Pion Production in the Low-Energy Limit

The low-energy production reaction $\pi +N\to \pi +\pi +N$ is discussed in the framework of a simplified kinematics. The discussion is based on the Khuri-Treiman representation for processes with a three-particle final state. Under the assumption that the pion-pion rescattering term is dominant, branching ratios are derived for various processes. Under the same assumption, a quantitative analysis is given for the effect of the final-state pion-pion interaction on the three-particle distribution functions.