Accelerating Berends-Giele recursion for gluons in arbitrary dimensions over finite fields

TL;DR

This paper demonstrates GPU-accelerated computation of gluonic amplitudes in arbitrary dimensions and over finite fields using Berends-Giele recursion, enabling efficient calculations in quantum chromodynamics.

Contribution

First implementation of gluonic amplitude computations on GPU in arbitrary dimensions over finite fields using Berends-Giele recursion.

Findings

GPU acceleration significantly speeds up amplitude calculations.

Supports arbitrary space-time dimensions and finite fields.

Open-source software available for community use.

Abstract

This work provides a proof of concept for the computation of pure gluonic amplitudes in quantum chromodynamics (QCD) on graphics processing units (GPUs). The implementation relies on the Berends-Giele recursion algorithm and, for the first time on a GPU, enables the numerical computation of amplitudes in an arbitrary number of space-time dimensions and over finite fields. This demonstrates the advantages of hardware acceleration, not only for the computation of tree-level amplitudes for real-radiation processes in four dimensions over complex numbers but also for generating loop integrands for virtual corrections in $d$ dimensions over finite fields. The associated computer program is publicly available.