Production of $X(3872)$ Accompanied by a Pion in $B$ Meson Decay

If the $X(3872)$ is a weakly bound charm-meson molecule, it can be produced by the creation of $D^{*0} \bar{D}^0$ or $D^{0} \bar{D}^{*0}$ at short distances followed by the formation of the bound state from the charm-meson pairs. It can also be produced by the creation of $D^{*} \bar{D}^*$ at short distances followed by the rescattering of the charm mesons into $X \pi$. An effective field theory for charm mesons and pions called XEFT predicts that the rate for producing $X$ accompanied by a pion should be roughly comparable to that for producing an isolated $X$. We use results of a previous isospin analysis of $B$ meson decays into $K D^{(*)} \bar D^{(*)}$ to estimate the short-distance amplitudes for creating $D^* \bar D^*$. We use XEFT to calculate the amplitudes for rescattering of $D^{*} \bar{D}^*$ into $X \pi$ with small relative momentum. The resulting predictions for decays of $B$ mesons into $K X\pi$ are consistent with measurements made by the Belle collaboration. If $K^* X$ events are removed, the remaining $K X\pi$ events are predicted to come primarily from the region of the Dalitz plot where the relative momentum of $X \pi$ is order $m_\pi$ or smaller.