Tree-Level Formalism

TL;DR

This paper reviews two innovative techniques, MHV diagrams and on-shell recursion relations, for efficiently calculating tree-level scattering amplitudes, highlighting their applications in supersymmetric, massive, and gravitational theories.

Contribution

It provides a comprehensive review of MHV diagrams and recursion relations, including their derivations and diverse applications in gauge and gravity theories.

Findings

Effective calculation methods for tree-level amplitudes

Applications to supersymmetric and massive theories

Extension to graviton amplitudes in General Relativity

Abstract

We review two novel techniques used to calculate tree-level scattering amplitudes efficiently: MHV diagrams, and on-shell recursion relations. For the MHV diagrams, we consider applications to tree-level amplitudes and focus in particular on the N=4 supersymmetric formulation. We also briefly describe the derivation of loop amplitudes using MHV diagrams. For the recursion relations, after presenting their general proof, we discuss several applications to massless theories with and without supersymmetry, to theories with massive particles, and to graviton amplitudes in General Relativity. This article is an invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories".