We predict the differential cross sections for production of the $X(3872)$ at the Tevatron and the Large Hadron Collider from both prompt QCD mechanisms and from decays of $b$ hadrons. The prompt cross section is calculated using the nonrelativistic QCD (NRQCD) factorization formula. Simplifying assumptions are used to reduce the nonperturbative parameters to a single nonrelativistic QCD matrix element that is determined from an estimate of the prompt cross section at the Tevatron. For $X(3872)$ with transverse momenta greater than about 4 GeV, the predicted cross section is insensitive to the simplifying assumptions. We also discuss critically a recent analysis that concluded that the prompt production rate at the Tevatron is too large by orders of magnitude for the $X(3872)$ to be a weakly bound charm-meson molecule. We point out that if charm-meson rescattering is properly taken into account, the upper bound is increased by orders of magnitude and is compatible with the observed production rate at the Tevatron.

• Received 13 November 2009

DOI:https://doi.org/10.1103/PhysRevD.81.114018