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

TL;DR

This paper uses heavy baryon chiral perturbation theory to analyze single pion production off nucleons, showing that one-loop contributions are negligible and that dominant effects come from pion-nucleon scattering graphs, with implications for extracting pion-pion scattering lengths.

Contribution

It provides a third-order chiral perturbation theory analysis of pion production, highlighting the minimal role of one-loop graphs and emphasizing the importance of pion-nucleon scattering graphs.

Findings

One-loop graphs are negligible in the process.

Dominant contributions come from pion-nucleon scattering graphs.

Data can potentially be used to extract pion-pion S-wave scattering lengths.

Abstract

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.