The reaction π N to π π N above threshold in heavy-baryon chiral perturbation theory

We study the reaction $\pi^\pm p \to \pi^\pm \pi^+ n$ and $\pi^- p \to \pi^0 \pi^0 n$ in heavy-baryon chiral perturbation theory of chiral order three from threshold up to pion laboratory kinetic energies of 400 MeV. We find that the contributions from amplitudes of chiral order three are large and play an essential role in reproducing the experimental data.