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

C. F. Berger; Z. Bern; L. J. Dixon; F. Febres Cordero; D. Forde; H. Ita; D. A. Kosower; D. Maitre

Paper

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

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.