Pion-induced pion production in heavy-baryon chiral perturbation theory

Abstract

We study the reaction $\ensuremath{\pi}+N\ensuremath{\rightarrow}2\ensuremath{\pi}+N$ within the framework of heavy-baryon chiral perturbation theory of chiral order three. The reaction cross section from threshold up to pion laboratory kinetic energies of 400 MeV is found to be in reasonable agreement with experimental data. A host of differential cross sections and angular correlations are also calculated and are found to be in semiquantitative agreement with the data. We find that contributions from amplitudes of chiral order three are large and play an essential role in reproducing the experimental data. Unitarity corrections arising from the imaginary parts of the loop-level Feynman diagrams are the only parameter-free predictions of the present calculations. It is found that the unitarity effects in some reaction channels are sizable. Finally, we evaluate polarization observables (asymmetries) for the transverse polarization of the proton target and find that the asymmetries are generally small ($\ensuremath{\le}0.4$) for the reaction under consideration.