Recursion Relations for Tree-level Amplitudes in the SU(N) Non-linear Sigma Model

TL;DR

This paper develops new on-shell recursion relations for tree-level amplitudes in the SU(N) non-linear sigma model, overcoming previous limitations of BCFW methods in effective field theories by leveraging scaling properties.

Contribution

It introduces a novel approach to derive recursion relations for non-renormalizable theories using semi-on-shell current scaling, expanding on existing amplitude calculation techniques.

Findings

Derived recursion relations valid for all tree-level amplitudes

Overcame BCFW limitations in effective field theories

Provided a systematic method for non-linear sigma models

Abstract

It is well-known that the standard BCFW construction cannot be used for on-shell amplitudes in effective field theories due to bad behavior for large shifts. We show how to solve this problem in the case of the SU(N) non-linear sigma model, i.e. non-renormalizable model with infinite number of interaction vertices, using scaling properties of the semi-on-shell currents, and we present new on-shell recursion relations for all on-shell tree-level amplitudes in this theory.