HELAC: a package to compute electroweak helicity amplitudes

TL;DR

HELAC addresses combinatorial growth in electroweak amplitude calculations by using Dyson-Schwinger recursive equations instead of standard Feynman graphs. The FORTRAN package computes tree-level electroweak helicity amplitudes with full mass effects in unitary and Feynman gauges, including multi-precision arithmetic for numerical stability. It employs a two-phase code structure with level-based sub-amplitude construction and automatic helicity and color handling, yielding cost scaling roughly as a^n with a ≈ 3. The results validate against established tools and demonstrate scalable performance and robustness across challenging phase-space points, making HELAC a practical tool for multi-particle EW processes.

Abstract

HELAC is a FORTRAN based package that is able to compute efficiently helicity amplitudes for arbitrary scattering processes within the standard electroweak theory. The algorithm exploits the virtues of the Dyson-Schwinger equations as compared to the traditional Feynman graph approach. All electroweak vertices are included in both the unitary and Feynman gauges, and computations including all mass effects are available. A version performing multi-precision computations with arbitrary - user defined - accuracy is also included, allowing access to any phase space point for arbitrary high energies.