Observation of $B^0\to \Lambda \overline{\Lambda }{K}^0$ and $B^0\to \Lambda \overline{\Lambda }{K}^{*0}$ at Belle

We study the charmless decays $B\to \Lambda \overline{\Lambda }h$, where $h$ stands for ${\pi }^{+}$, $K^{+}$, $K^0$,$K^{*+}$, or $K^{*0}$, using a $605{\mathrm{fb}}^{-1}$ data sample collected at the ${\rm Y}(4S)$ resonance with the Belle detector at the KEKB asymmetric energy $e^{+}{e}^{-}$ collider. We observe $B^0\to \Lambda \overline{\Lambda }{K}^0$ and $B^0\to \Lambda \overline{\Lambda }{K}^{*0}$ with branching fractions of $({4.76}_{-0.68}^{+0.84}(\mathrm{stat})\pm 0.61(\mathrm{syst}))\times {10}^{-6}$ and $({2.46}_{-0.72}^{+0.87}\pm 0.34)\times {10}^{-6}$, respectively. The significances of these signals in the threshold-mass enhanced mass region, $M_{\Lambda \overline{\Lambda }}<2.85\mathrm{GeV}/c^2$, are $12.4\sigma$ and $9.3\sigma$, respectively. We also update the branching fraction $\mathcal{B}(B^{+}\to \Lambda \overline{\Lambda }{K}^{+})=({3.38}_{-0.36}^{+0.41}\pm 0.41)\times {10}^{-6}$ with better accuracy, and report the following measurement or 90% confidence level upper limit in the threshold-mass-enhanced region: $\mathcal{B}(B^{+}\to \Lambda \overline{\Lambda }{K}^{*+})=({2.19}_{-0.88}^{+1.13}\pm 0.33)\times {10}^{-6}$ with $3.7\sigma$ significance; $\mathcal{B}(B^{+}\to \Lambda \overline{\Lambda }{\pi }^{+})<0.94\times {10}^{-6}$. A related search for $B^0\to \Lambda \overline{\Lambda }{\overline{D}}^0$ yields a branching fraction $\mathcal{B}(B^0\to \Lambda \overline{\Lambda }{\overline{D}}^0)=({1.05}_{-0.44}^{+0.57}\pm 0.14)\times {10}^{-5}$. This may be compared with the large, $\sim {10}^{-4}$, branching fraction observed for $B^0\to p\overline{p}{\overline{D}}^0$. The $M_{\Lambda \overline{\Lambda }}$ enhancements near threshold and related angular distributions for the observed modes are also reported.

Figure 1

Comparisons of possible decay diagrams between $B^{+}\to p\overline{p}{K}^{+}/B^0\to p\overline{\Lambda }{\pi }^{-}$ and $B^{+}\to \Lambda \overline{\Lambda }{K}^{+}$.

Figure 2

Distributions of $\Delta E$ (with $5.27\mathrm{GeV}/c^2<M_{\mathrm{bc}}<5.29\mathrm{GeV}/c^2$) and $M_{\mathrm{bc}}$ (with $|\Delta E|<0.05\mathrm{GeV}$) for (a) $B^{+}\to \Lambda \overline{\Lambda }{K}^{+}$, (b) $B^0\to \Lambda \overline{\Lambda }{K}^0$, and (c) $B^{+}\to \Lambda \overline{\Lambda }{\pi }^{+}$ modes. The dibaryon mass $M_{\Lambda \overline{\Lambda }}$ is required to be less than $2.85\mathrm{GeV}/{\mathrm{c}}^2$. The solid curves, dotted curves, and dashed curves represent the total fit result, fitted signal, and fitted background, respectively. The dot-dashed curves in plot (c) show the background contribution from the $B^{+}\to \Lambda \overline{\Lambda }{K}^{+}$ mode.

Figure 3

Distributions of $\Delta E$ (with $5.27\mathrm{GeV}/c^2<M_{\mathrm{bc}}<5.29\mathrm{GeV}/c^2$ and $0.816<M_{K\pi }<0.976\mathrm{GeV}/c^2$), $M_{\mathrm{bc}}$ (with $|\Delta E|<0.05\mathrm{GeV}$ and $0.816\mathrm{GeV}/c^2<M_{K\pi }<0.976\mathrm{GeV}/c^2$) and $M_{K\pi }$ (with $|\Delta E|<0.05\mathrm{GeV}$ and $5.27\mathrm{GeV}/c^2<M_{\mathrm{bc}}<5.29\mathrm{GeV}/c^2$) for (a) $B^{+}\to \Lambda \overline{\Lambda }{K}^{*+}$ and (b) $B^0\to \Lambda \overline{\Lambda }{K}^{*0}$ modes in the threshold-mass-enhanced region. The solid curves, dotted curves, and dashed curves represent the total fit result, fitted signal, and fitted background, respectively.

Figure 4

Differential branching fractions for (a) $B^{+}\to \Lambda \overline{\Lambda }{K}^{+}$, (b) $B^0\to \Lambda \overline{\Lambda }{K}^0$, and (c) $B^0\to \Lambda \overline{\Lambda }{K}^{*0}$ modes as a function of $M_{\Lambda \overline{\Lambda }}$. Note that two bins with $2.850\mathrm{GeV}/c^2<M_{\Lambda \overline{\Lambda }}<3.128\mathrm{GeV}/c^2$ and $3.315\mathrm{GeV}/c^2<M_{\Lambda \overline{\Lambda }}<3.735\mathrm{GeV}/c^2$ contain charmonium events and are excluded from the charmless signal yields. The solid histograms are from phase space MC simulation with area normalized to the charmless signal yield.

Figure 5

Differential branching fractions vs $\cos {\theta }_p$ for $B^{+}\to \Lambda \overline{\Lambda }{K}^{+}$ in the threshold-mass-enhanced region.

Figure 6

Differential branching fractions vs $\cos {\theta }_{\overline{\Lambda }}$ in the $\Lambda \overline{\Lambda }$ pair system for $B^{+}\to \Lambda \overline{\Lambda }{K}^{+}$ in the threshold-mass-enhanced region.

Figure 7

Differential branching fractions vs $\cos {\theta }_K$ in the $K^{*0}$ system for $B^0\to \Lambda \overline{\Lambda }{K}^{*0}$ in the threshold-mass-enhanced region. The solid curve is the result of the fit.

Figure 8

Distributions of $\Delta E$ (with $5.27\mathrm{GeV}/c^2<M_{\mathrm{bc}}<5.29\mathrm{GeV}/c^2$) and $M_{\mathrm{bc}}$ (with $|\Delta E|<0.05\mathrm{GeV}$) for the $B^0\to \Lambda \overline{\Lambda }{\overline{D}}^0$ mode. The result includes the whole $M_{\Lambda \overline{\Lambda }}$ region. The solid curves, dotted curves, and dashed curves show the total fit result, fitted signal, and fitted background, respectively.

Figure 9

Possible diagrams that contribute to $B^{+}\to p\overline{p}{\pi }^{+}/\Lambda \overline{\Lambda }{\pi }^{+}$ and $B^0\to p\overline{p}{\overline{D}}^0/\Lambda \overline{\Lambda }{\overline{D}}^0$.