Estimates of the $X(3872)$ Cross Section at a Hadron Collider

Abstract

The claim that the $X(3872)$ meson cannot be a charm-meson molecule because its prompt production cross section at hadron colliders is too large is based on an upper bound in terms of a cross section for producing charm-meson pairs. Assuming $X$ is sufficiently weakly bound, we derive an equality between the $X$ cross section and a charm-meson pair cross section that takes into account the threshold enhancement from the $X$ resonance. The cross section for producing $X$ is equal to that for producing $D^{\ast 0}{\bar{D}}^0$ integrated up to a relative momentum $k_{\max }=7.7{\gamma }_X$, where ${\gamma }_X$ is the binding momentum of $X$. We also derive an order-of-magnitude estimate of the $X$ cross section in terms of a naive charm-meson pair cross section that does not take into account the threshold enhancement, such as that produced by a Monte Carlo event generator. The cross section for producing $X$ can be approximated by the naive cross section for producing $D^{\ast 0}{\bar{D}}^0$ integrated up to a relative momentum $k_{\max }$ of order $(m_{\pi }^2{\gamma }_X{)}^{1/3}$. The estimates of the prompt $X$ cross section at hadron colliders are consistent with the cross sections observed at the Tevatron and the LHC.

Comments: 14 pages, 1 figure. Extensively revised to focus mainly on the production of $X(3872)$ at hadron colliders. Material on production of $X(3872)$ plus a pion was removed. Text overlap with arXiv:1903:04355