  Many two-dimensional conformal field theories have an alternative integrable
scattering description, which reproduces their spectrum of conformal weights.
Taking as an example the case of the Lee-Yang nonunitary CFT and the 3-state
Potts minimal model, we derive formulas, in terms of their integrable
description, for the OPE coefficients of a certain specific primary operator
and two identical but otherwise essentially arbitrary operators. As a side
result we also obtain a novel formula for the mass-gap relation for the
integrable massive deformation of the CFT. These results are obtained through
expressing the first nontrivial coefficient in the UV expansion of the energy
in terms of the integrable CFT data, i.e. the kink and anti-kink TBA solutions.
