Study of $X(3872)\rightarrow J/\psi\pi\pi$ in $B\rightarrow X(3872)K^-$ and $B\rightarrow X(3872)K_S^0$

We search for a charged partner of the $X(3872)$ in the decay $B^-\rightarrow X^- K$, $X^-\rightarrow J/\psi \pi^- \pi^0$, using 234 million $B \bar B$ events collected at the $\Upsilon(4S)$ resonance with the BaBar detector at the PEP-II $e^+ e^-$ asymmetric-energy storage ring. The resulting product branching fraction upper limits are $BR(B^0\to X^{-} K^+$, $X^-\rightarrow J/\psi \pi^-\pi^0) < 5.4 \times 10^{-6}$ and $BR(B^-\to X^{-}\overline{K}_0$, $X^- \rightarrow J/\psi\pi^-\pi^0) < 22 \times 10^{-6}$ at the $90\%$ confidence level. In addition, we update the previous BaBar result on $B^-\rightarrow X(3872)K^-$, $X(3872)\rightarrow J\psi\pi^+\pi^-$ with increased statistics and extend the search to include $B^0\rightarrow X(3872) K_S^0$ as well as $X(3872)\rightarrow J\psi\pi^0\pi^0$.