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O'Mega: An Optimizing Matrix Element Generator

Thorsten Ohl

TL;DR

O'Mega tackles the combinatorial explosion of tree-level scattering amplitudes by using One Particle Off-shell Wave functions (1POWs) and keystones organized into Directed Acyclic Graphs to minimize recomputation. It builds a DAG from the recursive 1POW definitions, selects keystones for a given process, and forms a redundancy-free, model-agnostic expression from the corresponding 1POWs and keystones. Implemented in OCaml with a modular functor design, O'Mega supports multiple backends (Fortran90/95, C++, Java) and advanced features such as Majorana fermions and MSSM, with an optional VM to accelerate execution. Empirically, the generated code achieves high efficiency and tight agreement with established tools like MADGRAPH, enabling robust use in WHIZARD and complex vector-boson scattering studies.

Abstract

I sketch the architecture of O'Mega, a new optimizing compiler for tree amplitudes in quantum field theory. O'Mega generates the most efficient code currently available for scattering amplitudes for many polarized particles in the standard model. A complete infrastructure for physics beyond the standard model is provided.

O'Mega: An Optimizing Matrix Element Generator

TL;DR

O'Mega tackles the combinatorial explosion of tree-level scattering amplitudes by using One Particle Off-shell Wave functions (1POWs) and keystones organized into Directed Acyclic Graphs to minimize recomputation. It builds a DAG from the recursive 1POW definitions, selects keystones for a given process, and forms a redundancy-free, model-agnostic expression from the corresponding 1POWs and keystones. Implemented in OCaml with a modular functor design, O'Mega supports multiple backends (Fortran90/95, C++, Java) and advanced features such as Majorana fermions and MSSM, with an optional VM to accelerate execution. Empirically, the generated code achieves high efficiency and tight agreement with established tools like MADGRAPH, enabling robust use in WHIZARD and complex vector-boson scattering studies.

Abstract

I sketch the architecture of O'Mega, a new optimizing compiler for tree amplitudes in quantum field theory. O'Mega generates the most efficient code currently available for scattering amplitudes for many polarized particles in the standard model. A complete infrastructure for physics beyond the standard model is provided.

Paper Structure

This paper contains 6 sections, 7 equations, 1 figure, 1 algorithm.

Table of Contents

  1. Introduction
  2. 1POWs And Keystones
  3. Directed Acyclical Graphs
  4. Algorithm
  5. Implementation
  6. Applications

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.