Full one-loop amplitudes from tree amplitudes

TL;DR

This paper introduces an efficient algorithm for calculating one-loop scattering amplitudes in quantum field theory, enabling automated computation of both cut-constructible and rational parts from tree amplitudes, demonstrated on gluon scattering in QCD.

Contribution

It presents a polynomial-complexity, generalized D-dimensional unitarity-based method for automated one-loop amplitude calculations from tree amplitudes.

Findings

Successfully computed four-, five-, and six-gluon scattering amplitudes in QCD at one-loop.

The algorithm efficiently handles both cut-constructible and rational parts.

Demonstrates the method's effectiveness and automation potential in complex amplitude calculations.

Abstract

We establish an efficient polynomial-complexity algorithm for one-loop calculations, based on generalized $D$-dimensional unitarity. It allows automated computations of both cut-constructible {\it and} rational parts of one-loop scattering amplitudes from on-shell tree amplitudes. We illustrate the method by (re)-computing all four-, five- and six-gluon scattering amplitudes in QCD at one-loop.