Production of the X(3872) at the Tevatron and the LHC

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.