Production of X(3872) accompanied by a soft pion at hadron colliders

If the X(3872) is a weakly bound charm-meson molecule, it can be produced by the creation of D*(0)(D) over bar (0) or D-0(D) over bar*(0) at short distances followed by the formation of the bound state from the charm-meson pair. The X can also be produced by the creation of D*(D) over bar* at short distances followed by the rescattering of the charm-meson pair into X pi. At a high-energy hadron collider, the prompt cross section from this mechanism has a narrow peak in the X pi invariant mass distribution near the D*(D) over bar* threshold from a charm-meson triangle singularity. An order-of-magnitude estimate of the ratio of the cross section for producing the peak in the X pi(+/-) distribution to the cross section for producing X without an accompanying pion suggests that the peak may be observable at the LHC.