Study of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3872</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Y</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>4260</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>B</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:mo>→</mml:mo><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>B</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>decays

We present results of a search for the $X(3872)$ in ${B}^{0}\ensuremath{\rightarrow}X(3872){K}_{S}^{0},X(3872)\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, improved measurements of ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}X(3872){K}^{\ensuremath{-}}$, and a study of the $J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ mass region above the $X(3872)$. We use $232\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $B\overline{B}$ pairs collected at the $\ensuremath{\Upsilon}(4S)$ resonance with the BABAR detector at the PEP-II ${e}^{+}{e}^{\ensuremath{-}}$ asymmetric-energy storage rings. The results include the 90% confidence interval $1.34\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}&lt;\mathcal{B}({B}^{0}\ensuremath{\rightarrow}X(3872){K}^{0},X\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})&lt;10.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ and the branching fraction $\mathcal{B}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}X(3872){K}^{\ensuremath{-}},X\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})=(10.1\ifmmode\pm\else\textpm\fi{}2.5\ifmmode\pm\else\textpm\fi{}1.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. We observe a $(2.7\ifmmode\pm\else\textpm\fi{}1.3\ifmmode\pm\else\textpm\fi{}0.2)\mathrm{MeV}/{c}^{2}$ 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 $\mathcal{B}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}Y(4260){K}^{\ensuremath{-}},Y(4260)\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})&lt;2.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$.

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