An Automated Implementation of On-Shell Methods for One-Loop Amplitudes

TL;DR

This paper introduces BlackHat, an automated C++ tool that uses on-shell and unitarity methods to efficiently compute one-loop amplitudes in quantum chromodynamics, demonstrating high numerical stability and accuracy.

Contribution

It presents the first automated implementation of on-shell methods for one-loop amplitude calculations, integrating recent techniques for improved efficiency and stability.

Findings

Successfully computed multi-gluon amplitudes in QCD

Achieved high numerical stability in calculations

Validated results against known analytic solutions

Abstract

We present the first results from BlackHat, an automated C++ program for calculating one-loop amplitudes. The program implements the unitarity method and on-shell recursion to construct amplitudes. As input to the calculation, it uses compact analytic formulae for tree amplitudes for four-dimensional helicity states. The program performs all related computations numerically. We make use of recently developed on-shell methods for evaluating coefficients of loop integrals, introducing a discrete Fourier projection as a means of improving efficiency and numerical stability. We illustrate the numerical stability of our approach by computing and analyzing six-, seven- and eight-gluon amplitudes in QCD and comparing against previously-obtained analytic results.