Study of the $X(3872)$ and $Y(4260)$ in $B^0\to J/\psi {\pi }^{+}{\pi }^{-}{K}^0$ and $B^{-}\to J/\psi {\pi }^{+}{\pi }^{-}{K}^{-}$ decays

We present results of a search for the $X(3872)$ in $B^0\to X(3872)K_S^0,X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$, improved measurements of $B^{-}\to X(3872)K^{-}$, and a study of the $J/\psi {\pi }^{+}{\pi }^{-}$ mass region above the $X(3872)$. We use $232\times {10}^6$ $B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ resonance with the BABAR detector at the PEP-II $e^{+}{e}^{-}$ asymmetric-energy storage rings. The results include the 90% confidence interval $1.34\times {10}^{-6}<\mathcal{B}(B^0\to X(3872)K^0,X\to J/\psi {\pi }^{+}{\pi }^{-})<10.3\times {10}^{-6}$ and the branching fraction $\mathcal{B}(B^{-}\to X(3872)K^{-},X\to J/\psi {\pi }^{+}{\pi }^{-})=(10.1\pm 2.5\pm 1.0)\times {10}^{-6}$. We observe a $(2.7\pm 1.3\pm 0.2)\mathrm{MeV}/c^2$ mass difference of the $X(3872)$ produced in the two decay modes. Furthermore, we search for the $Y(4260)$ in $B$ decays and set the $95\%$ C.L. upper limit $\mathcal{B}(B^{-}\to Y(4260)K^{-},Y(4260)\to J/\psi {\pi }^{+}{\pi }^{-})<2.9\times {10}^{-5}$.