One-Loop Calculations with BlackHat

TL;DR

BlackHat is an automated C++ tool that efficiently computes one-loop amplitudes in QCD using unitarity and on-shell recursion, demonstrating high numerical stability and accuracy for multi-gluon processes.

Contribution

The paper introduces BlackHat, a novel automated program that combines unitarity, on-shell recursion, and analytic formulae for stable, high-precision one-loop amplitude calculations in QCD.

Findings

Successfully computed six-, seven-, and eight-gluon amplitudes.

Demonstrated high numerical stability with discrete Fourier projection.

Validated results against known analytic solutions.

Abstract

We describe BlackHat, an automated C++ program for calculating one-loop amplitudes, and the techniques used in its construction. These include the unitarity method and on-shell recursion. The other ingredients are compact analytic formulae for tree amplitudes for four-dimensional helicity states. The program computes amplitudes numerically, using analytic formulae only for the tree amplitudes, the starting point for the recursion, and the loop integrals. We make use of recently developed on-shell methods for evaluating coefficients of loop integrals, in particular a discrete Fourier projection as a means of improving numerical stability. We illustrate the good numerical stability of this approach by computing six-, seven- and eight-gluon amplitudes in QCD and comparing against known analytic results.