Study of the $B^{-}\to J/\psi K^{-}{\pi }^{+}{\pi }^{-}$ decay and measurement of the $B^{-}\to X(3872)K^{-}$ branching fraction

We study the decay $B^{-}\to J/\psi K^{-}{\pi }^{+}{\pi }^{-}$ using $117\times {10}^6$ $B\overline{B}$ events collected at the $Y(4S)$ resonance with the BABAR detector at the PEP-II $e^{+}{e}^{-}$ asymmetric-energy storage ring. We measure the branching fractions $\mathcal{B}$ $(B^{-}\to J/\psi K^{-}{\pi }^{+}{\pi }^{-})=(116\pm 7(\mathrm{stat}.)\pm 9(\mathrm{syst}.))\times {10}^{-5}$ and $\mathcal{B}$ $(B^{-}\to X(3872){\mathrm{K}}^{-})\times$ $\mathcal{B}$ $(X(3872)\to \mathrm{J}/\psi {\pi }^{+}{\pi }^{-})=(1.28\pm 0.41)\times {10}^{-5}$ and find the mass of the $X(3872)$ to be $3873.4\pm 1.4\mathrm{MeV}/{\mathrm{c}}^2$. We search for the $h_c$ narrow state in the decay $B^{-}\to h_c{K}^{-}$, $h_c\to J/\psi {\pi }^{+}{\pi }^{-}$ and for the decay $B^{-}\to J/\psi D^0{\pi }^{-}$, with $D^0\to K^{-}{\pi }^{+}$. We set the $90\%$ C.L. limits $\mathcal{B}(B^{-}\to h_c{K}^{-})\times \mathcal{B}(h_c\to J/\psi {\pi }^{+}{\pi }^{-})<3.4\times {10}^{-6}$ and $\mathcal{B}(B^{-}\to J/\psi D^0{\pi }^{-})<5.2\times {10}^{-5}$.