $B^0\to K_S^0{K}_S^0{K}_L^0$

We present the first search for the decay $B^0\to K_S^0{K}_S^0{K}_L^0$ using a data sample of $232\times {10}^6$ $B\overline{B}$ pairs. We find no statistically significant evidence for the nonresonant component of this decay. Our central value for the branching fraction, assuming the true Dalitz distribution is uniform and excluding the $\varphi$ resonance, is $\mathcal{B}(B^0\to K_S^0{K}_S^0{K}_L^0)=({2.4}_{-2.5}^{+2.7}\pm 0.6)\times {10}^{-6}$ where the errors are statistical and systematic, respectively. We set a single-sided Bayesian upper limit of $\mathcal{B}(B^0\to K_S^0{K}_S^0{K}_L^0)<7.4\times {10}^{-6}$ at 90% confidence level using a uniform prior probability for physical values. Assuming the worst-case true Dalitz distribution, where the signal is entirely in the region of lowest efficiency, the 90% confidence level upper limit is $\mathcal{B}(B^0\to K_S^0{K}_S^0{K}_L^0)<16\times {10}^{-6}$.

Figure 1

Missing transverse momentum difference distributions for the signal Monte Carlo sample (solid) and the background-dominated $\Delta E$ sideband ($\Delta E>0.010\mathrm{GeV}$) after all other selection criteria (see text) have been applied. The signal Monte Carlo sample distribution has been arbitrarily normalized to the number of entries in the sideband distribution.

Figure 2

Neural network output ($NN$) distributions for the signal Monte Carlo sample (solid) and the background-dominated $\Delta E$ sideband ($\Delta E>0.010\mathrm{GeV}$) after all other selection criteria (see text) have been applied. The signal Monte Carlo sample distribution has been arbitrarily normalized to the number of entries in the sideband distribution.

Figure 3

The reconstruction efficiency for signal as a function of position in the symmetrized Dalitz plot.

Figure 4

A histogram of the reconstruction efficiency for signal for 322 uniformly distributed points in the Dalitz plot.

Figure 5

Fitted $\Delta E$ distributions of the $J/\psi K_L^0$ control sample for EMC (top) and IFR (bottom) $K_L^0$ candidates. The points with error bars are histograms of the data sample. The solid curve is the total PDF. The dotted-dashed curve is the signal PDF and the dashed curve is the background PDF.

Figure 6

Distributions of $\Delta E$ (left) and $NN$ (right) for the five components of the fit: (a) $K_S^0{K}_S^0{K}_L^0$ signal, (b) combinatoric background, (c) $K_S^0{K}_S^0{\pi }^0$, (d) $K_S^0{K}_S^0{K}_S^0$, and (e) $KK{K}^{*}$. The combinatoric $NN$ distribution is from the data sideband ($\Delta E>0.010\mathrm{GeV}$). The rest of the distributions are from Monte Carlo samples.

Figure 7

Distributions of $\Delta E$ (top) and $NN$ (bottom) for the $K_S^0{K}_S^0{K}_L^0$ fit. The plot of $\Delta E$ ($NN$) is for events passing a cut on $NN$ ($\Delta E$) which enhances the signal. The signal efficiency of this cut is 57% for the $\Delta E$ distribution and 71% for the $NN$ distribution. The points with error bars are histograms of data samples. The solid curves are total PDFs. The dashed curves are combinatoric backgrounds. The dotted-dashed curves are peaking $B$ backgrounds. The dotted curves are signal PDFs.

Figure 8

Scan of the fit negative log likelihood as a function of the $K_S^0{K}_S^0{K}_L^0$ branching fraction, where the minimum negative log likelihood has been subtracted. A uniform true Dalitz distribution has been assumed for the $K_S^0{K}_S^0{K}_L^0$ signal. The solid curve includes the systematic uncertainty with yield of $KK{K}^{*}$ fixed at 0 to calculate upper limit.