Multi-gluon one-loop amplitudes numerically
A. Lazopoulos
TL;DR
The paper presents a C++ implementation of the D_s-dimensional unitarity cut algorithm (EGKM) to numerically compute the virtual one-loop contributions to NLO QCD amplitudes with an arbitrary number of external gluons. It builds the amplitude from color-ordered tree-level amplitudes in five dimensions, using a systematic pentagon/box/triangle/bubble cut framework and reducing to scalar master integrals, with the D_s dependence extracted via two evaluations at different D_s. Numerical stability is mitigated by pole checks against analytic results and a fallback to quadruple precision when necessary, achieving agreement with established results. The work demonstrates scalable performance up to 22 external legs and outlines a clear plan to extend the approach to fermions and electroweak bosons for broader NLO automation.
Abstract
A c++ implementation of the D_s-dimensional unitarity cut algorithm for the numerical evaluation of the virtual contribution to NLO QCD amplitudes is presented. The current version includes an arbitrary number of external gluons with gluonic propagators in the loop. The building blocks are tree level color-ordered amplitudes with gluons and with gluons and two scalars in five dimensions. Numerical stability issues are addressed and agreement has been reached with the results published in the literature.