The four-dimensional on-shell three-point amplitude in spinor-helicity formalism and BCFW recursion relations

TL;DR

This paper reviews the structure of three-point scattering amplitudes in spinor-helicity formalism, emphasizing Lorentz invariance constraints and introducing BCFW recursion relations for massless particles.

Contribution

It provides a detailed analysis of on-shell three-point amplitudes in four dimensions and demonstrates their use in deriving tree-level BCFW recursion relations.

Findings

Lorentz Little Group constrains three-point amplitudes

Complete classification of massless and massive three-point amplitudes

Application of BCFW recursion to massless scattering processes

Abstract

Lecture notes on Poincar\'e-invariant scattering amplitudes and tree-level recursion relations in spinor-helicity formalism. We illustrate the non-perturbative constraints imposed over on-shell amplitudes by the Lorentz Little Group, and review how they completely fix the three-point amplitude involving either massless or massive particles. Then we present an introduction to tree-level BCFW recursion relations, and some applications for massless scattering, where the derived three-point amplitudes are employed.