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

Abstract

If the $X(3872)$ is a weakly bound charm-meson molecule, it can be produced by the creation of $D^{\ast 0}{\bar{D}}^0$ or $D^0{\bar{D}}^{\ast 0}$ 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 $D^{\ast }{\bar{D}}^{\ast }$ at short distances followed by the rescattering of the charm mesons into $X\pi$. We use results of a previous isospin analysis of $B$ meson decays into $K{D}^{(\ast )}{\bar{D}}^{(\ast )}$ to estimate the short-distance amplitudes for creating $D^{\ast }{\bar{D}}^{\ast }$. We use an effective field theory for charm mesons and pions called XEFT to calculate the amplitudes for rescattering of $D^{\ast }{\bar{D}}^{\ast }$ into $X\pi$ with small relative momentum. The $X\pi$ invariant mass distribution is predicted to have a narrow peak near the $D^{\ast }{\bar{D}}^{\ast }$ threshold from a charm-meson triangle singularity. We estimate the branching fractions into the peak from the triangle singularity for the decays $B^0\to K^{+}X{\pi }^{-}$ and $B^{+}\to K^{0}X{\pi }^{+}$.

Comments: 22 pages, 4 figures, 1 table. An error in identifying the region of validity in the $X(3872)\pi$ invariant mass was corrected