O'Mega: An Optimizing Matrix Element Generator

TL;DR

O'Mega introduces an optimizing compiler for tree-level scattering amplitudes in gauge theories, leveraging One Particle Off Shell Wave Functions (1POWs) and keystones to express amplitudes as sparse sums and using Directed Acyclic Graphs (DAGs) to minimize redundant computations. The approach reduces the combinatorial growth from factorial to exponential, enabling substantial runtime improvements and enabling practical exploration of complex multi-particle processes. Implemented in OCaml with Fortran90/95 backends and MSSM support, O'Mega achieves 2×–3× speedups over established tools like HELAC and MADGRAPH, and its outputs power event generation in WHIZARD for collider phenomenology. The work demonstrates both significant theoretical advantages in representation and meaningful practical impact for high-energy physics simulations.

Abstract

We sketch the architecture of O'Mega, a new optimizing compiler for tree amplitudes in quantum field theory, and briefly describe its usage. O'Mega generates the most efficient code currently available for scattering amplitudes for many polarized particles in the Standard Model and its extensions.

Figures (1)

• Figure 1: Module dependencies in O'Mega. The diamond shaped nodes denote abstract signatures defining functor domains and co-domains. The rectangular boxes denote modules and functors, while oval boxes stand for example applications.