  The X(3872) seems to be a loosely-bound hadronic molecule whose constituents
are two charm mesons. A novel feature of this molecule is that the mass
difference of the constituents is close to the mass of a lighter meson that can
be exchanged between them, namely the pion. We analyze this feature in a simple
model with spin-0 mesons only. Various observables are calculated to
next-to-leading order in the interaction strength of the exchanged meson.
Renormalization requires summing a geometric series of next-to-leading order
corrections. The dependence of observables on the ultraviolet cutoff can be
removed by renormalizations of the mass of the heaviest meson, the coupling
constant for the contact interaction between the heavy mesons, and
short-distance coefficients in the operator product expansion. The
next-to-leading order correction has an unphysical infrared divergence at the
threshold of the two heavier mesons that can be eliminated by a further
resummation that takes into account the nonzero width of the heaviest meson.
