A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes

TL;DR

This paper introduces a numerical unitarity method for efficiently calculating one-loop scattering amplitudes using tree-level amplitudes, enabling automatic and accurate computations for complex processes.

Contribution

The paper presents a 4-dimensional unitarity-based numerical approach for one-loop amplitudes, facilitating automatic calculations using tree-level ingredients.

Findings

Successfully evaluated 4, 5, and 6 gluon one-loop amplitudes numerically.

Achieved high accuracy by comparing with known analytic results.

Demonstrated the method's practicality for complex scattering processes.

Abstract

Recent progress in unitarity techniques for one-loop scattering amplitudes makes a numerical implementation of this method possible. We present a 4-dimensional unitarity method for calculating the cut-constructible part of amplitudes and implement the method in a numerical procedure. Our technique can be applied to any one-loop scattering amplitude and offers the possibility that one-loop calculations can be performed in an automatic fashion, as tree-level amplitudes are currently done. Instead of individual Feynman diagrams, the ingredients for our one-loop evaluation are tree-level amplitudes, which are often already known. To study the practicality of this method we evaluate the cut-constructible part of the 4, 5 and 6 gluon one-loop amplitudes numerically, using the analytically known 4, 5 and 6 gluon tree-level amplitudes. Comparisons with analytic answers are performed to ascertain the numerical accuracy of the method.