In the Chiral perturbation theory scheme ( Scholarpedia article - http://www.scholarpedia.org/article/Chiral_perturbation_theory ), one does, for example, meson-meson scattering, limiting to LO, NLO or at most NNLO. The basic units in the Lagrangian (like a nonlinear Sigma model) are \[U = \exp (i {\vec \pi}\cdot {\vec \tau}/f),\] for instance for pions. However,

Quoting verbatim from the book Quarks, baryons and chiral symmetry, by Hosaka, Toki:

"Since there is no small coupling constant, calculation of various amplitudes would require all Feynman diagrams of all orders of perturbation theory, which would make practical calculations formidable. In fact, however, there are examples in which computation of finite numbers of diagrams provides good description of, for instance, meson-meson scatterings. The termination of the diagrams is not,however, justified from a theoretical ground."

If termination is not justified on theoretical grounds, why are calculations terminated to LO or NLO in articles using this method? What if the NNLO contribution comes out to be larger (at least in principle)? Won't we get a divergent series then, just like the usual case if we had calculated using quark fields instead of meson fields?