Bethe-Schwinger Effective Range Theory and Lehmann and Weinberg Chiral Perturbation Theories

TL;DR

This paper reviews the development of low energy effective theories in hadronic physics, from Bethe-Schwinger to modern Chiral Perturbation Theories, emphasizing the importance of unitarity in calculations.

Contribution

It highlights the historical progression and unifies the concepts of effective range theory and Chiral Perturbation Theory with unitarity considerations.

Findings

Effective range theory originated in the 1940s for nucleon-nucleon scattering.

Chiral Perturbation Theory provides a consistent low energy framework.

Incorporating unitarity improves the accuracy of low energy calculations.

Abstract

This paper is a brief review of low energy soft hadronic physics, starting from the invention of the low energy effective range theory in the late 40's due to Bethe and Schwinger for nucleon-nucleon scattering, and its generalization to the static Chew-Low model for pion nucleon scattering, to the present development of the Lehmann and Weinberg Chiral Perturbation Theories. It is pointed out that a consistent low energy calculation can be achieved with the incorporation of the unitarity relation in the Chiral Perturbation Theory.