Exclusive production of theX(3872)inBmeson decay

Abstract

If the recently discovered charmoniumlike state $X(3872)$ is a loosely bound $S$-wave molecule of the charm mesons ${D}^{0}{\overline{D}}^{*0}$ or ${D}^{*0}{\overline{D}}^{0}$, it can be produced through the weak decay of the $B$ meson into ${D}^{0}{\overline{D}}^{*0}K$ or ${D}^{*0}{\overline{D}}^{0}K$ followed by the coalescence of the charm mesons at a long-distance scale set by the scattering length of the charm mesons. The long-distance factors in the amplitude for the decay $B\ensuremath{\rightarrow}XK$ are determined by the binding energy of $X$, while the short-distance factors are essentially determined by the amplitudes for $B\ensuremath{\rightarrow}{D}^{0}{\overline{D}}^{*0}K$ and $B\ensuremath{\rightarrow}{D}^{*0}{\overline{D}}^{0}K$ near the thresholds for the charm mesons. We obtain a crude determination of the short-distance amplitudes by analyzing data from the BABAR Collaboration on the branching fractions for $B\ensuremath{\rightarrow}{\overline{D}}^{(*)}{D}^{(*)}K$ using a factorization assumption, heavy-quark symmetry, and isospin symmetry. The resulting order-of-magnitude estimate of the branching fraction for ${B}^{+}\ensuremath{\rightarrow}X{K}^{+}$ is compatible with observations provided that $J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ is a major decay mode of the $X$. The branching fraction for ${B}^{0}\ensuremath{\rightarrow}X{K}^{0}$ is predicted to be suppressed by more than an order of magnitude compared to that for ${B}^{+}\ensuremath{\rightarrow}X{K}^{+}$.