Triangle singularities in the production of X(3872)

Abstract

If the $X(3872)$ is a loosely bound charm-meson molecule, it can be produced by the creation of its constituents $D^{*0} \bar{D}^0$ or $D^{0} \bar{D}^{*0}$ at short distances followed by the formation of the bound state from the charm-meson pair. It can also be produced by the creation of $D^* \bar{D}^*$ at short distances followed by the rescattering of the charm-meson pair into $X(3872) \gamma$ or $X(3872) \pi$ through a triangle loop. The reaction rate for such a process has a triangle singularity, because the three charm mesons that form the triangle loop can all be on shell simultaneously. Triangle singularities produce narrow peaks in the production of $X(3872)$ accompanied by a photon in $e^+e^-$ annihilation, in the production of $X(3872)$ accompanied by a pion in $B$ meson decays, and in the prompt production of $X(3872)$ accompanied by a pion at hadron colliders. The observation of those narrow peaks would prove definitively that $X(3872)$ is a loosely bound charm-meson molecule.