On convergence of the ChPT HFF expansion for one loop contribution to meson production in NN collisions

We consider the application of heavy fermion formalism based chiral perturbation theory to meson production in nucleon-nucleon collisions. It is shown that for one loop contributions the heavy fermion formalism expansion corrections for the nucleon propagator produce infinite series of correction terms which are of the same momentum power order. This destroys the one-to-one correspondence between the perturbative and small momentum expansion and thus negates the application of any finite order heavy fermion formalism chiral perturbation theory to the $NN\to NN \pi$ reactions.