One-loop analysis of the reaction pi N to pi pi N

Single pion production off nucleons is studied in the framework of heavy baryon chiral perturbation theory to third order in the chiral expansion. Using total and some older differential cross section data to pin down the low-energy constants, most of the recent differential cross sections and angular correlation functions can be described as well as total cross sections at higher energies. We show that the contributions from the one loop graphs are essentially negligible and that the dominant terms at second and third order are related to pion-nucleon scattering graphs with one pion added. We also discuss the possibility of extracting the pion-pion S-wave scattering lengths from the unpolarized data.